A New Apparatus for Seepage and Internal Erosion Soil Column Tests in Geotechnical Centrifuge

A New Apparatus for Seepage and Internal Erosion Soil Column Tests in Geotechnical Centrifuge | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A New Apparatus for Seepage and Internal Erosion Soil Column Tests in Geotechnical Centrifuge Chang Guo, Bo Huang, Jiying Fan, Wenyue Zhang, Yao Tang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4745756/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 31 Oct, 2025 Read the published version in Geotechnical Testing Journal → Version 1 posted You are reading this latest preprint version Abstract Understanding the hypergravity effect on seepage and internal erosion is the essential precondition for dam hydraulic disaster modeling using geotechnical centrifuges. Soil column testing is useful to bridge this knowledge gap, but previous attempts did not provide adequate functionality in centrifuge environments. This study develops a centrifuge-available apparatus for seepage and internal erosion soil column tests (CASIE). CASIE ensures a consistent and stable circulating water supply with no less than 34 000 ml/min at 80 g via double-bowl upstream and downstream water tanks and a vertical, multistage centrifugal pump. The hydraulic gradient can be controlled by adjusting the elevation of the upstream water tank using a servo lifting system with a vertical displacement range of 1.2 m and a maximum vertical speed of 155 mm/min. A rigid-wall permeameter is developed for multiple applications in soil column tests for seepage and internal erosion. The flowrate through the specimen can be measured using four parallel-installed oval gear flowmeters with a large measurement range of 10–10 000 ml/min. To validate the capabilities of CASIE, two suffusion (one form of internal erosion) tests were conducted at 1 g and 30 g . The results reveal that the scaling factor for the critical hydraulic gradient of 30 g to 1 g is 1/10. It is much less than the predicted value of 1, indicating that suffusion failure is more readily triggered in the hypergravity environment. Internal erosion seepage geotechnical centrifuge soil column test hypergravity effect multifunctional apparatus Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1 Introduction Seepage-induced internal erosion, initiated by mechanisms such as concentrated leak, backward erosion, contact erosion, or suffusion, is a crucial factor in earth dam failure [ 1 – 4 ]. Compared to physical modeling at normal gravity (1 g = 9.8 m/s 2 ), geotechnical centrifuges can replicate the in-situ pressure field of full-scale prototypes in small-scale models by generating a hypergravity (N times of g , N g ) environment [ 5 , 6 ]. Hence, this technology is promising in predicting disasters of earth dams. However, the previous centrifuge modeling on internal erosion of dams revealed that hypergravity significantly lowers the critical hydraulic gradient initiating failure compared with semi-empirical predictions based on the experimental results at 1 g [ 7 , 8 ]. This discrepancy highlights the challenges in replicating the internal erosion process in dams using geotechnical centrifuge models [ 9 – 12 ]. An improved understanding of the hypergravity effect on seepage-induced internal erosion is vital to address this challenge. Soil column testing is an effective method for investigating the seepage and internal erosion behaviors of soils at 1 g [ 13 – 18 ]. It has also been applied in geotechnical centrifuges to study Darcy and non-Darcy seepage [ 19 – 21 ], the initiation phase of backward erosion piping (i.e., heave) [ 22 ], and suffusion [ 23 ]. However, the demanding condition within the centrifuge swinging basket limits the functions of the testing apparatus available at 1 g , impeding a deeper exploration of seepage and internal erosion behaviors (e.g., accurate measurement and quantitative prediction of the critical hydraulic gradient in different g -levels) in the hypergravity environment. This calls for a better-instrumented apparatus to achieve more realistic hydraulic and mechanical boundary conditions and monitor key hydraulic characteristics (e.g., flowrate and hydraulic gradient) in the centrifuges. There are several challenges in its development, as reviewed in Table 1. The first challenge is to ensure a stable and controllable water supply to replicate the hydraulic conditions of engineering practice (e.g., cyclic hydraulic gradient due to waves [ 24 ]). Three solutions have been attempted. The first solution was using the falling-head method. For example, Singh and Gupta [ 19 ] and van Tonder and Jacobsz [ 20 ] performed centrifuge hydraulic conductivity tests by this method. Limited water was placed atop saturated soil specimens, resulting in low and uncontrollable hydraulic gradients. The second solution involves centrifuge water supply lines which connect tubes from the centrifuge swinging basket to the ground through a fluid rotary joint [ 5 , 21 , 22 , 25 , 26 ]. For example, Ovalle-Villamil and Sasanakul [ 21 ] used two centrifuge water supply lines to directly connect the input and output of the permeameter, forming a closed loop. Pneumatic tanks outside the centrifuge supplied high water pressure to soil specimens to study the high-speed non-Darcy flow in the hypergravity environment. However, this solution faces a limitation in the over-large hydraulic resistance from its over-long tubes, which would hinder the flexibility of hydraulic gradient control. The third solution was to achieve a circulating water supply within the swinging basket [ 23 , 27 ]. For example, Marot, Le et al [ 23 ] achieved a continuous water supply in suffusion tests using a pump, with water levels maintained by an overflow tank. This solution is promising, albeit with the critical challenge of establishing a stable and controllable hydraulic head within the constrained space of the centrifuge basket. Another challenge is to measure the flowrate through specimens. Many flowmeters are not applicable in the centrifugal environment due to the limitation of working principles, such as Coriolis mass flowmeter, or the unsuitable measurement range and accuracy, such as electromagnetic flowmeter. Hence, previous studies normally resorted to indirect measurement techniques. For example, flowrates were estimated using the descent rate of water level in the falling-head method [ 19 , 20 ] and the displacement rate of pneumatic tank pistons in the experiments of Ovalle-Villamil and Sasanakul [ 21 ]. They are only suitable with their corresponding water supply solution as mentioned before. Wang, Chen et al [ 27 ] utilized a triangular weir to evaluate the flowrate based on the theoretical relation between the flowrate and water height above the weir crotch. The accuracy of this method is not ideal due to the limited size of the model container and water level fluctuation, as mentioned by themselves. Furthermore, the behaviors of internal erosion are stress-dependent and the failure normally starts with local instability [ 14 ]. Hence, integrating functions, such as the axial stress control and the local hydraulic gradient measurement, are also anticipated in the soil column tests. This paper introduces a new geotechnical centrifuge-available apparatus for seepage and internal erosion soil column tests (CASIE). CASIE provides enhanced capabilities, including a consistent and stable circulating water supply, a controllable hydraulic gradient, and multi-functional permeameters with a wide-range flowrate measurement. The performance of CASIE was examined through a series of calibration tests and two suffusion tests at 1 g and 30 g . 2 Description of CASIE CASIE is developed for ZJU-400, a 400 g -ton beam geotechnical centrifuge at Zhejiang University, China. The centrifuge has a maximum acceleration of 150 g for static tests and an effective arm radius of 4.5 m. More details of this centrifuge can be found in Huang, Liu et al [ 6 ] and Fan, Zhao et al [ 28 ]. The main components of CASIE include a circulating water supply system, a servo lifting system, and instrumented permeameters (see the apparatus layout in Fig. 1 and the photograph in Fig. 2 ). Further specific design details are outlined below. 2.1 Circulating water supply system with double-bowl water tanks A circulating water supply system is designed to provide a consistent and stable water supply. The upstream and downstream tanks are placed on the servo lifting system and the centrifuge basket bottom plate, respectively. Each water tank is divided into a stabilizing bowl and an overflowing bowl via a partition (see Fig. 1 ). The stabilizing bowls are directly connected to the soil permeameter through the main tube (blue tube in Fig. 1 ). Water levels in stabilizing bowls are maintained by overflowing - any excess water in the stabilizing bowl overflows into the corresponding overflowing bowl through the partition. Consequently, the hydraulic gradient across the soil specimen can be controlled by adjusting the upstream water tank. A drainage tube (orange tube in Fig. 1 ) is installed to drain water from the upstream overflow bowl to the downstream overflow bowl via gravity flow. Through the main tube or the drainage tube, water in the upstream stabilizing bowl finally flows into the downstream overflowing bowl. To achieve circular flow, a vertical, multistage centrifugal pump (Grundfos CR1-27 A-FGJ-A-E-HQQE) with a rated flowrate of 30 000 ml/min and a rated head of 128.3 m at 1 g is utilized to pump water back to the upstream stabilizing bowl. The excessive pumping flow is necessary for sustaining a continuous overflow in the upstream stabilizing bowl, maintaining the stability of the upstream water level. The performance of this pump in the hypergravity environment is verified later. 2.2 Servo upstream lifting system with large load capacity and high precision This system is designed to control the elevation of the upstream tank, thus regulating the hydraulic gradient across the soil specimen. It consists of a steel frame, a lifting table, four synchronized screw jacks, a servo motor, and various accessories (see Figs. 1 and 2 ). The servo motor rotates the screws of the jacks to adjust the position of the upstream tank through traveling nuts. The safe load capacity of the lifting sub-system is 12 tons, sufficient for the 76 kg upstream water tank at 150 g . The maximum vertical movement range and the maximum vertical movement speed of the lifting table are 1.2 m with an accuracy of < 0.1 mm and 155 mm/min, respectively. Various hydraulic gradient paths (e.g., a cyclic hydraulic gradient [ 24 ]) can be applied via the servo control panel to replicate the hydraulic conditions of the engineering practice. 2.3 Multi-functional and multi-channel permeameter A rigid-wall permeameter is designed in CASIE, consisting of a Perspex cylinder, a top cap, a base pedestal, an axial loading unit, and a pressure measurement unit. Different applications might need varying cylinder dimensions. The cylinder for suffusion tests in this study has an inner diameter of 100 mm, a wall thickness of 40 mm, and a height of 220 mm. The height of specimens examined herein is 150 mm. Openings are drilled along the cylinder sidewall at vertical intervals of 30 mm to monitor pore pressures along the specimen. The cylinder is fastened to the top cap and the base pedestal using four threaded rods with nuts. The axial loading unit comprises a perforated plate (plate I), a loading rod, and multiple weights. The axial stress on the soil specimen can be controlled by adjusting the weights. The interior of the base pedestal is funnel-shaped with a second perforated plate (plate II) to support the soil. This funnel and the space above the specimen are filled with gravel to collect eroded soils and prevent jet flow. The pressure measurement unit is for hydraulic pressure measurement. It has multiple parallel three-way-shaped connectors (see Fig. 4 ). One horizontal way of each connector is used to connect the hole on the cylinder sidewall, the other horizontal way is for embedding the pore pressure transducers (PPTs), and the remaining upward way is for gas release during tube saturation via a waterproof screw. The connectors can be attached to the openings on the cylinder sidewall via tubes (see Fig. 1 ). Compared to mounting PPTs on the cylinder sidewall, one advantage of utilizing this unit is that the samples and PPTs can be saturated independently. It can prevent the desaturation of PPTs during sample preparation and improve the efficiency of tests using a single set of sensors for different specimens. Another advantage is that this method can measure the hydraulic pressure drop directly, avoiding the error caused by the non-uniformity of the centrifugal acceleration field. This permeameter facilitates multiple applications of seepage and internal erosion soil column testing. Figure 3 illustrates four examples. Firstly, downward seepage tests can be achieved by connecting the upstream and downstream to outlets I and II, respectively (see Fig. 3 (a)). A metal mesh with apertures smaller than the particle size covering the surface of the perforated plates can prevent particle loss. Constant axial stress can applied by weights to examine the influence of axial stress on seepage behavior. Secondly, Fig. 3 (b) depicts the configuration for heave (typical initiation phase of backward erosion piping) tests. The top surface of the specimen is exposed by removing plate I and securing the loading rod. The upward flow is achieved by connecting the upstream and downstream to outlets II and I, respectively. Finally, Fig. 3 (c) and (d) display two typical setups for suffusion tests, where a coarse metal mesh is affixed to the surface of plate I to permit the escape of fine particles during upward flow. Constant volume conditions can be achieved by fixing the loading rod (see Fig. 3 (d)). Up to four permeameters can be connected in parallel to conduct multi-channel tests during a single centrifuge operation (see Fig. 2 ). Each permeameter can be installed on the baseplate shown in Fig. 2 , equipped with an electric ball valve, allowing for sequential testing of specimens by manipulating the valves as needed. 