Deformation and force analysis of reinforced soil bridge abutment under dynamic vehicle loading

Deformation and force analysis of reinforced soil bridge abutment under dynamic vehicle loading | 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 Article Deformation and force analysis of reinforced soil bridge abutment under dynamic vehicle loading Yan-li Dong, Hao-dong Zhang, Hao-ran Feng, Zhi-yi Zhao, Jun Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5657639/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Apr, 2025 Read the published version in Scientific Reports → Version 1 posted 8 You are reading this latest preprint version Abstract The Geosynthetic Reinforced Soil-Integrated Bridge System (i.e. GRS-IBS) was developed to address the bumping issue from differential settlement at bridge abutments. This study focused on a Louisiana bridge abutment, using numerical simulation with the finite difference method to assess deformation and stress under dynamic loads. Results showed that deformation of the soil abutment and geogrid increased with the vehicle weight, with a more pronounced effect on lateral displacement than settlement. Settlement values initially decreased then rose with speeds between 30–60 km/h, mirroring the trend in lateral displacement and geogrid deformation. The lateral displacement of the geogrid was roughly half that of the panel. Shear stress on the abutment at 5 tons was double that at 1.75 tons, and geogrid stress was triple. Analysis indicated that a vehicle speed of around 45 km/h had the least impact on the reinforced soil abutment. The findings offer valuable insights for the use and maintenance of reinforced earth bridge abutments. Physical sciences/Engineering/Civil engineering Physical sciences/Engineering/Energy infrastructure dynamic vehicle loading reinforced soil abutment geosynthetic reinforced soil deformation analysis geogrid stress 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 1. Introduction Owing to the advancements in geosynthetics, the use of Geosynthetic Reinforced Soil (GRS) has expanded considerably. The Geosynthetic Reinforced Soil‒Integrated Bridge system (GRS‒IBS, hereinafter referred to as the reinforced soil abutment in this paper) was initially introduced for single- to medium-scale single-span bridge replacements and repairs in the Future Bridge Program by the U.S. Federal Highway Administration[ 1 ]. A typical cross-section of a GRS‒IBS[ 2 ] is shown in Fig. 1 . The GRS‒IBS was proposed as a rapid and cost-effective bridge support method that seamlessly integrates the roadway with the superstructure, thereby creating a jointless interface between the bridge and the approach[ 3 – 8 ]. Compared with traditional pile-supported abutments, many published case histories consistently demonstrate that the GRS‒IBS significantly reduces the differential settlement between the bridge and the approach roadway[ 9 – 15 ]. For example, Abu-Hejleh et al. [ 9 ], Adams et al. [ 10 ], Saghebfar et al. [ 11 ], Talebi et al. [ 12 , 13 ], and Gebremariam et al. [ 14 , 15 ] conducted field monitoring of actual projects. These findings revealed that the reinforced soil abutment exhibited excellent service performance under working load or overloading conditions. As illustrated in Fig. 1 , the reinforced soil foundation, the GRS abutment, and the integrated approach collectively form the GRS‒IBS. Typically, to increase the bearing width and capacity of the GRS abutment, the reinforced soil foundation is constructed with granular fill material, which is meticulously compacted and encapsulated within a geotextile. The bridge is positioned directly atop the GRS abutment, eliminating the need for a joint and avoiding the use of cast-in-place concrete. The GRS abutment employs alternating layers of compacted fill and densely spaced geosynthetic reinforcement to support the bridge. The GRS is also used to construct an integrated approach to transition to the superstructure. Since the bridge superstructure is directly installed on the GRS‒IBS abutment, the roadbed of the road-bridge transition section can seamlessly connect with the GRS‒IBS structure forming an integrated road-bridge structure with deformation coordination, which can effectively control the differential settlement of the road-bridge transition section and alleviate the problem of bumping[ 16 – 19 ]. Many static load tests have shown that the GRS-IBS presents good bearing capacity and deformation characteristics[ 20 – 26 ]. The results show that the maximum settlement and lateral displacement of the GRS abutment under static loading were much smaller than the values required by the FHWA. Moreover, many studies have investigated the seismic performance of GRS abutments and their results have shown that GRS abutments do not experience obvious structural failure under earthquake loading[ 27 – 31 ]. However, related studies under vehicle loading are scarce. Several studies on the effects of dynamic vehicle loading on bridges have focused mainly on bridge span structures or concrete rigid abutments. Therefore, the performance of the GRS‒IBS under vehicle loading must be investigated. These findings can substantially complement the evaluation of the working performance of reinforced soil abutments, fill the existing research gap in this domain, and provide a robust theoretical foundation and data support for the advancement of GRS abutment technology. 2. Objective In this study, a numerical model was developed to simulate the performance of a single-scale span GRS‒IBS under various loading conditions. The developed numerical model was first verified and validated using field measurements from the fully instrumented GRS‒IBS at the Maree Michel Bridge in Louisiana[ 11 ]. This numerical model was subsequently employed to simulate the different vehicle loading conditions. The performance was evaluated in terms of the settlement of the GRS abutment, lateral displacement at the panel, geogrid deformation, and stress of the GRS abutment. Applied vehicle weights equal to 1.75 tons and 5.0 tons were selected for evaluation in this study under differential speed values of 30 km/h, 45 km/h, and 60 km/h. 3. Overview of the Maree Michel Bridge (GRS‒IBS) A field-monitored GRS‒IBS project constructed in Louisiana was chosen for the numerical modelling performed in this study. The Maree Michel Bridge [ 11 , 32 ] was the first GRS‒IBS bridge built on footings supported directly by a geosynthetic reinforced soil system in Louisiana, USA, awarded as an Annual Demonstration Project. The cross-section of the abutment of the Maree GRS‒IBS was simulated in the numerical model, as shown in Fig. 2 . The geometry of the numerical model was based on the actual dimensions of the Maree Michel Bridge constructed in the field, with some minor modifications to simplify the numerical mesh. The span length of this bridge is 19.8 m, and the total width of the upper part of the bridge is approximately 9.1 m. The length and width of the abutment were 13.5 m and 11.9 m, respectively. The wall height from the top to the foundation was 5.3 m, and the distance from the girder seat to the foundation was approximately 4 m. The panel was composed of 203 mm×203 mm×406 mm concrete blocks with a compressive strength of 27.6 MPa. The geotextiles of the woven PP material were used as reinforcements in the reinforced zone, with a vertical spacing of 0.2 m between the primary reinforcement layers. The primary reinforcement layers in the reinforced zone extended to the cut slopes of the same length, as shown in Fig. 1 . Five layers of bearing bed reinforcement layers were used in the reinforced zone. The bearing bed reinforcement was performed with a spacing of 0.1 m among the first layers of the geotextiles at the top of the abutment to increase the load carrying capacity. The length of the reinforcement was 2.6 m. The reinforced soil foundation was seated on limestone bedrock and surrounded by the foundation soil. The integrated approach involved six lifts of wrapped-around fill material behind the bridge slab. The same type of woven geotextile was used as the reinforcement in the integrated approach, with a vertical spacing of 0.2 m. 4. Numerical modelling FLAC 3D software with a version of 7.0 developed by Itasca was selected in this study to simulate the Maree GRS‒IBS. The detailed dimensions of the bridge model are shown in Fig. 2 and Fig. 3 . The water table and the influence of the reinforced soil were neglected during the modelling process in this study. For simplicity, the reinforced soil foundation was simulated as a fixed boundary. The beam seat was simplified as a concrete slab with an X-axis length of 0.7 m, a Y-axis length of 13.5 m and a Z-axis height of 0.4 m. The panel was modelled as a concrete with a thickness of 0.2 m. There was limited information available on the pavement material from the published papers pertaining to the Maree Michel Bridge. Consideration this reason and to simplicity, we have integrated only the pavement height into the model's overall height, without differentiating among various materials. 4.1 Parameters of the GRS abutment and reinforcements As shown in Fig. 3 , the numerical model built by FLAC 3D was divided into four groups, including the integrated approach, beam seat, and geosynthetic-reinforced soil abutment. The integrated approach included fill and geotextile, and the geosynthetic-reinforced soil abutment included fill, geotextile and abutment facing blocks. Table 1 lists all the constitutive models and input parameters for different components simulated in the numerical model apart from the geotextile. Notably, the input parameter values were in accordance with those of actual engineering[ 34 , 35 ]. The Mohr‒Coulomb model was used to simulate the fill of the geosynthetic-reinforced soil abutment and integrated approach. The elastic model was used to simulate the abutment facing block. Tab. 1. Constitutive models and input parameters for different components simulated in the numerical model The selected geotextiles were made of woven PP material, which was considered a linear elastic material. The built-in structural element of the geogrid of FLAC was used to represent the reinforcement of the geotextiles in the geosynthetic-reinforced soil abutment. For consistency, the following “geotextile” reinforcement is represented by the term “geogrid”. The lengths of the geogrid reinforcements were simplified to be the same, whereas the values of vertical spacing between these reinforcements were the same as those in actual engineering; specifically, the spacing in the reinforcement area was 0.2 m, and that in the bearing bed reinforcement area was 0.1 m. Additionally, six layers of geogrid reinforcements were used in the integrated approach with a vertical spacing of 0.2 m. All the geotextiles are modelled as linear elastic materials with only normal stiffness but without bending stiffness. The physical parameters of the geogrid are provided in Table 2 . Table 2 Parameters of the geogrid Thickness (mm) Modulus of elasticity E (kPa) Poisson's ratioν Tangential stiffness (kPa/m) Tensile stiffness (kPa/m) 5 200×10 6 0.33 8.5×10 3 25 4.2 Model boundary setting The bottom boundary was located at z = 0 m (i.e., the bottom of the numerical model). The top boundary was located at z = 5.3 m (i.e., the plane with the total height of the numerical model) in front of the abutment facing on the basis of the symmetry of the bridge slab. The bottom boundary were fixed in the x-, y-, and z-directions, and no deformation was allowed. The top boundary was free to move. The left lateral boundary was located on the plane at x = 0 m. The right lateral boundary was located at x = 11.9 m. The left lateral boundary was fixed in the x- and y-directions, whereas the right lateral boundary was free to move. In the simulation of a semi-infinite body, the numerical method, which depends on the dispersion of the finite area, needs to add suitable conditions to the boundary to solve the interference problem caused by the reflection of vibration waves generated while the vehicle is travelling. The static boundary and free field boundary are adopted in the dynamic analysis of the FLAC 3D software. The application of the above two boundary conditions allows a gap to exist between a certain part of the main unit, which effectively solves the problem of vibration wave reflection. The free field boundary is selected as the boundary condition in this paper. All the attributes, conditions, and variables on the boundary elements are transferred to the elements on the free field boundary. In the process of a software simulation, the calculation is terminated when the ratio of the converged maximum unbalanced force to the typical internal force is less than 10 − 6 . 4.3 Model verification Field measurements of the GRS‒IBS at the Maree Michel Bridge were used to verify the numerical model. To monitor and evaluate the performance of the inservice GRS‒IBS abutment, six types of instrumentation were installed in the southern abutment of the Maree Michel Bridge. One set of horizontal shape acceleration arrays at the top layer of the abutment was installed 0.9 m behind the face of the wall. The ends of the horizontal shape acceleration arrays were attached to settlement plates. The measurement represents the overall settlement of the abutment[ 32 ]. The settlement results of the Maree Michel Bridge abutment monitored in the field after construction were selected to validate the numerical model. Figure 3 shows comparisons between the simulation results and the in situ monitoring results. Here, the dots and lines marked “measured value” in Fig. 4 represent the in situ monitoring results. The simulation results of settlement matched the in situ monitoring results reasonably well, especially the maximum settlement, although the differences were slightly greater at the end of the curve. This comparison verified the reasonableness of the numerical model and parameters. 4.4 Determination of the vehicle dynamic load In the selection of vehicle dynamic load models, a load that is simply simplified as a static or rectangular load model differs considerably from the action mode of the vehicle dynamic load, which approaches from afar and then moves away. The impact load model is mainly used for sections where heavy vehicles travel. Therefore, on the basis of the applicable situations and advantages and disadvantages of each simplified model and in conjunction with the research object of this paper and the current theoretical research on vehicle load models both domestically and internationally, the half-wave sinusoidal load model is ultimately chosen to simulate traffic loads, with its waveform shown in Fig. 5 . In this simplified model, a half-wave represents the action of a vehicle load once, and \(\:{t}_{0}\) represents the interval between the actions of two vehicles' loads. The vehicle load acting on the pavement can be represented by the following equations[ 36 – 37 ]: $$\:\begin{array}{c}F\left(t\right)=p+q\left(t\right)\end{array}$$ 1 $$\:\begin{array}{c}q\left(t\right)={q}_{max}{\text{s}\text{i}\text{n}}^{2}\left(\frac{\pi\:}{2}+\frac{\pi\:t}{T}\right)\end{array}$$ 2 $$\:\begin{array}{c}T=\frac{12R}{v}\end{array}$$ 3 where p = static vehicle wheel