2.4 Measurement of flowrate Oval gear flowmeters are utilized in CASIE to measure the flowrate through the soil specimen. Considering the limited measurement range of one single flowmeter, four oval gear flowmeters with a measurement range of 10–100, 30–300, 100–1000, and 800-10000 ml/min, respectively, are connected in parallel. The accuracy of each flowmeter is 0.2% of the corresponding full scale. Each flowmeter is connected in series to an electric ball valve (see Fig. 1 ). By controlling these valves, the most suitable flowmeter can be selected, ensuring flowrate measurements across a wide flowrate range of 10-10000 ml/min during the tests. The calibration and performance of the gear flowmeters in the hypergravity environment are discussed later. 3 Calibration of Main Functions in the Hypergravity Environment 3.1 Calibration of centrifugal pump To verify the centrifugal pump capability, simple calibration tests were performed. A network camera was positioned above the upstream tank to record the time duration (Δ t ) required to fill the upstream stabilizing bowl with a volume of V . The pumping flowrate can be determined using V/ Δ t . The calibration tests were executed at 30, 50, and 80 g , with pumping heights ( H pump ) of 0.2, 0.45, and 0.7 m, respectively. Figure 5 illustrates the relationship between specific energy ( g · H pump , a crucial property to quantify pump capacity) and the pumping flowrate. The solid line, along with its tolerance range, is suggested by the manufacturer. Although data with specific energy lower than 600 m 2 /s 2 are not provided, the calibration results closely align with the extrapolation of the suggested curves. The pumping flowrate is more than 34 000 ml/min (equivalent to a velocity of 70 m/s in a soil column with an internal diameter of 100 mm), ensuring an adequate water supply in CASIE. 3.2 Calibration of flowmeters The oval gear flowmeter mainly consists of two oval gears with fixed axes within an ‘8’-shaped chamber (see Fig. 6 ). Two gears divide the chamber into three cells: an inlet cell (A), an outlet cell (B), and a temporary water-carrying cell (C). During each half cycle of gears rotating, the differential pressure between cells A and B rotates the gears, transferring water from cell C into cell B, and forming a new temporary water-carrying cell in the other part of the ‘8’-shaped chamber. Each cycle of gears rotating triggers an electronic pulse sensor to generate a square wave signal. As the volume of the water-carrying cell C is constant, the flowrate is theoretically proportional to the frequency of the gear rotation, which can be calculated from the number of square wave signals. This proportional coefficient, defined as the sensitivity of the sensor ( K ), is theoretically equal to twice the volume of the water-carrying cell C (see Fig. 6 (a)). However, in a hypergravity environment, deformation of the gears and axes may occur, leading to gaps between the gears and the chamber. A small amount of water might leak through the gaps, resulting in measurement inaccuracies. Especially, the deformation may increase the hydraulic resistance inside the cells, leading to a higher hydraulic pressure loss in the chambers and thus enhancing the leakage. Therefore, it is necessary to verify the accuracy of gear flowmeters in the hypergravity environment. The calibration tests were conducted via the falling head method, as illustrated in Fig. 7 . The pump was stopped after filling the upstream tank stabilizing bowl. The flowmeters were directly set between the upstream and downstream water tanks. By manipulating the upstream tank elevation and the connecting tube length, various flowrates from the upstream stabilizing bowl to the downstream stabilizing bowl would be achieved and measured via the flowmeters. The actual flowrate, Q real (i.e., the rate of decline in the water volume within the upstream stabilizing bowl) can be expressed as $${Q_{\text{r}\text{e}\text{a}\text{l}}}=\frac{{dh}}{{dt}}S$$ 1 where h is the mobilized water level in the upstream tank stabilizing bowl and S is the inner cross-sectional area of the upstream stabilizing bowl. To monitor h , a PPT was placed in the upstream stabilizing bowl to measure the hydraulic pressure ( p t ), and two accelerometers were set on the lifting table and centrifuge bottom plate to measure the corresponding accelerations, N t g and N b g , respectively (see Fig. 7 ). Given that the acceleration of one point in the centrifuge is proportional to the distance to centrifuge rotation center, the acceleration at h can be derived as $${N_h}={N_t} - \frac{{h{N_b}}}{R}$$ 2 where R is the distance from the rotation center to the centrifuge bottom plate. Subsequently, P t can be integrated by $${p_t}=\int_{0}^{h} {{\rho _w}{N_h}gdh} ={\rho _w}{N_t}g(h - \frac{{{N_b}{h^2}}}{{{N_t}R}})$$ 3 h in the upstream stabilizing bowl was solved as $$h=\frac{{{N_t}}}{{{N_b}}}R - \sqrt {\frac{{{N_t}^{2}}}{{{N_b}^{2}}}{R^2} - \frac{{{p_t}R}}{{{\rho _w}{N_b}g}}}$$ 4 Then, the actual flowrate Q real can be back-calculated by combing Eqs. ( 1 ) and ( 4 ). Four flowmeters were tested at 10, 30, 50, and 80 g . The flowmeter of 10–100 ml/min was not calibrated at 80 g due to the difficulty of achieving such a flowrate range. Figure 8 compares the actual flowrate Q real by Eq. ( 1 ) and the flowrate Q measured by the flowmeters. The values of Q real and Q measured show good proportional relationships. The slopes of the Q real - Q measured proportional relationship of different flowmeters at varying g -levels are summarized in Table 2 . These slopes are also equivalent to the ratios of sensitivity measured at N g ( K N ) to that suggested by the manufacturer ( K 1 ), K N /K 1 . All values of K N /K 1 are slightly larger than 1, indicating a slight underestimation of the real flowrate by oval gear flowmeters in the hypergravity environment. The measurement range shows a limited effect on K N /K 1 . With the g -level increasing, the slopes of the proportional fitting lines slightly increase from 1.069 to 1.120, demonstrating hypergravity increases the obstruction on the gear rotation. For more accurate measurement in the hypergravity environment, the values of sensitivity suggested by the manufacturer ( K 1 ) should be modified as K N , based on the average empirical coefficients at the corresponding g -level listed in Table 2 . 4 Typical Experimental Material and Methodology using CASIE 4.1 Soil material The testing soil was a type of river sand from a reservoir in Lingshou County, Hebei Province, China. Mineralogical analysis reveals the predominant constituents of this sand are quartz, albite, and feldspar. Its finer particles contain a small amount of potassium amphibole, polysilicon lepidolite, and chlorite. Therefore, the darker fine particles make it easy to distinguish through images of soils. The raw materials were sieved, from which particles with sizes of 0.075–0.106, and 0.85–1.67 mm were mixed in a ratio of 3:7 (see particle size distribution curve in Fig. 9 ). This artificially rearranged material is recognized as a typical gap-graded sand susceptible to suffusion according to the criteria by Kézdi [ 29 ], Kenney and Lau [ 30 ], and Burenkova [ 31 ]. The target relative density was 90%. More details about the sand are summarized in Table 3 . 4.2 Testing program Two suffusion tests were conducted at 1 g and 30 g , respectively, to verify the feasibility of CASIE. The aim is to explore the hypergravity effect on internal erosion. Hence, the specimen in the hypergravity environment is regarded as a small-size full-scale specimen identical to that at 1 g rather than a small-scale model. A constant volume condition was simulated as illustrated in Fig. 3 (d). Four PPTs were used to measure No. 1, 2, 4, and 5 openings at the cylinder sidewall shown in Fig. 1 . The measurement range of PPTs used at 1 g and 30 g were 0–50 kPa and 0-400 kPa, respectively, with a 0.2% full-scale accuracy. 4.3 Specimen preparation and testing procedure The samples were prepared using the moist tamping method. It is a widely used method to prepare specimens in soil column tests for internal erosion [ 17 , 32 , 33 ] because it effectively avoids the separation of coarse and fine particles. The sand was mixed with a moisture content of around 12% and compacted to the target relative density in ten 15-mm layers. Carbon dioxide was slowly supplied into the permeameter from the bottom (outlet I) to the top (outlet II). After 2 hours, the outlet I was connected to water with a hydraulic gradient of less than 0.05 for at least 24 hours. Subsequently, the pressure measurement unit was connected to the permeameter. Before the test at 30 g , the relative elevation between the upstream and downstream water levels was set as 0 mm and all the electric valves closed. Once a steady centrifugal acceleration of 30 g was achieved, the valve linked to the 30–300 ml/min flowmeter was activated. The hydraulic loading path at 30 g is illustrated in Fig. 10 . The relative elevation was progressively increased from 0 mm to 755 mm over 30 loading stages. Each stage ended once a stable flowrate was reached. When the flowrate approached approximately 200 ml/min or 900 ml/min, the flowmeter was switched to the one with a larger measurement range. This switch slightly influenced the readings of PPTs due to the varying hydraulic resistance of different flowmeters, but this did not impact the relationship between the hydraulic gradient and the flowrate. At around 84 minutes, the flowrate did not increase obviously with the hydraulic gradient increasing, indicating a violent washout of fine particles. Hence, the test was stopped. At 1 g , it is hard to achieve a high hydraulic gradient by controlling the elevation of the upstream tank. Therefore, a pressure-controllable Mariotte's bottle, similar to the approach utilized by Chang and Zhang [ 17 ], was employed as a substitute for the upstream tank. The air inlet tube was connected to a precision pneumatic regulator (SMC IR2000) and an air pump. The hydraulic gradient was controlled incrementally by adjusting the inlet air pressure. 5 Preliminary Results and Discussion 5.1 Suffusion process at different g -levels Figure 11 illustrates the evolution of the hydraulic gradient and flowrate at 30 g . The gradients, including local hydraulic gradients of Zone I, II, and III ( i 4 − 5 , i 2 − 4 , and i 1 − 2 , respectively) and the global hydraulic gradient ( i average = i 1−5 ), were calculated using i = Δ P /( ρ w Ng Δ L ) (5) where Δ P is the hydraulic pressure drop measured by PPTs, ρ w is the water density, and Δ L is the length between openings. Figure 12 decipts the photographs of one side of the soil specimen captured by a digital camera during the test at 30 g . Before the test, the color of the specimen in Fig. 12 (a) was uniform, representing a homogeneous distribution of fine and coarse particles. At the initial stage of the test, the hydraulic gradients over each zone in the soil specimen and the flowrate synchronously increased in a stair-step pattern over the loading stages. At around 6 minutes, the growth rate of the hydraulic gradient in Zone I, i 4 − 5 , slowed down (see Fig. 11 (a)). In this phase, slight movements of some fine particles around coarse particles were observed (see Fig. 12 (b), 30 g -1). i 4 − 5 reduced suddenly at 7 minutes, indicating the "onset of instability" in Zone I. This phenomenon is consistent with the results of Fannin and Moffat [ 14 ]. After about 21 minutes, more coarse particles became distinguishable in the view of the permeameter's sidewall due to the loss of many fine particles (see Fig. 12 (c), 30 g -2), with i 4 − 5 stabilizing around 0.7. The growth rate of i 2 − 4 also slowed down. During this period, the values of hydraulic gradients within each loading stage began to change obviously. i 4 − 5 and i 2 − 4 showed a decreasing trend, but i 2 − 4 was increasing. The flowrate also increased within each stage. It reveals a noticeable fine particle loss in Zone I and II. Around 37 minutes, some isolated small regions predominantly consisting of coarse particles appeared (Fig. 12 (d), 30 g -3). Ten minutes later (Fig. 12 (e), 30 g -4), these regions expanded in the following loading stages. Both i 2 − 4 and i average approached a constant value of around 2 although the flowrate (Fig. 11 (b)) was increasing. Meanwhile, i 1 − 2 increased to around 3.7, and i 4 − 5 decreased to around 0.4 (30 g -5). It indicates a drastic fine particle erosion and thus specimen failure. The specimen tested at 1 g shows a similar evolution process to that observed at 30 g (see Fig. 13 (a)). At around 22 min, the "onset of instability" happened at Zone I. Subsequently, the growth rate of i 4 − 5 constantly reduced, and finally, i 4 − 5 began to decrease after the elapsed time of around 64 min. Meanwhile, i 2 − 4 kept pace with the increase of i average but grew slower. This state remained until a sudden decrease of i average at around 92 min, when the flowrate increased drastically, indicating the failure of the specimen. Figure 13 compares the relationship between the average hydraulic gradient, i average , and the seepage velocity, v , at 1 and 30 g , where v is the flowrate divided by the specimen cross-sectional area. The hypergravity environment causes a limited effect on the shape of the v-i average curve. Two curves started from the original point and displayed good linearity initially. During this process, the movement of fine particles might be only within void space, resulting in a linear v-i average relationship. Subsequently, the seepage velocity increased disproportionately with the increase in hydraulic gradient, indicating further fine particle movement and local instability. The secant slope of the curves increased gradually until reaching an obvious cross-point, after which the velocity increased sharply with the v-i average curve rising almost vertically. This cross-point (i.e., the critical hydraulic gradient) marked the violent washout of fine particles, as Skempton and Brogan [ 34 ] described. The critical hydraulic gradient at 1 g is around 18, while that of 30 g equals 1.8. 