load, N; q = additional dynamic vehicle, the value varies with time t, which is equivalent to a sinusoidal distributed load, N; \(\:{q}_{max}\) = amplitude of the additional dynamic vehicle load, N; T = period of the vehicle dynamic load, s; R = radius of the equivalent tire contact area, m; \(\:v\) = velocity of the vehicle, m/s. The value of \(\:{q}_{max}\) generally does not exceed 1/3 of the static load of the vehicle. In this paper, \(\:{q}_{max}\) is taken as 0.3p. By simplifying the Eq. ( 2 ) through a periodic transformation, the load action formula of a half-wave sinusoidal load can be obtained as follows [ 38 ]: $$\:\begin{array}{c}F\left(t\right)=p+0.3p{\text{s}\text{i}\text{n}}^{2}\left(\frac{\pi\:t}{T}\right)\end{array}$$ 4 According to specifications (Ministry of Transportation, 2015)[ 39 ], the Maree Michel Bridge supported by a geosynthetic-reinforced soil abutment is a tertiary highway with a velocity range between 30 km/h and 60 km/h. The average weight of small vehicles is approximately 1.75 tons, and that of large vehicles is approximately 5.0 tons. Three typical velocities for small and large vehicles were selected: 30 km/h, 45 km/h, and 60 km/h. The parameters of the vehicle dynamic loading are shown in Table 3 . Additionally, one cycle of half-wave sine vehicle loading is applied to the beam seat on the geosynthetic-reinforced soil abutment. Table 3 Vehicle dynamic loading Dynamic load group number Vehicle weight /T Speed /km/h 1 1.75 30 2 1.75 45 3 1.75 60 4 5 30 5 5 45 6 5 60 4.5 Data monitoring point setting The monitoring points of the reinforced soil abutment model are set along the Z-axis direction. At X = 9 m, 11 monitoring sites are set with 0.5 m intervals from 0.25 m to 5.25 m in the Z-direction. For example, the first monitoring point is set at (6, 6.75, 0.25), the second at (6, 6.75, 1), and the last at (6, 6.75, 5.25). The same interval of 0.5 m is used from Z = 0.25 m to 4 m, with 8 points when X = 11.8 m. That is, the first monitoring point at X = 11.8 m is set at (11.8, 6.75, 0.25), the second monitoring point is set at (11.8, 6.75, 1), and so on. A total of 19 monitoring points are set up, as shown in Fig. 6 . The monitoring points on the geotextile are set inside the reinforced soil abutment. The geotextile sheets with id 31, 25, 19, 13, and 7 are monitored at Z = 0.1 m, 1.3 m, 2.5 m, 3.4 m, and 4 m, respectively. 5. Deformation analysis of the reinforced soil bridge abutment In this study, the GRS‒IBS models were analysed to evaluate the performance of the integral bridge under different dynamic vehicle loadings. The term “S” or “small” represents a small vehicle with a weight of 1.75 tons, whereas “L” or “large” represents a large vehicle with a weight of 5.0 tons. The former numbers in the legend, such as 30 km/h, 45 km/h, and 60 km/h, represent the velocity of the vehicle. The latter numbers in the legend, such as 9 and 11.8, represent the monitoring position. To better demonstrate the settlement and lateral displacement of the reinforced soil abutment at 11.8 m in the X-direction, the deformation of the reinforced soil abutment under dynamic loadings of 47.5 km/h and 52.5 km/h was added. 5.1 GRS-IBS Settlement analysis To investigate the effect of velocity on the settlement of the GRS abutment, the results are summarised in Fig. 7 and Fig. 8 . Figure 7 and Fig. 8 show the settlement comparison curves of the GRS abutment under different small and large vehicle dynamic loadings, respectively. The solid and dotted lines indicate the settlement of the GRS abutment monitored at X = 9 m and X = 11.8 m, respectively. Differential settlements exist between the two monitoring points (i.e., X = 9 m and X = 11.8). Table 4 Differential settlement (( \(\:\left|\varDelta\:s\right|/H\) )%) between X = 9 m and X = 11.8m Monitor height(m) 30km/h (S) 45km/h (S) 60km/h (S) 30km/h (L) 45km/h (L) 60km/h (L) 0.25 0.04 0.04 0.04 0.11 0.10 0.12 1.00 0.09 0.06 0.10 0.32 0.28 0.40 1.50 0.08 0.05 0.09 0.36 0.31 0.48 2.00 0.04 0.01 0.06 0.36 0.29 0.51 2.50 0.02 0.05 0.02 0.32 0.24 0.49 3.00 0.08 0.12 0.03 0.26 0.17 0.47 3.50 0.13 0.19 0.09 0.19 0.10 0.42 4.00 0.21 0.26 0.15 0.12 0.01 0.35 Note: s refers to the monitored settlement(mm); H refers to the totall height of the Abutment(m). As shown in Fig. 7 and Fig. 8 , the settlements of the geosynthetic-reinforced soil abutment present similar trends along with the elevation of the GRS abutment. Under the same dynamic loading conditions, larger vehicles cause greater maximum settlement values (e.g., 5.11 mm, 4.97 mm, and 4.5 mm) than do smaller vehicles (e.g., 4.83 mm, 4.78 mm, and 4.6 mm). This comparison indicates that heavier vehicles exert greater dynamic forces on the abutments, leading to more considerable deformation. At locations farther from the loading point (e.g., X = 9 m), the settlement values decrease with increasing vehicle speed. This decrease is observed because higher speeds reduce the duration of the dynamic load acting on the abutment, thereby minimizing cumulative deformation. However, at locations closer to the loading point (e.g., X = 11.8 m), the settlement behaviour exhibited a nonmonotonic trend. The settlement values tend to be greater at the extremes (30 km/h and 60 km/h) and lower at intermediate speeds (45 km/h). This nonlinear behaviour is likely due to the vehicle‒bridge coupling effect becoming more pronounced at higher speeds, which alters the dynamic response of the abutment. As depicted in Figs. 7 to 8 and Table 4 , it can be inferred that the differential settlement between the points at X = 9 m and X = 11.8 m was negligible, even though the maximum value reached approximately 0.5% of the total height of the GRS abutment. The GRS abutment demonstrated commendable deformation performance under various dynamic vehicle loadings. According to the above analysis, it can be concluded that the settlement behaviour of GRS abutments is considerably influenced by vehicle speed and weight. Lower speeds and heavier vehicles generally result in larger settlements, whereas higher speeds can reduce settlement due to shorter load application durations. However, the interaction between these factors is complex and highly dependent on the monitoring location. Long-term monitoring and predictive modelling are crucial for managing settlement behaviour and ensuring the long-term stability and safety of GRS abutments. 5.2 Analysis of the lateral displacement at the face wall Figure 9 shows the lateral displacement curve of the reinforced soil abutment at 11.8 m in the X-direction under dynamic loading. The solid line represents the lateral displacement under small vehicle loading, whereas the dotted line corresponds to large vehicle loading. The trend in lateral displacement at the monitoring points is similar for small and large vehicle loading conditions. As the height of the abutment increases, the lateral displacement also increases, converging between 3.5 m and 4 m. This trend aligns closely with the settlement behaviour observed at the same location, indicating a strong correlation between lateral displacement and settlement. The data indicate that the lateral displacement values are considerably greater under large vehicle loading than under small vehicle loading. For example, under 30 km/h dynamic loading, the lateral displacement is 7.57 mm for large vehicles but 3.03 mm for small vehicles. This comparison suggests that vehicle weight is a predominant factor influencing lateral displacement, akin to its impact on settlement. The data further reveal that the maximum lateral displacement under dynamic loading ranging from 30 km/h to 60 km/h is minimal at 45 km/h and increases at the extremes (30 km/h and 60 km/h). This trend aligns with the previously observed settlement behaviour, as the lateral restraint provided by the panel results in displacement increasing in conjunction with the abutment's settlement value. On the basis of the analysis, it can be concluded that the lateral displacement values are more sensitive to dynamic loading conditions than the settlement values are, making them critical parameters for assessing structural integrity. These findings emphasise the need for robust design, long-term monitoring, and effective traffic management strategies to ensure the stability and safety of reinforced soil abutments. 