5.2 Preliminary discussion about hypergravity effect on suffusion The test results demonstrated that the critical hydraulic gradient at 30 g is significantly lower than that at 1 g , suggesting that erosion is more likely to be triggered in the hypergravity environment. This finding aligns with the results reported by van Beek and Zwanenburg [ 7 ] and Ovalle-Villamil and Sasanakul [ 8 ]. This is contradictory to the existing theories on heave and suffusion [ 13 , 34 – 36 ], which believe that the seepage force acting on particles and the submerged weight of the particles reach an equilibrium state at the critical hydraulic gradient. The seepage force, the sum of drag force and hydrostatic force, is proportional to the seepage velocity in Darcy's flow based on the limit equilibrium analysis of a single particle by Indraratna and Radampola [ 35 ]. Hence, the N-fold increase in seepage velocity under the same hydraulic gradient at N g would cause an N-fold seepage force. The scaling factor for the particle's submerged weight is also N due to the N times of gravity. It means that the ratios of seepage force to submerged weight of particles at different g -levels should remain constant, and the scaling factor for critical hydraulic gradient should be 1 theoretically. However, the actual scaling ratio of the failure hydraulic gradient between 30 g and 1 g is around 1/10. The observed deviation on the scaling factor for critical hydraulic gradient might be related to the transition from Darcy to non-Darcy flow regimes. The seepage regime can be estimated using the Reynolds number, Re = vd eff / η , where η is the kinematic viscosity of the fluid in the porous medium, and d eff is the effective particle size proposed by Carrier [ 37 ]. The effect of hypergravity on increasing seepage velocity can significantly expedite the transition to a non-Darcy seepage regime. Considering the continuous loss of fine particles during the suffusion process, the mean of the initial specimen's effective particle size and the coarse particle's effective particle size (0.712 mm) is used as d eff to estimate the approximate seepage Reynolds number. Taking 1 as the critical Reynolds number that delineates Darcy from non-Darcy flow [ 21 , 22 ], the corresponding seepage velocity for the specific specimens in this study is 125.18 × 10 − 5 m/s. When the seepage velocity exceeds this value, the flow regime is non-Darcy. As shown in Fig. 14 , the demarcation lines of 125.18 × 10 − 5 m/s at 30 g and 1 g are at the i average of 1.4 and 21.5, respectively. The former is lower than its critical hydraulic gradient, indicating significant erosion in non-Darcy conditions. In contrast, the latter exceeds its critical hydraulic gradient, suggesting a limited effect of non-Darcy flow. In non-Darcy flow, the increase in drag force with rising seepage velocity is greater than that in Darcy flow [ 38 ]. Therefore, erosion under non-Darcy flow is more aggressive, resulting in a smaller critical hydraulic gradient, which limits the similarity of centrifuge modeling. Further experiments are anticipated to investigate the effects of hypergravity on internal erosion behaviors using CASIE, aiming to develop a scaling law for the design of centrifuge physical modeling tests and the interpretation of the modeling results. 6 Summaries and Conclusions This study introduces a new multi-functional apparatus, CASIE, designed for conducting seepage and internal erosion tests via soil column tests in geotechnical centrifuges. CASIE aims to explore the hypergravity effects on soil seepage and internal erosion behaviors. CASIE facilitates a continuous and steady circulating water supply for the soil column in the centrifuge environment using upstream and downstream water tanks with stabilizing and overflowing bowls and a vertical, multistage centrifugal pump. The water supply flowrate at 80 g is not less than 34 000 ml/min, sufficient for testing requirements. The hydraulic gradient across the soil specimen can be controlled by adjusting the elevation of the upstream water tank via a servo lifting system. The maximum vertical displacement and the maximum vertical speed of the servo lifting system are 1.2 m and 155 mm/min, respectively. A rigid wall permeameter is developed to conduct soil column tests in various applications (e.g. seepage, heave, and suffusion) in CASIE. Up to four permeameters can be connected in parallel allowing multi-channel tests during a single centrifuge operation. Oval gear flowmeters were proven to measure the flowrate through the specimen in the hypergravity environment. Four flowmeters connected in parallel ensure a broad measurement capacity spanning from 10-10000 ml/min. The sensitivities of the flowmeters were recalibrated in the hypergravity environment. Preliminary suffusion tests conducted at 30 g and 1 g revealed that the erosion evolution process was similar at these two different g -levels. The hypergravity did not affect the curve shape of the velocity-hydraulic gradient relationship. However, the scaling factor for the critical hydraulic gradient between 30 g and 1 g in the preliminary tests was only 1/10, remarkably lower than the theoretical prediction of 1. It suggests that suffusion can be triggered more readily in the hypergravity environment. This might be related to the accelerated transition from Darcy to non-Darcy flow regime due to the N-fold increase in the seepage velocity rate at N g . Further experiments are expected to explore the hypergravity effects on seepage and internal erosion behaviors using CASIE, aiming to establish a scaling law for centrifuge physical modeling design. Declarations Competing Interests: The authors declare no competing interests. Author Contribution Chang Guo and Wenyue Zhang carried out the experiment. Chang Guo wrote the manuscript with support from Bo Huang and Yao Tang. Bo Huang, Jiying Fan, and Yao Tang supervised the project. Bo Huang conceived the original idea. Acknowledgments The work presented in this article was supported by the Natural Science Foundation of Zhejiang Province (grant number LCZ19E080002) and the National Natural Science Foundation of China (Grant No. 51988101). References Fell R, Wan CF, Cyganiewicz J, Foster M (2003) Time for Development of Internal Erosion and Piping in Embankment Dams . Journal of Geotechnical and Geoenvironmental Engineering 129: 307-314. http://doi.org/10.1061/(ASCE)1090-0241(2003)129:4(307) Zhang LM, Xu Y, Jia JS (2009) Analysis of earth dam failures: A database approach . Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 3: 184-189. https://doi.org/10.1080/17499510902831759 Bonelli S, Nicot F (2013) Erosion in Geomechanics Applied to Dams and Levees. 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Tables Table 1 Overview of geotechnical centrifuge apparatuses related to seepage and internal erosion soil column tests Apparatus Maximum acceleration reported by authors Water supply Water level control Flow rate measurement Soil column tests Axial stress controllability Hydraulic gradient measurement Applications Singh and Gupta [19] 200 g Discontinuous, via fall head method Unstable and uncontrollable Indirect, via the descent rate of water level No No Seepage van Tonder and Jacobsz [20] 23 g No Yes Ovalle-Villamil and Sasanakul [21, 22] 30 g Continuous, via pneumatic tanks outside of the swinging basket and two centrifuge water lines Unstable but controllable Indirect, via the displacement rate of pneumatic tank pistons No Yes Seepage and heave Marot, Le et al [23] 40 g Continuous, via a pump in the swinging basket Stable, via overflow, but uncontrollable No No No Suffusion van Beek and Zwanenburg [7] 80 g Continuous, via a pump in the swinging basket Stable, via overflow, and controllable, via a plunger No Not applicable Wang, Chen et al [27] 30 g Continuous, via a pump in the swinging basket Stable, via overflow but uncontrollable Indirect, via a triangular weir Not applicable Shepley and Bolton [26] 60 g Continuous, via water source outside of the swinging basket and one centrifuge water line Stable and controllable, via a manual flow-control valve outside of the swinging basket Direct, via a turbine flowmeter outside of the swinging basket Not applicable CASIE 80 g Continuous, via a pump in the swinging basket Stable, via overflow, and controllable, via a servo upstream lifting system Direct, via oval gear flowmeters in swinging basket Yes Yes Seepage, heave, and suffusion Table 2 Calibration results of flowmeters The slope of sensitivity at N g to 1 g , K N / K 1 Centrifugal acceleration, N: g 10 30 50 80 Flowmeter 10-100 ml/min 1.065 1.094 1.156 N/A 30-300 ml/min 1.051 1.121 1.183 1.178 100-1000 ml/min 1.063 1.059 1.070 1.087 800-10000 ml/min 1.095 1.101 1.041 1.098 Average 1.068 1.093 1.109 1.120 Table 3 Soil properties Soil Properties Specific gravity 2.662 Fine particle ratio: % 30 Maximum void ratio 0.775 Minimum void ratio 0.351 Target relative density: % 90 Effective particle size, d eff : mm 0.253 Uniformity coefficient 13.3 Coefficient of curvature 7.44 ( H/F ) min [29] 0 4 (unstable) Conditional factors of uniformity [31] h' =1.34; h'' =17.1 0.67lg( h'' )+1=1.83> h' (unstable) Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4745756","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":332693317,"identity":"27493434-52d7-4c10-b8a5-6ad8990d9609","order_by":0,"name":"Chang Guo","email":"","orcid":"","institution":"Institute of Geotechnical Engineering, College of Architectural and Civil Engineering, Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Chang","middleName":"","lastName":"Guo","suffix":""},{"id":332693319,"identity":"daba1c96-8b06-4f74-a73d-cde657a84013","order_by":1,"name":"Bo Huang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYFACHjCZwMDewGAAZDA2EK+F5wDJWiQSwAzCWvjbe49J/NxRm8cv+fxBMQ+DjeyGA8zPHuDTInHmXJpk75njxZKzExKMeRjSjDccYDM3wKfFQCLHTIK37VjihtsJB4BaDiduOMDDJoFXi/wbM8m/IC03DzYAtfwnQosEj5k0b1tN4oYbzAxALQcIa5E4k2NsLdt2oFiyJ43BcI5BsvHMw2xmeLXwt58xvPm2rS6Pn/34M4M3FXayfcebn+HVAgWHQQSbATgymYlQDwR1IIL5AXGKR8EoGAWjYKQBANQaR3Tsfr0WAAAAAElFTkSuQmCC","orcid":"","institution":"Institute of Geotechnical Engineering, College of Architectural and Civil Engineering, Zhejiang University","correspondingAuthor":true,"prefix":"","firstName":"Bo","middleName":"","lastName":"Huang","suffix":""},{"id":332693321,"identity":"c016b89d-b9fb-4a43-9fe4-57df05f46c93","order_by":2,"name":"Jiying Fan","email":"","orcid":"","institution":"Institute of Geotechnical Engineering, College of Architectural and Civil Engineering, Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Jiying","middleName":"","lastName":"Fan","suffix":""},{"id":332693322,"identity":"7f03eb06-5b8d-44de-972b-cf82d49d78db","order_by":3,"name":"Wenyue Zhang","email":"","orcid":"","institution":"Department of Civil and Environmental Engineering, Tokyo Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Wenyue","middleName":"","lastName":"Zhang","suffix":""},{"id":332693323,"identity":"61920756-72c2-4033-81a5-06db98c38de1","order_by":4,"name":"Yao Tang","email":"","orcid":"","institution":"Institute of Geotechnical Engineering, College of Architectural and Civil Engineering, Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Yao","middleName":"","lastName":"Tang","suffix":""}],"badges":[],"createdAt":"2024-07-15 22:23:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4745756/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4745756/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1520/GTJ20240182","type":"published","date":"2025-11-01T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62549622,"identity":"3b238985-b281-44c3-a272-36e02f7a0412","added_by":"auto","created_at":"2024-08-15 16:55:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":80352,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of CASIE\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/09316c580077df4c0f1a570c.png"},{"id":62549626,"identity":"c861d640-14e7-4cf8-8049-24096ee9ca4e","added_by":"auto","created_at":"2024-08-15 16:55:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":246238,"visible":true,"origin":"","legend":"\u003cp\u003ePhotograph of CASIE\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/541b70d054e4924b345203f2.png"},{"id":62549624,"identity":"f8458470-a0ad-4ecc-8896-d79818ae4e20","added_by":"auto","created_at":"2024-08-15 16:55:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":58564,"visible":true,"origin":"","legend":"\u003cp\u003eTypical applications of permeameter: (a) downward seepage (constant axial stress); (b) heave; (c) suffusion (constant axial stress); (d) suffusion (constant volume)\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/43918914569fc7296c5d886d.png"},{"id":62550107,"identity":"d5c5c241-78a6-459b-bf0e-f02731278ae7","added_by":"auto","created_at":"2024-08-15 17:03:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":47180,"visible":true,"origin":"","legend":"\u003cp\u003ePressure measurement unit: (a) 3D view; (b) sectional view of one three-way connector\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/81b97d6aaeb1268506cc9081.png"},{"id":62550108,"identity":"ea3d3b2e-2a3a-4f58-a848-e361c34137fb","added_by":"auto","created_at":"2024-08-15 17:03:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":21860,"visible":true,"origin":"","legend":"\u003cp\u003eCapability of centrifugal pump in thehypergravity environment\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/6245a0dba3bf8c61f24337dc.png"},{"id":62550109,"identity":"173a7be2-37f2-48e6-83da-1a866e2f796f","added_by":"auto","created_at":"2024-08-15 17:03:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":30440,"visible":true,"origin":"","legend":"\u003cp\u003eOperation principle of oval gear flowmeter: input cell (A), output cell (B), and temporary water-carrying cell (C)\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/904a270113d3474a83b74301.png"},{"id":62549627,"identity":"994578ad-9086-464e-9960-a72295b5657f","added_by":"auto","created_at":"2024-08-15 16:55:04","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":20825,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the flowmeter calibration method: falling head method using upstream water tank\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/770d9a9504d7d61f75a6b0f4.png"},{"id":62549632,"identity":"e880014f-90e6-461d-a894-ddaa3f6ad4cc","added_by":"auto","created_at":"2024-08-15 16:55:04","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":21273,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of oval gear flowmeters in the hypergravity environment\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/88ff2fb0ad48ee21fe7ebd06.png"},{"id":62550113,"identity":"d64dbb5a-9d28-4c5b-91de-e5584ab7810d","added_by":"auto","created_at":"2024-08-15 17:03:04","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":10033,"visible":true,"origin":"","legend":"\u003cp\u003eParticle size distribution\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/be19e9cafe4c1c33717969a7.png"},{"id":62549629,"identity":"91256d80-ac91-4b44-a5c4-6faa28e0c390","added_by":"auto","created_at":"2024-08-15 16:55:04","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":25410,"visible":true,"origin":"","legend":"\u003cp\u003eLoading path for suffusiontest at 30 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/3f68f2fdff92694de5315ca3.png"},{"id":62550765,"identity":"490a202b-3262-4f1c-a05e-da15c7988265","added_by":"auto","created_at":"2024-08-15 17:19:04","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":37760,"visible":true,"origin":"","legend":"\u003cp\u003eSuffusion evolution at 30 \u003cem\u003eg\u003c/em\u003e: (a) hydraulic gradient; (b) flowrate\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/34bdcfa9aa0c2f72da3b88c4.png"},{"id":62550112,"identity":"86ff82c3-2ae4-4cc5-afd7-63d54a6c8087","added_by":"auto","created_at":"2024-08-15 17:03:04","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":450512,"visible":true,"origin":"","legend":"\u003cp\u003ePhotographs of the erosion process at 30 \u003cem\u003eg\u003c/em\u003e: (a) before the test, homogeneous fine particle distribution; (b) 30\u003cem\u003eg\u003c/em\u003e-1, slight fine particle movement; (c) 30\u003cem\u003eg\u003c/em\u003e-2, more coarse particles becoming visible; (d) 30\u003cem\u003eg\u003c/em\u003e-3, small pure coarse sand regions; (e) 30\u003cem\u003eg\u003c/em\u003e-4, expanded pure coarse sand regions; (f) 30\u003cem\u003eg\u003c/em\u003e-5, further expanded pure coarse sand regions\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/25a4e0249adcb2f1d69c68c7.png"},{"id":62550467,"identity":"43811d5b-fab0-41ae-8d10-458fb570f245","added_by":"auto","created_at":"2024-08-15 17:11:04","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":26548,"visible":true,"origin":"","legend":"\u003cp\u003eSuffusion evolution at 1 \u003cem\u003eg\u003c/em\u003e: (a) hydraulic gradient; (b) flowrate\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/e640b4ea213acf4168c4505f.png"},{"id":62549634,"identity":"7eac8975-2a52-4507-ba70-6a61b66334ed","added_by":"auto","created_at":"2024-08-15 16:55:04","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":30805,"visible":true,"origin":"","legend":"\u003cp\u003eVelocity versus hydraulic gradient: (a) 30 \u003cem\u003eg\u003c/em\u003e; (a) 1 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/62b7b734ee9fbaa0dfb8d164.png"},{"id":95651017,"identity":"837c6f26-e2c9-48a7-9365-325cfbb3f3ac","added_by":"auto","created_at":"2025-11-11 15:18:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1981057,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4745756/v1/6355f5c4-41ac-4d3b-a8e1-dd0222956825.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A New Apparatus for Seepage and Internal Erosion Soil Column Tests in Geotechnical Centrifuge","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eSeepage-induced internal erosion, initiated by mechanisms such as concentrated leak, backward erosion, contact erosion, or suffusion, is a crucial factor in earth dam failure [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Compared to physical modeling at normal gravity (1 \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;9.8 m/s\u003csup\u003e2\u003c/sup\u003e), geotechnical centrifuges can replicate the in-situ pressure field of full-scale prototypes in small-scale models by generating a hypergravity (N times of \u003cem\u003eg\u003c/em\u003e, N \u003cem\u003eg\u003c/em\u003e) environment [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Hence, this technology is promising in predicting disasters of earth dams. However, the previous centrifuge modeling on internal erosion of dams revealed that hypergravity significantly lowers the critical hydraulic gradient initiating failure compared with semi-empirical predictions based on the experimental results at 1 \u003cem\u003eg\u003c/em\u003e [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. This discrepancy highlights the challenges in replicating the internal erosion process in dams using geotechnical centrifuge models [\u003cspan additionalcitationids=\"CR10 CR11\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. An improved understanding of the hypergravity effect on seepage-induced internal erosion is vital to address this challenge.\u003c/p\u003e \u003cp\u003eSoil column testing is an effective method for investigating the seepage and internal erosion behaviors of soils at 1 \u003cem\u003eg\u003c/em\u003e [\u003cspan additionalcitationids=\"CR14 CR15 CR16 CR17\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. It has also been applied in geotechnical centrifuges to study Darcy and non-Darcy seepage [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], the initiation phase of backward erosion piping (i.e., heave) [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], and suffusion [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. However, the demanding condition within the centrifuge swinging basket limits the functions of the testing apparatus available at 1 \u003cem\u003eg\u003c/em\u003e, impeding a deeper exploration of seepage and internal erosion behaviors (e.g., accurate measurement and quantitative prediction of the critical hydraulic gradient in different \u003cem\u003eg\u003c/em\u003e-levels) in the hypergravity environment. This calls for a better-instrumented apparatus to achieve more realistic hydraulic and mechanical boundary conditions and monitor key hydraulic characteristics (e.g., flowrate and hydraulic gradient) in the centrifuges. There are several challenges in its development, as reviewed in Table\u0026nbsp;1.\u003c/p\u003e \u003cp\u003eThe first challenge is to ensure a stable and controllable water supply to replicate the hydraulic conditions of engineering practice (e.g., cyclic hydraulic gradient due to waves [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]). Three solutions have been attempted. The first solution was using the falling-head method. For example, Singh and Gupta [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] and van Tonder and Jacobsz [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] performed centrifuge hydraulic conductivity tests by this method. Limited water was placed atop saturated soil specimens, resulting in low and uncontrollable hydraulic gradients. The second solution involves centrifuge water supply lines which connect tubes from the centrifuge swinging basket to the ground through a fluid rotary joint [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. For example, Ovalle-Villamil and Sasanakul [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] used two centrifuge water supply lines to directly connect the input and output of the permeameter, forming a closed loop. Pneumatic tanks outside the centrifuge supplied high water pressure to soil specimens to study the high-speed non-Darcy flow in the hypergravity environment. However, this solution faces a limitation in the over-large hydraulic resistance from its over-long tubes, which would hinder the flexibility of hydraulic gradient control. The third solution was to achieve a circulating water supply within the swinging basket [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. For example, Marot, Le et al [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] achieved a continuous water supply in suffusion tests using a pump, with water levels maintained by an overflow tank. This solution is promising, albeit with the critical challenge of establishing a stable and controllable hydraulic head within the constrained space of the centrifuge basket.\u003c/p\u003e \u003cp\u003eAnother challenge is to measure the flowrate through specimens. Many flowmeters are not applicable in the centrifugal environment due to the limitation of working principles, such as Coriolis mass flowmeter, or the unsuitable measurement range and accuracy, such as electromagnetic flowmeter. Hence, previous studies normally resorted to indirect measurement techniques. For example, flowrates were estimated using the descent rate of water level in the falling-head method [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] and the displacement rate of pneumatic tank pistons in the experiments of Ovalle-Villamil and Sasanakul [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. They are only suitable with their corresponding water supply solution as mentioned before. Wang, Chen et al [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] utilized a triangular weir to evaluate the flowrate based on the theoretical relation between the flowrate and water height above the weir crotch. The accuracy of this method is not ideal due to the limited size of the model container and water level fluctuation, as mentioned by themselves.\u003c/p\u003e \u003cp\u003eFurthermore, the behaviors of internal erosion are stress-dependent and the failure normally starts with local instability [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Hence, integrating functions, such as the axial stress control and the local hydraulic gradient measurement, are also anticipated in the soil column tests.\u003c/p\u003e \u003cp\u003eThis paper introduces a new geotechnical centrifuge-available apparatus for seepage and internal erosion soil column tests (CASIE). CASIE provides enhanced capabilities, including a consistent and stable circulating water supply, a controllable hydraulic gradient, and multi-functional permeameters with a wide-range flowrate measurement. The performance of CASIE was examined through a series of calibration tests and two suffusion tests at 1 \u003cem\u003eg\u003c/em\u003e and 30 \u003cem\u003eg\u003c/em\u003e.\u003c/p\u003e"},{"header":"2 Description of CASIE","content":"\u003cp\u003eCASIE is developed for ZJU-400, a 400 \u003cem\u003eg\u003c/em\u003e-ton beam geotechnical centrifuge at Zhejiang University, China. The centrifuge has a maximum acceleration of 150 \u003cem\u003eg\u003c/em\u003e for static tests and an effective arm radius of 4.5 m. More details of this centrifuge can be found in Huang, Liu et al [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] and Fan, Zhao et al [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The main components of CASIE include a circulating water supply system, a servo lifting system, and instrumented permeameters (see the apparatus layout in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and the photograph in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Further specific design details are outlined below.