5.3 Geogrid deformation analysis Figures 10 and 11 present the settlement and lateral displacement of the geogrid within the GRS abutment under dynamic vehicle loading conditions. As shown in Fig. 10 , the maximum settlement of the geogrid occurs at elevations between 3 m and 4 m in the Z-direction of the abutment, particularly in areas with relatively high geogrid densities. This finding suggests that the deformation of the geogrid is concentrated in the regions where it is most densely packed, likely due to the redistribution of stresses in these areas. The settlement values under large vehicle loading are considerably greater than those under small vehicle loading. With increasing dynamic vehicle loading, the settlement value of the geogrid correspondingly increases. This trend is consistent across small and large vehicle loadings, indicating that the magnitude of the applied load directly influences the deformation of the geogrid. Figure 11 reveals that the lateral displacement of the geogrid is approximately half of the lateral displacement observed at 11.8 m in the X-direction of the GRS abutment. The maximum lateral displacement of the geogrid occurs under a dynamic loading rate of 30 km/h, mainly in areas with relatively high geogrid intensities. In addition, as the height of the abutment increases, the lateral displacement of the geogrid also increases, indicating that the upper sections of the geogrid are more susceptible to deformation under dynamic loading. The analysis of Figs. 10 and 11 reveals that the vehicle speed, weight, and geogrid density influence the settlement and lateral displacement of the geogrid. Although the settlement of the geogrid increases with vehicle speed, the lateral displacement exhibits a nonmonotonic trend, with the maximum value occurring at 30 km/h and the minimum occurring at 45 km/h. This discrepancy confirms that vehicle speed primarily influences lateral displacement through its effect on settlement. The geogrid's ability to redistribute stresses plays a critical role in mitigating lateral deformation, particularly at intermediate speeds. 5.4 Stress analysis of the GRS abutment Figure 12 presents the cloud map of the maximum shear stress in the GRS abutment under various dynamic vehicle loading conditions. This figure shows that the maximum shear stress under large vehicle dynamic loading is approximately twice that observed under small vehicle loading. Notably, the shear stress under a dynamic load of 60 km/h is the smallest among the loading conditions. This comparison suggests that higher speeds reduce shear stress due to shorter loading duration, which limits stress propagation and accumulation in the soil-abutment system. The stress concentration is evident on both sides of the beam seat, where the dynamic vehicle loading is applied. Additionally, the shear stress decreases with increasing vehicle speed and is more pronounced in the lower part of the abutment. This distribution pattern indicates that the lower sections of the abutment bear a considerable portion of the load, emphasizing the importance of reinforcing these areas. Figure 13 shows the maximum stress distribution within the geogrid under different vehicle dynamic loading scenarios. According to the theory of tensile membrane action, peak stress is influenced primarily by the overlying load. The top layer of the reinforced material helps offset some of the downwards stress, which in turn reduces settlement in the lower part. This reduction in settlement causes the lower reinforced material to experience tensile stress due to the upwards rotation of the panel foundation. However, in the current state, this tensile stress plays a relatively minor role, resulting in lower stress values in the tendon material. For small and large vehicles, the geogrid results in the lowest peak stress under a dynamic load of 45 km/h, the second-highest peak stress under a dynamic load of 60 km/h, and the highest peak stress under a dynamic load of 30 km/h. This finding indicates that the stress on the GRS abutment is minimised when the vehicle speed is approximately 45 km/h. The above analysis demonstrates that vehicle speed and weight influence the maximum shear stress and geogrid stress in reinforced soil abutments. The stress on the abutment and geogrid is minimised at a vehicle speed of approximately 45 km/h, highlighting the importance of optimal speed ranges in reducing dynamic effects. Vehicle weight considerably increases stress levels, emphasising the need to consider traffic composition in design. The geogrid's ability to redistribute stresses plays a critical role in mitigating deformation and enhancing structural stability. 6. Conclusions In this study, the deformation of a GRS‒IBS under different dynamic vehicle loadings was simulated via FLAC 3D software. The results were analysed from five aspects: settlement, lateral displacement of the face wall, geogrid deformation, maximum shear stress of the GRS‒IBS, and geogrid stress. The following conclusions were drawn. (1) The overall settlement of the reinforced soil abutment increases with increasing height of the abutment. For different vehicle dynamic loadings, the settlement increases with increasing dynamic load at X = 9 m from the abutment. At X = 11.8 m, near the loading position, the settlement is "large on both sides, small in the middle" under vehicle speeds ranging from 30 km/h to 60 km/h. This nonmonotonic behaviour is attributed to dynamic amplification effects caused by vehicle‒bridge coupling at intermediate speeds. (2) The trend of lateral displacement at the GRS face wall is consistent with the trend of settlement, with larger values at the extremes and smaller values in the middle under vehicle dynamic loading. As the vehicle weight increases, the lateral displacement at the face wall also increases. The displacement converges at an elevation of approximately 4 m, indicating a stabilising effect in the upper sections of the abutment. (3) The lateral displacement of the geogrid under dynamic vehicle loading is consistent with the overall settlement trend of the GRS‒IBS. Notably, the lateral displacement of the geogrid is half of the transverse displacement of the reinforced soil abutment panel at that location. (4) As the vehicle dynamic loading increases, the maximum shear stress within the reinforced soil abutment and the maximum stress in the geogrid increase. The maximum stress value under large vehicle dynamic loading is approximately 2 to 3 times greater than that under small vehicle dynamic loading. (5) Vehicle weight is identified as the primary factor affecting the deformation and stress behaviour of reinforced soil abutments. For the same vehicle weight, the vehicle speed considerably influences the abutment response. When the vehicle speed is approximately 45 km/h (within the range of 37.5 km/h to 52.5 km/h), the impact on all aspects of the reinforced soil abutment, including settlement, lateral displacement, and