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Circulating water supply system with double-bowl water tanks\u003c/h2\u003e \u003cp\u003eA circulating water supply system is designed to provide a consistent and stable water supply. The upstream and downstream tanks are placed on the servo lifting system and the centrifuge basket bottom plate, respectively. Each water tank is divided into a stabilizing bowl and an overflowing bowl via a partition (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The stabilizing bowls are directly connected to the soil permeameter through the main tube (blue tube in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Water levels in stabilizing bowls are maintained by overflowing - any excess water in the stabilizing bowl overflows into the corresponding overflowing bowl through the partition. Consequently, the hydraulic gradient across the soil specimen can be controlled by adjusting the upstream water tank.\u003c/p\u003e \u003cp\u003eA drainage tube (orange tube in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) is installed to drain water from the upstream overflow bowl to the downstream overflow bowl via gravity flow. Through the main tube or the drainage tube, water in the upstream stabilizing bowl finally flows into the downstream overflowing bowl. To achieve circular flow, a vertical, multistage centrifugal pump (Grundfos CR1-27 A-FGJ-A-E-HQQE) with a rated flowrate of 30 000 ml/min and a rated head of 128.3 m at 1 \u003cem\u003eg\u003c/em\u003e is utilized to pump water back to the upstream stabilizing bowl. The excessive pumping flow is necessary for sustaining a continuous overflow in the upstream stabilizing bowl, maintaining the stability of the upstream water level. The performance of this pump in the hypergravity environment is verified later.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Servo upstream lifting system with large load capacity and high precision\u003c/h2\u003e \u003cp\u003eThis system is designed to control the elevation of the upstream tank, thus regulating the hydraulic gradient across the soil specimen. It consists of a steel frame, a lifting table, four synchronized screw jacks, a servo motor, and various accessories (see Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The servo motor rotates the screws of the jacks to adjust the position of the upstream tank through traveling nuts. The safe load capacity of the lifting sub-system is 12 tons, sufficient for the 76 kg upstream water tank at 150 \u003cem\u003eg\u003c/em\u003e. The maximum vertical movement range and the maximum vertical movement speed of the lifting table are 1.2 m with an accuracy of \u0026lt;\u0026thinsp;0.1 mm and 155 mm/min, respectively. Various hydraulic gradient paths (e.g., a cyclic hydraulic gradient [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]) can be applied via the servo control panel to replicate the hydraulic conditions of the engineering practice.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Multi-functional and multi-channel permeameter\u003c/h2\u003e \u003cp\u003eA rigid-wall permeameter is designed in CASIE, consisting of a Perspex cylinder, a top cap, a base pedestal, an axial loading unit, and a pressure measurement unit. Different applications might need varying cylinder dimensions. The cylinder for suffusion tests in this study has an inner diameter of 100 mm, a wall thickness of 40 mm, and a height of 220 mm. The height of specimens examined herein is 150 mm. Openings are drilled along the cylinder sidewall at vertical intervals of 30 mm to monitor pore pressures along the specimen. The cylinder is fastened to the top cap and the base pedestal using four threaded rods with nuts. The axial loading unit comprises a perforated plate (plate I), a loading rod, and multiple weights. The axial stress on the soil specimen can be controlled by adjusting the weights. The interior of the base pedestal is funnel-shaped with a second perforated plate (plate II) to support the soil. This funnel and the space above the specimen are filled with gravel to collect eroded soils and prevent jet flow.\u003c/p\u003e \u003cp\u003eThe pressure measurement unit is for hydraulic pressure measurement. It has multiple parallel three-way-shaped connectors (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). One horizontal way of each connector is used to connect the hole on the cylinder sidewall, the other horizontal way is for embedding the pore pressure transducers (PPTs), and the remaining upward way is for gas release during tube saturation via a waterproof screw. The connectors can be attached to the openings on the cylinder sidewall via tubes (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Compared to mounting PPTs on the cylinder sidewall, one advantage of utilizing this unit is that the samples and PPTs can be saturated independently. It can prevent the desaturation of PPTs during sample preparation and improve the efficiency of tests using a single set of sensors for different specimens. Another advantage is that this method can measure the hydraulic pressure drop directly, avoiding the error caused by the non-uniformity of the centrifugal acceleration field.\u003c/p\u003e \u003cp\u003eThis permeameter facilitates multiple applications of seepage and internal erosion soil column testing. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates four examples. Firstly, downward seepage tests can be achieved by connecting the upstream and downstream to outlets I and II, respectively (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (a)). A metal mesh with apertures smaller than the particle size covering the surface of the perforated plates can prevent particle loss. Constant axial stress can applied by weights to examine the influence of axial stress on seepage behavior. Secondly, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (b) depicts the configuration for heave (typical initiation phase of backward erosion piping) tests. The top surface of the specimen is exposed by removing plate I and securing the loading rod. The upward flow is achieved by connecting the upstream and downstream to outlets II and I, respectively. Finally, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (c) and (d) display two typical setups for suffusion tests, where a coarse metal mesh is affixed to the surface of plate I to permit the escape of fine particles during upward flow. Constant volume conditions can be achieved by fixing the loading rod (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (d)).\u003c/p\u003e \u003cp\u003eUp to four permeameters can be connected in parallel to conduct multi-channel tests during a single centrifuge operation (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Each permeameter can be installed on the baseplate shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, equipped with an electric ball valve, allowing for sequential testing of specimens by manipulating the valves as needed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Measurement of flowrate\u003c/h2\u003e \u003cp\u003eOval gear flowmeters are utilized in CASIE to measure the flowrate through the soil specimen. Considering the limited measurement range of one single flowmeter, four oval gear flowmeters with a measurement range of 10\u0026ndash;100, 30\u0026ndash;300, 100\u0026ndash;1000, and 800-10000 ml/min, respectively, are connected in parallel. The accuracy of each flowmeter is 0.2% of the corresponding full scale. Each flowmeter is connected in series to an electric ball valve (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). By controlling these valves, the most suitable flowmeter can be selected, ensuring flowrate measurements across a wide flowrate range of 10-10000 ml/min during the tests. The calibration and performance of the gear flowmeters in the hypergravity environment are discussed later.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Calibration of Main Functions in the Hypergravity Environment","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Calibration of centrifugal pump\u003c/h2\u003e\n \u003cp\u003eTo verify the centrifugal pump capability, simple calibration tests were performed. A network camera was positioned above the upstream tank to record the time duration (\u0026Delta;\u003cem\u003et\u003c/em\u003e) required to fill the upstream stabilizing bowl with a volume of \u003cem\u003eV\u003c/em\u003e. The pumping flowrate can be determined using \u003cem\u003eV/\u003c/em\u003e\u0026Delta;\u003cem\u003et\u003c/em\u003e. The calibration tests were executed at 30, 50, and 80 \u003cem\u003eg\u003c/em\u003e, with pumping heights (\u003cem\u003eH\u003c/em\u003e\u003csub\u003epump\u003c/sub\u003e) of 0.2, 0.45, and 0.7 m, respectively. Figure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the relationship between specific energy (\u003cem\u003eg\u003c/em\u003e\u0026middot;\u003cem\u003eH\u003c/em\u003e\u003csub\u003epump\u003c/sub\u003e, a crucial property to quantify pump capacity) and the pumping flowrate. The solid line, along with its tolerance range, is suggested by the manufacturer. Although data with specific energy lower than 600 m\u003csup\u003e2\u003c/sup\u003e/s\u003csup\u003e2\u003c/sup\u003e are not provided, the calibration results closely align with the extrapolation of the suggested curves. The pumping flowrate is more than 34 000 ml/min (equivalent to a velocity of 70 m/s in a soil column with an internal diameter of 100 mm), ensuring an adequate water supply in CASIE.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Calibration of flowmeters\u003c/h2\u003e\n \u003cp\u003eThe oval gear flowmeter mainly consists of two oval gears with fixed axes within an \u0026lsquo;8\u0026rsquo;-shaped chamber (see Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e). Two gears divide the chamber into three cells: an inlet cell (A), an outlet cell (B), and a temporary water-carrying cell (C). During each half cycle of gears rotating, the differential pressure between cells A and B rotates the gears, transferring water from cell C into cell B, and forming a new temporary water-carrying cell in the other part of the \u0026lsquo;8\u0026rsquo;-shaped chamber. Each cycle of gears rotating triggers an electronic pulse sensor to generate a square wave signal. As the volume of the water-carrying cell C is constant, the flowrate is theoretically proportional to the frequency of the gear rotation, which can be calculated from the number of square wave signals. This proportional coefficient, defined as the sensitivity of the sensor (\u003cem\u003eK\u003c/em\u003e), is theoretically equal to twice the volume of the water-carrying cell C (see Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e (a)).\u003c/p\u003e\n \u003cp\u003eHowever, in a hypergravity environment, deformation of the gears and axes may occur, leading to gaps between the gears and the chamber. A small amount of water might leak through the gaps, resulting in measurement inaccuracies. Especially, the deformation may increase the hydraulic resistance inside the cells, leading to a higher hydraulic pressure loss in the chambers and thus enhancing the leakage. Therefore, it is necessary to verify the accuracy of gear flowmeters in the hypergravity environment.\u003c/p\u003e\n \u003cp\u003eThe calibration tests were conducted via the falling head method, as illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. The pump was stopped after filling the upstream tank stabilizing bowl. The flowmeters were directly set between the upstream and downstream water tanks. By manipulating the upstream tank elevation and the connecting tube length, various flowrates from the upstream stabilizing bowl to the downstream stabilizing bowl would be achieved and measured via the flowmeters. The actual flowrate, \u003cem\u003eQ\u003c/em\u003e\u003csub\u003ereal\u003c/sub\u003e (i.e., the rate of decline in the water volume within the upstream stabilizing bowl) can be expressed as\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${Q_{\\text{r}\\text{e}\\text{a}\\text{l}}}=\\frac{{dh}}{{dt}}S$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u003cem\u003eh\u003c/em\u003e is the mobilized water level in the upstream tank stabilizing bowl and \u003cem\u003eS\u003c/em\u003e is the inner cross-sectional area of the upstream stabilizing bowl. To monitor \u003cem\u003eh\u003c/em\u003e, a PPT was placed in the upstream stabilizing bowl to measure the hydraulic pressure (\u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e), and two accelerometers were set on the lifting table and centrifuge bottom plate to measure the corresponding accelerations, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eg\u003c/em\u003e and \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eg\u003c/em\u003e, respectively (see Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e). Given that the acceleration of one point in the centrifuge is proportional to the distance to centrifuge rotation center, the acceleration at \u003cem\u003eh\u003c/em\u003e can be derived as\u003c/p\u003e\n \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$${N_h}={N_t} - \\frac{{h{N_b}}}{R}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u003cem\u003eR\u003c/em\u003e is the distance from the rotation center to the centrifuge bottom plate. Subsequently, \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e can be integrated by\u003c/p\u003e\n \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e$${p_t}=\\int_{0}^{h} {{\\rho _w}{N_h}gdh} ={\\rho _w}{N_t}g(h - \\frac{{{N_b}{h^2}}}{{{N_t}R}})$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cem\u003eh\u003c/em\u003e in the upstream stabilizing bowl was solved as\u003c/p\u003e\n \u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e$$h=\\frac{{{N_t}}}{{{N_b}}}R - \\sqrt {\\frac{{{N_t}^{2}}}{{{N_b}^{2}}}{R^2} - \\frac{{{p_t}R}}{{{\\rho _w}{N_b}g}}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThen, the actual flowrate \u003cem\u003eQ\u003c/em\u003e\u003csub\u003ereal\u003c/sub\u003e can be back-calculated by combing Eqs. (\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) and (\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eFour flowmeters were tested at 10, 30, 50, and 80 \u003cem\u003eg\u003c/em\u003e. The flowmeter of 10\u0026ndash;100 ml/min was not calibrated at 80 \u003cem\u003eg\u003c/em\u003e due to the difficulty of achieving such a flowrate range. Figure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e compares the actual flowrate \u003cem\u003eQ\u003c/em\u003e\u003csub\u003ereal\u003c/sub\u003e by Eq. (\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) and the flowrate \u003cem\u003eQ\u003c/em\u003e\u003csub\u003emeasured\u003c/sub\u003e by the flowmeters. The values of \u003cem\u003eQ\u003c/em\u003e\u003csub\u003ereal\u003c/sub\u003e and \u003cem\u003eQ\u003c/em\u003e\u003csub\u003emeasured\u003c/sub\u003e show good proportional relationships. The slopes of the \u003cem\u003eQ\u003c/em\u003e\u003csub\u003ereal\u003c/sub\u003e-\u003cem\u003eQ\u003c/em\u003e\u003csub\u003emeasured\u003c/sub\u003e proportional relationship of different flowmeters at varying \u003cem\u003eg\u003c/em\u003e-levels are summarized in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. These slopes are also equivalent to the ratios of sensitivity measured at N \u003cem\u003eg\u003c/em\u003e (\u003cem\u003eK\u003c/em\u003e\u003csub\u003eN\u003c/sub\u003e) to that suggested by the manufacturer (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003eK\u003c/em\u003e\u003csub\u003eN\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e. All values of \u003cem\u003eK\u003c/em\u003e\u003csub\u003eN\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e are slightly larger than 1, indicating a slight underestimation of the real flowrate by oval gear flowmeters in the hypergravity environment. The measurement range shows a limited effect on \u003cem\u003eK\u003c/em\u003e\u003csub\u003eN\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e. With the \u003cem\u003eg\u003c/em\u003e-level increasing, the slopes of the proportional fitting lines slightly increase from 1.069 to 1.120, demonstrating hypergravity increases the obstruction on the gear rotation. For more accurate measurement in the hypergravity environment, the values of sensitivity suggested by the manufacturer (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e) should be modified as \u003cem\u003eK\u003c/em\u003e\u003csub\u003eN\u003c/sub\u003e, based on the average empirical coefficients at the corresponding \u003cem\u003eg\u003c/em\u003e-level listed in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4 Typical Experimental Material and Methodology using CASIE","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1 Soil material\u003c/h2\u003e\n \u003cp\u003eThe testing soil was a type of river sand from a reservoir in Lingshou County, Hebei Province, China. Mineralogical analysis reveals the predominant constituents of this sand are quartz, albite, and feldspar. Its finer particles contain a small amount of potassium amphibole, polysilicon lepidolite, and chlorite. Therefore, the darker fine particles make it easy to distinguish through images of soils. The raw materials were sieved, from which particles with sizes of 0.075\u0026ndash;0.106, and 0.85\u0026ndash;1.67 mm were mixed in a ratio of 3:7 (see particle size distribution curve in Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e). This artificially rearranged material is recognized as a typical gap-graded sand susceptible to suffusion according to the criteria by K\u0026eacute;zdi [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e], Kenney and Lau [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e], and Burenkova [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e]. The target relative density was 90%. More details about the sand are summarized in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e4.2 Testing program\u003c/h2\u003e\n \u003cp\u003eTwo suffusion tests were conducted at 1 \u003cem\u003eg\u003c/em\u003e and 30 \u003cem\u003eg\u003c/em\u003e, respectively, to verify the feasibility of CASIE. The aim is to explore the hypergravity effect on internal erosion. Hence, the specimen in the hypergravity environment is regarded as a small-size full-scale specimen identical to that at 1 \u003cem\u003eg\u003c/em\u003e rather than a small-scale model. A constant volume condition was simulated as illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e (d). Four PPTs were used to measure No. 1, 2, 4, and 5 openings at the cylinder sidewall shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The measurement range of PPTs used at 1 \u003cem\u003eg\u003c/em\u003e and 30 \u003cem\u003eg\u003c/em\u003e were 0\u0026ndash;50 kPa and 0-400 kPa, respectively, with a 0.2% full-scale accuracy.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e4.3 Specimen preparation and testing procedure\u003c/h2\u003e\n \u003cp\u003eThe samples were prepared using the moist tamping method. It is a widely used method to prepare specimens in soil column tests for internal erosion [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e] because it effectively avoids the separation of coarse and fine particles. The sand was mixed with a moisture content of around 12% and compacted to the target relative density in ten 15-mm layers. Carbon dioxide was slowly supplied into the permeameter from the bottom (outlet I) to the top (outlet II). After 2 hours, the outlet I was connected to water with a hydraulic gradient of less than 0.05 for at least 24 hours. Subsequently, the pressure measurement unit was connected to the permeameter.\u003c/p\u003e\n \u003cp\u003eBefore the test at 30 \u003cem\u003eg\u003c/em\u003e, the relative elevation between the upstream and downstream water levels was set as 0 mm and all the electric valves closed. Once a steady centrifugal acceleration of 30 \u003cem\u003eg\u003c/em\u003e was achieved, the valve linked to the 30\u0026ndash;300 ml/min flowmeter was activated. The hydraulic loading path at 30 \u003cem\u003eg\u003c/em\u003e is illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e. The relative elevation was progressively increased from 0 mm to 755 mm over 30 loading stages. Each stage ended once a stable flowrate was reached. When the flowrate approached approximately 200 ml/min or 900 ml/min, the flowmeter was switched to the one with a larger measurement range. This switch slightly influenced the readings of PPTs due to the varying hydraulic resistance of different flowmeters, but this did not impact the relationship between the hydraulic gradient and the flowrate. At around 84 minutes, the flowrate did not increase obviously with the hydraulic gradient increasing, indicating a violent washout of fine particles. Hence, the test was stopped.\u003c/p\u003e\n \u003cp\u003eAt 1\u003cem\u003eg\u003c/em\u003e, it is hard to achieve a high hydraulic gradient by controlling the elevation of the upstream tank. Therefore, a pressure-controllable Mariotte\u0026apos;s bottle, similar to the approach utilized by Chang and Zhang [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e], was employed as a substitute for the upstream tank. The air inlet tube was connected to a precision pneumatic regulator (SMC IR2000) and an air pump. The hydraulic gradient was controlled incrementally by adjusting the inlet air pressure.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5 Preliminary Results and Discussion","content":"\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Suffusion process at different \u003cem\u003eg\u003c/em\u003e-levels\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e illustrates the evolution of the hydraulic gradient and flowrate at 30 \u003cem\u003eg\u003c/em\u003e. The gradients, including local hydraulic gradients of Zone I, II, and III (\u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e, \u003cem\u003ei\u003c/em\u003e\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/sub\u003e, and \u003cem\u003ei\u003c/em\u003e\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;2\u003c/sub\u003e, respectively) and the global hydraulic gradient (\u003cem\u003ei\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e = \u003cem\u003ei\u003c/em\u003e\u003csub\u003e1\u0026minus;5\u003c/sub\u003e), were calculated using\u003c/p\u003e \u003cp\u003e \u003cem\u003ei\u003c/em\u003e\u0026thinsp;=\u0026thinsp;Δ\u003cem\u003eP\u003c/em\u003e/(\u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eNg\u003c/em\u003eΔ\u003cem\u003eL\u003c/em\u003e) (5)\u003c/p\u003e \u003cp\u003ewhere Δ\u003cem\u003eP\u003c/em\u003e is the hydraulic pressure drop measured by PPTs, \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e is the water density, and Δ\u003cem\u003eL\u003c/em\u003e is the length between openings.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e decipts the photographs of one side of the soil specimen captured by a digital camera during the test at 30 \u003cem\u003eg\u003c/em\u003e. Before the test, the color of the specimen in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (a) was uniform, representing a homogeneous distribution of fine and coarse particles. At the initial stage of the test, the hydraulic gradients over each zone in the soil specimen and the flowrate synchronously increased in a stair-step pattern over the loading stages. At around 6 minutes, the growth rate of the hydraulic gradient in Zone I, \u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e, slowed down (see Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e (a)). In this phase, slight movements of some fine particles around coarse particles were observed (see Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (b), 30\u003cem\u003eg\u003c/em\u003e-1). \u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e reduced suddenly at 7 minutes, indicating the \"onset of instability\" in Zone I. This phenomenon is consistent with the results of Fannin and Moffat [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. After about 21 minutes, more coarse particles became distinguishable in the view of the permeameter's sidewall due to the loss of many fine particles (see Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (c), 30\u003cem\u003eg\u003c/em\u003e-2), with \u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e stabilizing around 0.7. The growth rate of \u003cem\u003ei\u003c/em\u003e\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/sub\u003e also slowed down. During this period, the values of hydraulic gradients within each loading stage began to change obviously. \u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e and \u003cem\u003ei\u003c/em\u003e\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/sub\u003e showed a decreasing trend, but \u003cem\u003ei\u003c/em\u003e\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/sub\u003e was increasing. The flowrate also increased within each stage. It reveals a noticeable fine particle loss in Zone I and II. Around 37 minutes, some isolated small regions predominantly consisting of coarse particles appeared (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (d), 30\u003cem\u003eg\u003c/em\u003e-3). Ten minutes later (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (e), 30\u003cem\u003eg\u003c/em\u003e-4), these regions expanded in the following loading stages. Both \u003cem\u003ei\u003c/em\u003e\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/sub\u003e and \u003cem\u003ei\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e approached a constant value of around 2 although the flowrate (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e (b)) was increasing. Meanwhile, \u003cem\u003ei\u003c/em\u003e\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;2\u003c/sub\u003e increased to around 3.7, and \u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e decreased to around 0.4 (30\u003cem\u003eg\u003c/em\u003e-5). It indicates a drastic fine particle erosion and thus specimen failure.\u003c/p\u003e \u003cp\u003eThe specimen tested at 1 \u003cem\u003eg\u003c/em\u003e shows a similar evolution process to that observed at 30 \u003cem\u003eg\u003c/em\u003e (see Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e (a)). At around 22 min, the \"onset of instability\" happened at Zone I. Subsequently, the growth rate of \u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e constantly reduced, and finally, \u003cem\u003ei\u003c/em\u003e\u003csub\u003e4\u0026thinsp;\u0026minus;\u0026thinsp;5\u003c/sub\u003e began to decrease after the elapsed time of around 64 min. Meanwhile, \u003cem\u003ei\u003c/em\u003e\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;4\u003c/sub\u003e kept pace with the increase of \u003cem\u003ei\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e but grew slower. This state remained until a sudden decrease of \u003cem\u003ei\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e at around 92 min, when the flowrate increased drastically, indicating the failure of the specimen.