stress, is minimised. Declarations Author Contribution Yan-li Dong provided the evolution of overarching research goals and aims and conducted a thorough review and final approval of the manuscript prior to submission. Hao-dong Zhang and Hao-ran Feng wrote the manuscript. Zhi-yi Zhao performed the data analysis. Jun Zhang performed the validation and format correction. All authors contributed to the writing and editing of the manuscript. Acknowledgments This research is supported by the National Natural Science Foundation of China (grant 52278360), the Open Research Fund of Key Laboratory of Construction and Safety of Water Engineering of the Ministry of Water Resources, China Institute of Water Resources and Hydropower Research (Grant NO. 202202), and Fundamental Research Program of Shanxi Province (Grant NO. 202103021223211). These sponsorships are greatly appreciated. Data Availability The datasets generated and/or analysed during the current study are not publicly available due to the data forms part of ongoing study but are available from the corresponding author on reasonable request. Data requests can be made to corresponding author via this email: [email protected] . References Adams, M., Nicks, J., Stabile, T., Schlatter, W., & Hartmann, J. (2012). Geosynthetic reinforced soil integrated bridge system interim implementation guide (No. FHWA-HRT-11-026). Federal Highway Administration (US). Adams, M., Nicks, J., Stabile, T., Wu, J. T., Schlatter, W., & Hartmann, J. (2011). Geosynthetic reinforced soil integrated bridge system, synthesis report (No. FHWA-HRT-11-027). United States. Federal Highway Administration. Talebi, M., Meehan, C. L., Cacciola, D. V., & Becker, M. L. (2014). Design and construction of a geosynthetic reinforced soil integrated bridge system. 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Saghebfar, M., Abu-Farsakh, M., Ardah, A., Chen, Q., & Fernandez, B. A. (2017). Performance monitoring of geosynthetic reinforced soil integrated bridge system (GRS-IBS) in Louisiana. Geotextiles and Geomembranes , 45(2), 34-47. Itasca Consulting Group, Inc.(2020). Flac3D version 7.0 manual, Minneapolis, MN 55401 USA. Ardah, A., Abu-Farsakh, M., & Voyiadjis, G. (2021). Numerical parametric study of geosynthetic reinforced soil integrated bridge system (GRS-IBS). Geotextiles and Geomembranes , 49(1), 289-303. Abu-Farsakh, M. Y., Ardah, A., & Voyiadjis, G. Z. (2019). Numerical parametric study to evaluate the performance of a Geosynthetic Reinforced Soil–Integrated Bridge System (GRS-IBS) under service loading. Transportation Geotechnics , 20, 100238. Xiao, C., Ai, CF., Qiu, YJ. (2016). Analysis of shear stress characteristics of typical asphalt pavement under dynamic load. Journal of Highway and Transportation Research and Development , 33(07), 19-26.(in Chinese) Zhang, XQ., Yan, SW., Deng, WD. (2001), Principle analysis of reinforced pavement under automobile loading. Chinese Journal of Geotechnical Engineering , (01), 94-98.(in Chinese) Hou, Y., Guo, ZY., Tian, B., Yang, Z. (2002). Deformation response analysis of asphalt pavement structure under dynamic load. China Journal of Highway and Transport , (03), 8-12.(in Chinese) Ministry of Transportation. (2015) General Code for Design of Highway Bridges and culverts: JTG D60mur2015. Beijing: Ministry of Transport . (in Chinese) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 25 Apr, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Accepted 08 Apr, 2025 Reviews received at journal 07 Apr, 2025 Reviewers agreed at journal 06 Apr, 2025 Reviews received at journal 05 Apr, 2025 Reviewers agreed at journal 05 Apr, 2025 Reviewers invited by journal 04 Apr, 2025 Submission checks completed at journal 01 Apr, 2025 First submitted to journal 30 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-5657639","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":440137085,"identity":"6188087f-2b26-46b8-9000-b5c006f0c0ee","order_by":0,"name":"Yan-li Dong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYDCCAyCiQEKOn70BzGdsIE6LgYSxZM8B0rQwJG64kUCkFr7jvYdf8xhYGDPcfHtM4geDjeyGA8zPHuDTInnmXJo1j4GEHOPsvDTJHoY04w0H2MwN8GkxuJFjZgzUYswsnWMmzcBwOHHDAR42CWK0JLZJngFp+U+UFuPHIC09EjwgLQcIa5E8c8aMcQ7QYRI8OcaWPQbJxjMPs5nh1cJ3vMf4w5uKOjn742cMb/yosJPtO978DK8WIGCT4kG4E4iZCagHKfn4g7CiUTAKRsEoGMkAAJWgRRdc/dquAAAAAElFTkSuQmCC","orcid":"","institution":"Key Laboratory of Highway Construction and Maintenance Technology in Loess Region, Ministry of Transport, Shanxi Transportation Research Institute","correspondingAuthor":true,"prefix":"","firstName":"Yan-li","middleName":"","lastName":"Dong","suffix":""},{"id":440137087,"identity":"91ae84fe-469d-4a0d-ba71-25ba8208d4d1","order_by":1,"name":"Hao-dong Zhang","email":"","orcid":"","institution":"North University of 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Institute","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-12-17 02:53:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5657639/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5657639/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-97989-y","type":"published","date":"2025-04-25T15:58:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":80222888,"identity":"0728b5e1-9f03-47b1-a718-1e07ec675ef0","added_by":"auto","created_at":"2025-04-09 11:10:08","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":64273,"visible":true,"origin":"","legend":"\u003cp\u003eTypical cross section of GRS-IBS\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/1856d2598bdbf3af158b96b2.jpg"},{"id":80223452,"identity":"bf53f748-91ab-4884-b9c1-f8bc338b9e31","added_by":"auto","created_at":"2025-04-09 11:18:08","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":70093,"visible":true,"origin":"","legend":"\u003cp\u003eGeometry of the numerical model created by FLAC 3D[33]\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/5cdc3a4f9ce39d39ceaa8868.jpg"},{"id":80222887,"identity":"44fc602f-7f1f-4467-97dd-005d16ea68f1","added_by":"auto","created_at":"2025-04-09 11:10:08","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":72012,"visible":true,"origin":"","legend":"\u003cp\u003eModel mesh of reinforced soil bridge abutment\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/b08497908aacdb7e0c52dfb2.jpg"},{"id":80224313,"identity":"545f40fe-34a6-4e50-bbb6-4750d7cc5468","added_by":"auto","created_at":"2025-04-09 11:26:08","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":44431,"visible":true,"origin":"","legend":"\u003cp\u003eComparison between measured results and simulation results\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/8a1724d5930936dbc812fb91.jpg"},{"id":80223453,"identity":"6292d3db-b3aa-4e5d-83f6-1dc9dca91160","added_by":"auto","created_at":"2025-04-09 11:18:08","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":11324,"visible":true,"origin":"","legend":"\u003cp\u003eHalf wave sinusoidal load model\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/3aed2ecdcf35078305442589.jpg"},{"id":80222891,"identity":"734df226-8ead-441c-880a-20927f08129c","added_by":"auto","created_at":"2025-04-09 11:10:08","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":53012,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of monitoring points\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/5cd640e2a7033cfa395c6983.jpg"},{"id":80222893,"identity":"0742334d-7e65-4b0b-a1ca-ba5475681570","added_by":"auto","created_at":"2025-04-09 11:10:08","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":58136,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of velocity of small vehicle on GRS Settlement\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/4d18a7118c2a9acd7391f323.jpg"},{"id":80225028,"identity":"98861a1b-664b-4355-9ef4-4fdd5ade5590","added_by":"auto","created_at":"2025-04-09 11:34:09","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":63846,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of velocity of large vehicle on GRS Settlement\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/c8ea9c999d1c78fb0c80fa7c.jpg"},{"id":80223461,"identity":"1891edb6-b132-4398-a7e6-2e7b8ebfc018","added_by":"auto","created_at":"2025-04-09 11:18:08","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":58918,"visible":true,"origin":"","legend":"\u003cp\u003eLateral displacement curves of reinforced soil abutment at 11.8m in X direction under dynamic loading\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/dbe1ace8181b8ea4f8388ab5.jpg"},{"id":80222910,"identity":"7c1ce95d-3682-4c71-a749-bba478c2dc9f","added_by":"auto","created_at":"2025-04-09 11:10:09","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":137437,"visible":true,"origin":"","legend":"\u003cp\u003eSettlement of geogrid inside reinforced soil abutment under dynamic vehicle load(Unit:mm)\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/9f10307e0b458ccdf9f6e6ee.png"},{"id":80222897,"identity":"64355186-2445-4153-a44b-29bbaeb09b82","added_by":"auto","created_at":"2025-04-09 11:10:08","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":160921,"visible":true,"origin":"","legend":"\u003cp\u003eLateral displacement of geogrid inside reinforced soil abutment under dynamic vehicle load(Unit:mm)\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/a242c4f0b38cc26f4be01e7a.png"},{"id":80223456,"identity":"e28e9ba6-b931-43d3-a4c1-52c16aa3a45c","added_by":"auto","created_at":"2025-04-09 11:18:08","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":233184,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum shear stress cloud of \u0026nbsp;GRS-IBS under dynamic vehicle load(Unit:N)\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/0a95e5338527043bf56bb4b4.png"},{"id":80223473,"identity":"b20b88dd-8318-4673-a470-d1d614a45afe","added_by":"auto","created_at":"2025-04-09 11:18:09","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":237410,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum strain cloud map of geogrid in GRS abutment under different dynamic vehicle load(Unit:mm)\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/ae9772ffa9157f9a2b473a20.png"},{"id":81569779,"identity":"61f963ec-3e54-4c28-a34a-0b219ff85b4d","added_by":"auto","created_at":"2025-04-28 16:11:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2044900,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5657639/v1/e258bced-a2bd-4cc8-a647-2a2db023264a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Deformation and force analysis of reinforced soil bridge abutment under dynamic vehicle loading","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOwing to the advancements in geosynthetics, the use of Geosynthetic Reinforced Soil (GRS) has expanded considerably. The Geosynthetic Reinforced Soil‒Integrated Bridge system (GRS‒IBS, hereinafter referred to as the reinforced soil abutment in this paper) was initially introduced for single- to medium-scale single-span bridge replacements and repairs in the Future Bridge Program by the U.S. Federal Highway Administration[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. A typical cross-section of a GRS‒IBS[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The GRS‒IBS was proposed as a rapid and cost-effective bridge support method that seamlessly integrates the roadway with the superstructure, thereby creating a jointless interface between the bridge and the approach[\u003cspan additionalcitationids=\"CR4 CR5 CR6 CR7\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCompared with traditional pile-supported abutments, many published case histories consistently demonstrate that the GRS‒IBS significantly reduces the differential settlement between the bridge and the approach roadway[\u003cspan additionalcitationids=\"CR10 CR11 CR12 CR13 CR14\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. For example, Abu-Hejleh et al. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], Adams et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], Saghebfar et al. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], Talebi et al. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], and Gebremariam et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] conducted field monitoring of actual projects. These findings revealed that the reinforced soil abutment exhibited excellent service performance under working load or overloading conditions. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the reinforced soil foundation, the GRS abutment, and the integrated approach collectively form the GRS‒IBS. Typically, to increase the bearing width and capacity of the GRS abutment, the reinforced soil foundation is constructed with granular fill material, which is meticulously compacted and encapsulated within a geotextile. The bridge is positioned directly atop the GRS abutment, eliminating the need for a joint and avoiding the use of cast-in-place concrete. The GRS abutment employs alternating layers of compacted fill and densely spaced geosynthetic reinforcement to support the bridge. The GRS is also used to construct an integrated approach to transition to the superstructure. Since the bridge superstructure is directly installed on the GRS‒IBS abutment, the roadbed of the road-bridge transition section can seamlessly connect with the GRS‒IBS structure forming an integrated road-bridge structure with deformation coordination, which can effectively control the differential settlement of the road-bridge transition section and alleviate the problem of bumping[\u003cspan additionalcitationids=\"CR17 CR18\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMany static load tests have shown that the GRS-IBS presents good bearing capacity and deformation characteristics[\u003cspan additionalcitationids=\"CR21 CR22 CR23 CR24 CR25\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The results show that the maximum settlement and lateral displacement of the GRS abutment under static loading were much smaller than the values required by the FHWA. Moreover, many studies have investigated the seismic performance of GRS abutments and their results have shown that GRS abutments do not experience obvious structural failure under earthquake loading[\u003cspan additionalcitationids=\"CR28 CR29 CR30\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. However, related studies under vehicle loading are scarce. Several studies on the effects of dynamic vehicle loading on bridges have focused mainly on bridge span structures or concrete rigid abutments. Therefore, the performance of the GRS‒IBS under vehicle loading must be investigated. These findings can substantially complement the evaluation of the working performance of reinforced soil abutments, fill the existing research gap in this domain, and provide a robust theoretical foundation and data support for the advancement of GRS abutment technology.\u003c/p\u003e"},{"header":"2. Objective","content":"\u003cp\u003eIn this study, a numerical model was developed to simulate the performance of a single-scale span GRS‒IBS under various loading conditions. The developed numerical model was first verified and validated using field measurements from the fully instrumented GRS‒IBS at the Maree Michel Bridge in Louisiana[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. This numerical model was subsequently employed to simulate the different vehicle loading conditions. The performance was evaluated in terms of the settlement of the GRS abutment, lateral displacement at the panel, geogrid deformation, and stress of the GRS abutment. Applied vehicle weights equal to 1.75 tons and 5.0 tons were selected for evaluation in this study under differential speed values of 30 km/h, 45 km/h, and 60 km/h.