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e compares the relationship between the average hydraulic gradient, \u003cem\u003ei\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e, and the seepage velocity, \u003cem\u003ev\u003c/em\u003e, at 1 and 30 \u003cem\u003eg\u003c/em\u003e, where \u003cem\u003ev\u003c/em\u003e is the flowrate divided by the specimen cross-sectional area. The hypergravity environment causes a limited effect on the shape of the \u003cem\u003ev-i\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e curve. Two curves started from the original point and displayed good linearity initially. During this process, the movement of fine particles might be only within void space, resulting in a linear \u003cem\u003ev-i\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e relationship. Subsequently, the seepage velocity increased disproportionately with the increase in hydraulic gradient, indicating further fine particle movement and local instability. The secant slope of the curves increased gradually until reaching an obvious cross-point, after which the velocity increased sharply with the \u003cem\u003ev-i\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e curve rising almost vertically. This cross-point (i.e., the critical hydraulic gradient) marked the violent washout of fine particles, as Skempton and Brogan [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] described. The critical hydraulic gradient at 1 \u003cem\u003eg\u003c/em\u003e is around 18, while that of 30 \u003cem\u003eg\u003c/em\u003e equals 1.8.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Preliminary discussion about hypergravity effect on suffusion\u003c/h2\u003e \u003cp\u003eThe test results demonstrated that the critical hydraulic gradient at 30\u003cem\u003eg\u003c/em\u003e is significantly lower than that at 1 \u003cem\u003eg\u003c/em\u003e, suggesting that erosion is more likely to be triggered in the hypergravity environment. This finding aligns with the results reported by van Beek and Zwanenburg [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] and Ovalle-Villamil and Sasanakul [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. This is contradictory to the existing theories on heave and suffusion [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan additionalcitationids=\"CR35\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], which believe that the seepage force acting on particles and the submerged weight of the particles reach an equilibrium state at the critical hydraulic gradient. The seepage force, the sum of drag force and hydrostatic force, is proportional to the seepage velocity in Darcy's flow based on the limit equilibrium analysis of a single particle by Indraratna and Radampola [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Hence, the N-fold increase in seepage velocity under the same hydraulic gradient at N \u003cem\u003eg\u003c/em\u003e would cause an N-fold seepage force. The scaling factor for the particle's submerged weight is also N due to the N times of gravity. It means that the ratios of seepage force to submerged weight of particles at different \u003cem\u003eg\u003c/em\u003e-levels should remain constant, and the scaling factor for critical hydraulic gradient should be 1 theoretically. However, the actual scaling ratio of the failure hydraulic gradient between 30 \u003cem\u003eg\u003c/em\u003e and 1 \u003cem\u003eg\u003c/em\u003e is around 1/10.\u003c/p\u003e \u003cp\u003eThe observed deviation on the scaling factor for critical hydraulic gradient might be related to the transition from Darcy to non-Darcy flow regimes. The seepage regime can be estimated using the Reynolds number, Re\u0026thinsp;=\u0026thinsp;\u003cem\u003evd\u003c/em\u003e\u003csub\u003eeff\u003c/sub\u003e/\u003cem\u003eη\u003c/em\u003e, where \u003cem\u003eη\u003c/em\u003e is the kinematic viscosity of the fluid in the porous medium, and \u003cem\u003ed\u003c/em\u003e\u003csub\u003eeff\u003c/sub\u003e is the effective particle size proposed by Carrier [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The effect of hypergravity on increasing seepage velocity can significantly expedite the transition to a non-Darcy seepage regime. Considering the continuous loss of fine particles during the suffusion process, the mean of the initial specimen's effective particle size and the coarse particle's effective particle size (0.712 mm) is used as \u003cem\u003ed\u003c/em\u003e\u003csub\u003eeff\u003c/sub\u003e to estimate the approximate seepage Reynolds number. Taking 1 as the critical Reynolds number that delineates Darcy from non-Darcy flow [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], the corresponding seepage velocity for the specific specimens in this study is 125.18 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e m/s. When the seepage velocity exceeds this value, the flow regime is non-Darcy. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e, the demarcation lines of 125.18 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e m/s at 30\u003cem\u003eg\u003c/em\u003e and 1\u003cem\u003eg\u003c/em\u003e are at the \u003cem\u003ei\u003c/em\u003e\u003csub\u003eaverage\u003c/sub\u003e of 1.4 and 21.5, respectively. The former is lower than its critical hydraulic gradient, indicating significant erosion in non-Darcy conditions. In contrast, the latter exceeds its critical hydraulic gradient, suggesting a limited effect of non-Darcy flow. In non-Darcy flow, the increase in drag force with rising seepage velocity is greater than that in Darcy flow [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Therefore, erosion under non-Darcy flow is more aggressive, resulting in a smaller critical hydraulic gradient, which limits the similarity of centrifuge modeling. Further experiments are anticipated to investigate the effects of hypergravity on internal erosion behaviors using CASIE, aiming to develop a scaling law for the design of centrifuge physical modeling tests and the interpretation of the modeling results.\u003c/p\u003e \u003c/div\u003e"},{"header":"6 Summaries and Conclusions","content":"\u003cp\u003eThis study introduces a new multi-functional apparatus, CASIE, designed for conducting seepage and internal erosion tests via soil column tests in geotechnical centrifuges. CASIE aims to explore the hypergravity effects on soil seepage and internal erosion behaviors.\u003c/p\u003e \u003cp\u003eCASIE facilitates a continuous and steady circulating water supply for the soil column in the centrifuge environment using upstream and downstream water tanks with stabilizing and overflowing bowls and a vertical, multistage centrifugal pump. The water supply flowrate at 80 \u003cem\u003eg\u003c/em\u003e is not less than 34 000 ml/min, sufficient for testing requirements. The hydraulic gradient across the soil specimen can be controlled by adjusting the elevation of the upstream water tank via a servo lifting system. The maximum vertical displacement and the maximum vertical speed of the servo lifting system are 1.2 m and 155 mm/min, respectively.\u003c/p\u003e \u003cp\u003eA rigid wall permeameter is developed to conduct soil column tests in various applications (e.g. seepage, heave, and suffusion) in CASIE. Up to four permeameters can be connected in parallel allowing multi-channel tests during a single centrifuge operation. Oval gear flowmeters were proven to measure the flowrate through the specimen in the hypergravity environment. Four flowmeters connected in parallel ensure a broad measurement capacity spanning from 10-10000 ml/min. The sensitivities of the flowmeters were recalibrated in the hypergravity environment.\u003c/p\u003e \u003cp\u003ePreliminary suffusion tests conducted at 30 \u003cem\u003eg\u003c/em\u003e and 1 \u003cem\u003eg\u003c/em\u003e revealed that the erosion evolution process was similar at these two different \u003cem\u003eg\u003c/em\u003e-levels. The hypergravity did not affect the curve shape of the velocity-hydraulic gradient relationship. However, the scaling factor for the critical hydraulic gradient between 30 \u003cem\u003eg\u003c/em\u003e and 1 \u003cem\u003eg\u003c/em\u003e in the preliminary tests was only 1/10, remarkably lower than the theoretical prediction of 1. It suggests that suffusion can be triggered more readily in the hypergravity environment. This might be related to the accelerated transition from Darcy to non-Darcy flow regime due to the N-fold increase in the seepage velocity rate at N \u003cem\u003eg\u003c/em\u003e. Further experiments are expected to explore the hypergravity effects on seepage and internal erosion behaviors using CASIE, aiming to establish a scaling law for centrifuge physical modeling design.\u003c/p\u003e"},{"header":"Declarations","content":" \u003cp\u003e\u003cstrong\u003eCompeting Interests:\u003c/strong\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eChang Guo and Wenyue Zhang carried out the experiment. Chang Guo wrote the manuscript with support from Bo Huang and Yao Tang. Bo Huang, Jiying Fan, and Yao Tang supervised the project. Bo Huang conceived the original idea.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe work presented in this article was supported by the Natural Science Foundation of Zhejiang Province (grant number LCZ19E080002) and the National Natural Science Foundation of China (Grant No. 51988101).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eFell R, Wan CF, Cyganiewicz J, Foster M (2003) Time for Development of Internal Erosion and Piping in Embankment Dams\u003cem\u003e.\u003c/em\u003e Journal of Geotechnical and Geoenvironmental Engineering 129: 307-314. http://doi.org/10.1061/(ASCE)1090-0241(2003)129:4(307)\u003c/li\u003e\n\u003cli\u003eZhang LM, Xu Y, Jia JS (2009) Analysis of earth dam failures: A database approach\u003cem\u003e.\u003c/em\u003e Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 3: 184-189. https://doi.org/10.1080/17499510902831759\u003c/li\u003e\n\u003cli\u003eBonelli S, Nicot F (2013) Erosion in Geomechanics Applied to Dams and Levees. 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Dissertation, University of British Columbia. https://dx.doi.org/10.14288/1.0063080\u003c/li\u003e\n\u003cli\u003eChang DS, Zhang LM (2011) A Stress-controlled Erosion Apparatus for Studying Internal Erosion in Soils\u003cem\u003e.\u003c/em\u003e Geotechnical Testing Journal 34. https://doi.org/10.1520/GTJ103889\u003c/li\u003e\n\u003cli\u003eZhang W, Takahashi A (2024) Assessment of the Applicability of a Constant-Head Borehole Permeameter Test to River Levees\u003cem\u003e.\u003c/em\u003e Geotechnical Testing Journal 47: 846-862. http://doi.org/10.1520/GTJ20230433\u003c/li\u003e\n\u003cli\u003eSingh DN, Gupta AK (2000) Modelling hydraulic conductivity in a small centrifuge\u003cem\u003e.\u003c/em\u003e Canadian Geotechnical Journal 37: 1150-1155. http://doi.org/10.1139/t00-027\u003c/li\u003e\n\u003cli\u003evan Tonder WD, Jacobsz SW (2017) Seepage column hydraulic conductivity tests in the geotechnical centrifuge\u003cem\u003e.\u003c/em\u003e Journal of The South African Institution of Civil Engineering 59: 16-24. http://dx.doi.org/10.17159/2309-8775/2017/v59n3a3 \u003c/li\u003e\n\u003cli\u003eOvalle-Villamil W, Sasanakul I (2018) A new insight into the behaviour of seepage flow in centrifuge modelling. 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Balkema, Rotterdam, pp 357-360. \u003c/li\u003e\n\u003cli\u003eKe L, Takahashi A (2014) Triaxial Erosion Test for Evaluation of Mechanical Consequences of Internal Erosion\u003cem\u003e.\u003c/em\u003e Geotechnical Testing Journal 37: 347-364. https://doi.org/10.1520/gtj20130049\u003c/li\u003e\n\u003cli\u003eNguyen CD, Benahmed N, And\u0026ograve; E, Sibille L, Philippe P (2019) Experimental investigation of microstructural changes in soils eroded by suffusion using X-ray tomography\u003cem\u003e.\u003c/em\u003e Acta Geotechnica 14: 749 - 765. https://doi.org/article/10.1007/s11440-019-00787-w\u003c/li\u003e\n\u003cli\u003eSkempton AW, Brogan JM (1994) Experiments on piping in sandy gravels\u003cem\u003e.\u003c/em\u003e G\u0026eacute;otechnique 44: 449-460. https://doi.org/10.1680/geot.1994.44.3.449\u003c/li\u003e\n\u003cli\u003eIndraratna B, Radampola S (2002) Analysis of Critical Hydraulic Gradient for Particle Movement in Filtration\u003cem\u003e.\u003c/em\u003e Journal of Geotechnical and Geoenvironmental Engineering 128: 347-350. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:4(347)\u003c/li\u003e\n\u003cli\u003eLi M, Fannin RJ (2008) Comparison of two criteria for internal stability of granular soil\u003cem\u003e.\u003c/em\u003e Canadian Geotechnical Journal 45: 1303-1309. https://doi.org/10.1139/t08-046\u003c/li\u003e\n\u003cli\u003eCarrier WD (2003) Goodbye, Hazen; Hello, Kozeny-Carman\u003cem\u003e.\u003c/em\u003e Journal of Geotechnical and Geoenvironmental Engineering 129: 1054-1056. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:11(1054)\u003c/li\u003e\n\u003cli\u003eMorrison FA (2013) An introduction to fluid mechanics. Cambridge University Press, London. \u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1\u0026nbsp;Overview of geotechnical centrifuge apparatuses related to seepage and internal erosion soil column tests\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.34020618556701%\" rowspan=\"2\"\u003e\n \u003cp\u003eApparatus\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\" rowspan=\"2\"\u003e\n \u003cp\u003eMaximum acceleration reported by authors\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.556701030927837%\" rowspan=\"2\"\u003e\n \u003cp\u003eWater supply\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.49484536082474%\" rowspan=\"2\"\u003e\n \u003cp\u003eWater level control\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\" rowspan=\"2\"\u003e\n \u003cp\u003eFlow rate measurement\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.927835051546392%\" colspan=\"3\"\u003e\n \u003cp\u003eSoil column tests\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"34.48275862068966%\"\u003e\n \u003cp\u003eAxial stress controllability\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"34.48275862068966%\"\u003e\n \u003cp\u003eHydraulic gradient measurement\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"31.03448275862069%\"\u003e\n \u003cp\u003eApplications\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.458333333333334%\"\u003e\n \u003cp\u003eSingh and Gupta [19]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\"\u003e\n \u003cp\u003e200 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.75%\" rowspan=\"2\"\u003e\n \u003cp\u003eDiscontinuous, via fall head method\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.666666666666668%\" rowspan=\"2\"\u003e\n \u003cp\u003eUnstable and uncontrollable\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.541666666666666%\" rowspan=\"2\"\u003e\n \u003cp\u003eIndirect, via the descent rate of water level\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\" rowspan=\"2\"\u003e\n \u003cp\u003eSeepage\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"27.5%\"\u003e\n \u003cp\u003evan Tonder and Jacobsz [20]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.5%\"\u003e\n \u003cp\u003e23 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.458333333333334%\"\u003e\n \u003cp\u003eOvalle-Villamil and Sasanakul [21, 22]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\"\u003e\n \u003cp\u003e30 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.75%\"\u003e\n \u003cp\u003eContinuous, via pneumatic tanks outside of the swinging basket and two centrifuge water lines\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.666666666666668%\"\u003e\n \u003cp\u003eUnstable but controllable\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.541666666666666%\"\u003e\n \u003cp\u003eIndirect, via the displacement rate of pneumatic tank pistons\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\"\u003e\n \u003cp\u003eSeepage and heave\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.458333333333334%\"\u003e\n \u003cp\u003eMarot, Le et al [23]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\"\u003e\n \u003cp\u003e40 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.75%\"\u003e\n \u003cp\u003eContinuous, via a pump in the swinging basket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.666666666666668%\"\u003e\n \u003cp\u003eStable, via overflow, but uncontrollable\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.541666666666666%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\"\u003e\n \u003cp\u003eSuffusion\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.34020618556701%\"\u003e\n \u003cp\u003evan Beek and Zwanenburg [7]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e80 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.556701030927837%\"\u003e\n \u003cp\u003eContinuous, via a pump in the swinging basket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.49484536082474%\"\u003e\n \u003cp\u003eStable, via overflow, and controllable, via a plunger\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.927835051546392%\" colspan=\"3\"\u003e\n \u003cp\u003eNot applicable\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.34020618556701%\"\u003e\n \u003cp\u003eWang, Chen et al [27]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e30 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.556701030927837%\"\u003e\n \u003cp\u003eContinuous, via a pump in the swinging basket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.49484536082474%\"\u003e\n \u003cp\u003eStable, via overflow but uncontrollable\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003eIndirect, via a triangular weir\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.927835051546392%\" colspan=\"3\"\u003e\n \u003cp\u003eNot applicable\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.34020618556701%\"\u003e\n \u003cp\u003eShepley and Bolton [26]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.278350515463918%\"\u003e\n \u003cp\u003e60 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.556701030927837%\"\u003e\n \u003cp\u003eContinuous, via water source outside of the swinging basket and one centrifuge water line\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.49484536082474%\"\u003e\n \u003cp\u003eStable and controllable, via a\u0026nbsp;manual flow-control valve outside of the swinging basket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.402061855670103%\"\u003e\n \u003cp\u003eDirect, via a turbine flowmeter outside of the swinging basket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.927835051546392%\" colspan=\"3\"\u003e\n \u003cp\u003eNot applicable\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.458333333333334%\"\u003e\n \u003cp\u003eCASIE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\"\u003e\n \u003cp\u003e80 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.75%\"\u003e\n \u003cp\u003eContinuous, via a pump in the swinging basket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.666666666666668%\"\u003e\n \u003cp\u003eStable, via overflow, and controllable, via a servo upstream lifting system\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.541666666666666%\"\u003e\n \u003cp\u003eDirect, via oval gear flowmeters in swinging basket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.416666666666666%\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.375%\"\u003e\n \u003cp\u003eSeepage, heave, and suffusion\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;2\u0026nbsp;Calibration results of flowmeters\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"482\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.02074688796681%\" colspan=\"2\" rowspan=\"2\"\u003e\n \u003cp\u003eThe slope of sensitivity at N \u003cem\u003eg\u003c/em\u003e to\u003cem\u003e\u0026nbsp;\u003c/em\u003e1\u003cem\u003e\u0026nbsp;g\u003c/em\u003e,\u003cem\u003e\u0026nbsp;K\u003c/em\u003e\u003csub\u003eN\u003c/sub\u003e/\u003cem\u003eK\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.97925311203319%\" colspan=\"4\"\u003e\n \u003cp\u003eCentrifugal acceleration, N: \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.825726141078839%\" rowspan=\"4\"\u003e\n \u003cp\u003eFlowmeter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.40248962655602%\"\u003e\n \u003cp\u003e10-100 ml/min\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.692946058091286%\"\u003e\n \u003cp\u003e1.065\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.692946058091286%\"\u003e\n \u003cp\u003e1.094\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.692946058091286%\"\u003e\n \u003cp\u003e1.156\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.692946058091286%\"\u003e\n \u003cp\u003eN/A\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.88235294117647%\"\u003e\n \u003cp\u003e30-300 ml/min\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.051\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.121\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.178\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.88235294117647%\"\u003e\n \u003cp\u003e100-1000 ml/min\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.063\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.059\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.070\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.087\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.88235294117647%\"\u003e\n \u003cp\u003e800-10000 ml/min\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.041\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.529411764705882%\"\u003e\n \u003cp\u003e1.098\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.11434511434511%\" colspan=\"2\"\u003e\n \u003cp\u003eAverage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.721413721413722%\"\u003e\n \u003cp\u003e1.068\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.721413721413722%\"\u003e\n \u003cp\u003e1.093\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.721413721413722%\"\u003e\n \u003cp\u003e1.109\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.721413721413722%\"\u003e\n \u003cp\u003e1.120\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;3\u0026nbsp;Soil properties\u003c/p\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"520\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"100%\" colspan=\"2\"\u003e\n \u003cp\u003eSoil Properties\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eSpecific gravity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e2.662\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eFine particle ratio: %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eMaximum void ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e0.775\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eMinimum void ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e0.351\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eTarget relative density: %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eEffective particle size, \u003cem\u003ed\u003c/em\u003e\u003csub\u003eeff\u003c/sub\u003e: mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e0.253\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eUniformity coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e13.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eCoefficient of curvature\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e7.44\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003e(\u003cem\u003eH/F\u003c/em\u003e)\u003csub\u003emin\u0026nbsp;\u003c/sub\u003e[29]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e0 \u0026lt; 1 (unstable)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003e(\u003cem\u003eD\u003c/em\u003e\u003csub\u003e15c\u003c/sub\u003e/\u003cem\u003ed\u003c/em\u003e\u003csub\u003e85f\u003c/sub\u003e)\u003csub\u003emax\u0026nbsp;\u003c/sub\u003e[30]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e9.49 \u0026gt; 4 (unstable)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"45.38461538461539%\"\u003e\n \u003cp\u003eConditional factors of uniformity\u0026nbsp;[31]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"54.61538461538461%\"\u003e\n \u003cp\u003e\u003cem\u003eh\u0026apos;\u003c/em\u003e=1.34; \u003cem\u003eh\u0026apos;\u0026apos;\u003c/em\u003e=17.1\u003c/p\u003e\n \u003cp\u003e0.67lg(\u003cem\u003eh\u0026apos;\u0026apos;\u003c/em\u003e)+1=1.83\u0026gt;\u003cem\u003e\u0026nbsp;h\u0026apos;\u003c/em\u003e (unstable)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Internal erosion, seepage, geotechnical centrifuge, soil column test, hypergravity effect, multifunctional apparatus","lastPublishedDoi":"10.21203/rs.3.rs-4745756/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4745756/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUnderstanding the hypergravity effect on seepage and internal erosion is the essential precondition for dam hydraulic disaster modeling using geotechnical centrifuges. Soil column testing is useful to bridge this knowledge gap, but previous attempts did not provide adequate functionality in centrifuge environments. This study develops a centrifuge-available apparatus for seepage and internal erosion soil column tests (CASIE). CASIE ensures a consistent and stable circulating water supply with no less than 34 000 ml/min at 80 \u003cem\u003eg\u003c/em\u003e via double-bowl upstream and downstream water tanks and a vertical, multistage centrifugal pump. The hydraulic gradient can be controlled by adjusting the elevation of the upstream water tank using a servo lifting system with a vertical displacement range of 1.2 m and a maximum vertical speed of 155 mm/min. A rigid-wall permeameter is developed for multiple applications in soil column tests for seepage and internal erosion. The flowrate through the specimen can be measured using four parallel-installed oval gear flowmeters with a large measurement range of 10\u0026ndash;10 000 ml/min. To validate the capabilities of CASIE, two suffusion (one form of internal erosion) tests were conducted at 1 \u003cem\u003eg\u003c/em\u003e and 30 \u003cem\u003eg\u003c/em\u003e. The results reveal that the scaling factor for the critical hydraulic gradient of 30 \u003cem\u003eg\u003c/em\u003e to 1 \u003cem\u003eg\u003c/em\u003e is 1/10. It is much less than the predicted value of 1, indicating that suffusion failure is more readily triggered in the hypergravity environment.\u003c/p\u003e","manuscriptTitle":"A New Apparatus for Seepage and Internal Erosion Soil Column Tests in Geotechnical Centrifuge","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-15 16:54:59","doi":"10.21203/rs.3.rs-4745756/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"834ce9af-5df6-4f70-900c-c77db36895ca","owner":[],"postedDate":"August 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-11T15:17:58+00:00","versionOfRecord":{"articleIdentity":"rs-4745756","link":"https://doi.org/10.1520/GTJ20240182","journal":{"identity":"geotechnical-testing-journal","isVorOnly":true,"title":"Geotechnical Testing Journal"},"publishedOn":"2025-11-01 00:00:00","publishedOnDateReadable":"November 1st, 2025"},"versionCreatedAt":"2024-08-15 16:54:59","video":"","vorDoi":"10.1520/GTJ20240182","vorDoiUrl":"https://doi.org/10.1520/GTJ20240182","workflowStages":[]},"version":"v1","identity":"rs-4745756","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4745756","identity":"rs-4745756","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}