\u003c/p\u003e"},{"header":"3. Overview of the Maree Michel Bridge (GRS‒IBS)","content":"\u003cp\u003eA field-monitored GRS‒IBS project constructed in Louisiana was chosen for the numerical modelling performed in this study. The Maree Michel Bridge [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] was the first GRS‒IBS bridge built on footings supported directly by a geosynthetic reinforced soil system in Louisiana, USA, awarded as an Annual Demonstration Project. The cross-section of the abutment of the Maree GRS‒IBS was simulated in the numerical model, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The geometry of the numerical model was based on the actual dimensions of the Maree Michel Bridge constructed in the field, with some minor modifications to simplify the numerical mesh. The span length of this bridge is 19.8 m, and the total width of the upper part of the bridge is approximately 9.1 m. The length and width of the abutment were 13.5 m and 11.9 m, respectively. The wall height from the top to the foundation was 5.3 m, and the distance from the girder seat to the foundation was approximately 4 m. The panel was composed of 203 mm\u0026times;203 mm\u0026times;406 mm concrete blocks with a compressive strength of 27.6 MPa. The geotextiles of the woven PP material were used as reinforcements in the reinforced zone, with a vertical spacing of 0.2 m between the primary reinforcement layers. The primary reinforcement layers in the reinforced zone extended to the cut slopes of the same length, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Five layers of bearing bed reinforcement layers were used in the reinforced zone. The bearing bed reinforcement was performed with a spacing of 0.1 m among the first layers of the geotextiles at the top of the abutment to increase the load carrying capacity. The length of the reinforcement was 2.6 m. The reinforced soil foundation was seated on limestone bedrock and surrounded by the foundation soil. The integrated approach involved six lifts of wrapped-around fill material behind the bridge slab. The same type of woven geotextile was used as the reinforcement in the integrated approach, with a vertical spacing of 0.2 m.\u003c/p\u003e"},{"header":"4. Numerical modelling","content":"\u003cp\u003eFLAC 3D software with a version of 7.0 developed by Itasca was selected in this study to simulate the Maree GRS‒IBS. The detailed dimensions of the bridge model are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The water table and the influence of the reinforced soil were neglected during the modelling process in this study. For simplicity, the reinforced soil foundation was simulated as a fixed boundary. The beam seat was simplified as a concrete slab with an X-axis length of 0.7 m, a Y-axis length of 13.5 m and a Z-axis height of 0.4 m. The panel was modelled as a concrete with a thickness of 0.2 m. There was limited information available on the pavement material from the published papers pertaining to the Maree Michel Bridge. Consideration this reason and to simplicity, we have integrated only the pavement height into the model's overall height, without differentiating among various materials.\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Parameters of the GRS abutment and reinforcements\u003c/h2\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the numerical model built by FLAC 3D was divided into four groups, including the integrated approach, beam seat, and geosynthetic-reinforced soil abutment. The integrated approach included fill and geotextile, and the geosynthetic-reinforced soil abutment included fill, geotextile and abutment facing blocks. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e lists all the constitutive models and input parameters for different components simulated in the numerical model apart from the geotextile. Notably, the input parameter values were in accordance with those of actual engineering[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The Mohr‒Coulomb model was used to simulate the fill of the geosynthetic-reinforced soil abutment and integrated approach. The elastic model was used to simulate the abutment facing block.\u003c/p\u003e \u003cp\u003e\u003cstrong\u003eTab.\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e1.\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eConstitutive models and input parameters for different components simulated in the numerical model\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"620\" height=\"257\"\u003e\u003c/p\u003e \u003cp\u003eThe selected geotextiles were made of woven PP material, which was considered a linear elastic material. The built-in structural element of the geogrid of FLAC was used to represent the reinforcement of the geotextiles in the geosynthetic-reinforced soil abutment. For consistency, the following \u0026ldquo;geotextile\u0026rdquo; reinforcement is represented by the term \u0026ldquo;geogrid\u0026rdquo;. The lengths of the geogrid reinforcements were simplified to be the same, whereas the values of vertical spacing between these reinforcements were the same as those in actual engineering; specifically, the spacing in the reinforcement area was 0.2 m, and that in the bearing bed reinforcement area was 0.1 m. Additionally, six layers of geogrid reinforcements were used in the integrated approach with a vertical spacing of 0.2 m. All the geotextiles are modelled as linear elastic materials with only normal stiffness but without bending stiffness. The physical parameters of the geogrid are provided in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters of the geogrid\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThickness\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModulus of elasticity E\u003c/p\u003e \u003cp\u003e(kPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoisson's ratioν\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTangential stiffness (kPa/m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTensile stiffness\u003c/p\u003e \u003cp\u003e(kPa/m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e200\u0026times;10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.5\u0026times;10\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Model boundary setting\u003c/h2\u003e \u003cp\u003eThe bottom boundary was located at z\u0026thinsp;=\u0026thinsp;0 m (i.e., the bottom of the numerical model). The top boundary was located at z\u0026thinsp;=\u0026thinsp;5.3 m (i.e., the plane with the total height of the numerical model) in front of the abutment facing on the basis of the symmetry of the bridge slab. The bottom boundary were fixed in the x-, y-, and z-directions, and no deformation was allowed. The top boundary was free to move. The left lateral boundary was located on the plane at x\u0026thinsp;=\u0026thinsp;0 m. The right lateral boundary was located at x\u0026thinsp;=\u0026thinsp;11.9 m. The left lateral boundary was fixed in the x- and y-directions, whereas the right lateral boundary was free to move.\u003c/p\u003e \u003cp\u003eIn the simulation of a semi-infinite body, the numerical method, which depends on the dispersion of the finite area, needs to add suitable conditions to the boundary to solve the interference problem caused by the reflection of vibration waves generated while the vehicle is travelling. The static boundary and free field boundary are adopted in the dynamic analysis of the FLAC 3D software. The application of the above two boundary conditions allows a gap to exist between a certain part of the main unit, which effectively solves the problem of vibration wave reflection. The free field boundary is selected as the boundary condition in this paper. All the attributes, conditions, and variables on the boundary elements are transferred to the elements on the free field boundary. In the process of a software simulation, the calculation is terminated when the ratio of the converged maximum unbalanced force to the typical internal force is less than 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Model verification\u003c/h2\u003e \u003cp\u003eField measurements of the GRS‒IBS at the Maree Michel Bridge were used to verify the numerical model. To monitor and evaluate the performance of the inservice GRS‒IBS abutment, six types of instrumentation were installed in the southern abutment of the Maree Michel Bridge. One set of horizontal shape acceleration arrays at the top layer of the abutment was installed 0.9 m behind the face of the wall. The ends of the horizontal shape acceleration arrays were attached to settlement plates. The measurement represents the overall settlement of the abutment[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. The settlement results of the Maree Michel Bridge abutment monitored in the field after construction were selected to validate the numerical model. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows comparisons between the simulation results and the in situ monitoring results. Here, the dots and lines marked \u0026ldquo;measured value\u0026rdquo; in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e represent the in situ monitoring results. The simulation results of settlement matched the in situ monitoring results reasonably well, especially the maximum settlement, although the differences were slightly greater at the end of the curve. This comparison verified the reasonableness of the numerical model and parameters.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Determination of the vehicle dynamic load\u003c/h2\u003e \u003cp\u003eIn the selection of vehicle dynamic load models, a load that is simply simplified as a static or rectangular load model differs considerably from the action mode of the vehicle dynamic load, which approaches from afar and then moves away. The impact load model is mainly used for sections where heavy vehicles travel. Therefore, on the basis of the applicable situations and advantages and disadvantages of each simplified model and in conjunction with the research object of this paper and the current theoretical research on vehicle load models both domestically and internationally, the half-wave sinusoidal load model is ultimately chosen to simulate traffic loads, with its waveform shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this simplified model, a half-wave represents the action of a vehicle load once, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{0}\\)\u003c/span\u003e\u003c/span\u003erepresents the interval between the actions of two vehicles' loads.\u003c/p\u003e \u003cp\u003eThe vehicle load acting on the pavement can be represented by the following equations[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}F\\left(t\\right)=p+q\\left(t\\right)\\end{array}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}q\\left(t\\right)={q}_{max}{\\text{s}\\text{i}\\text{n}}^{2}\\left(\\frac{\\pi\\:}{2}+\\frac{\\pi\\:t}{T}\\right)\\end{array}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}T=\\frac{12R}{v}\\end{array}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;static vehicle wheel load, N;\u003c/p\u003e \u003cp\u003eq\u0026thinsp;=\u0026thinsp;additional dynamic vehicle, the value varies with time t, which is equivalent to a sinusoidal distributed load, N;\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{max}\\)\u003c/span\u003e \u003c/span\u003e= amplitude of the additional dynamic vehicle load, N;\u003c/p\u003e \u003cp\u003eT\u0026thinsp;=\u0026thinsp;period of the vehicle dynamic load, s;\u003c/p\u003e \u003cp\u003eR\u0026thinsp;=\u0026thinsp;radius of the equivalent tire contact area, m;\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:v\\)\u003c/span\u003e \u003c/span\u003e = velocity of the vehicle, m/s.\u003c/p\u003e \u003cp\u003eThe value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{max}\\)\u003c/span\u003e\u003c/span\u003e generally does not exceed 1/3 of the static load of the vehicle. In this paper, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{max}\\)\u003c/span\u003e\u003c/span\u003e is taken as 0.3p. By simplifying the Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) through a periodic transformation, the load action formula of a half-wave sinusoidal load can be obtained as follows [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}F\\left(t\\right)=p+0.3p{\\text{s}\\text{i}\\text{n}}^{2}\\left(\\frac{\\pi\\:t}{T}\\right)\\end{array}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAccording to specifications (Ministry of Transportation, 2015)[\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], the Maree Michel Bridge supported by a geosynthetic-reinforced soil abutment is a tertiary highway with a velocity range between 30 km/h and 60 km/h. The average weight of small vehicles is approximately 1.75 tons, and that of large vehicles is approximately 5.0 tons. Three typical velocities for small and large vehicles were selected: 30 km/h, 45 km/h, and 60 km/h. The parameters of the vehicle dynamic loading are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Additionally, one cycle of half-wave sine vehicle loading is applied to the beam seat on the geosynthetic-reinforced soil abutment.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVehicle dynamic loading\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDynamic load group number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVehicle weight /T\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSpeed /km/h\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Data monitoring point setting\u003c/h2\u003e \u003cp\u003eThe monitoring points of the reinforced soil abutment model are set along the Z-axis direction. At X\u0026thinsp;=\u0026thinsp;9 m, 11 monitoring sites are set with 0.5 m intervals from 0.25 m to 5.25 m in the Z-direction. For example, the first monitoring point is set at (6, 6.75, 0.25), the second at (6, 6.75, 1), and the last at (6, 6.75, 5.25). The same interval of 0.5 m is used from Z\u0026thinsp;=\u0026thinsp;0.25 m to 4 m, with 8 points when X\u0026thinsp;=\u0026thinsp;11.8 m. That is, the first monitoring point at X\u0026thinsp;=\u0026thinsp;11.8 m is set at (11.8, 6.75, 0.25), the second monitoring point is set at (11.8, 6.75, 1), and so on. A total of 19 monitoring points are set up, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The monitoring points on the geotextile are set inside the reinforced soil abutment. The geotextile sheets with id 31, 25, 19, 13, and 7 are monitored at Z\u0026thinsp;=\u0026thinsp;0.1 m, 1.3 m, 2.5 m, 3.4 m, and 4 m, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Deformation analysis of the reinforced soil bridge abutment","content":"\u003cp\u003eIn this study, the GRS‒IBS models were analysed to evaluate the performance of the integral bridge under different dynamic vehicle loadings. The term \u0026ldquo;S\u0026rdquo; or \u0026ldquo;small\u0026rdquo; represents a small vehicle with a weight of 1.75 tons, whereas \u0026ldquo;L\u0026rdquo; or \u0026ldquo;large\u0026rdquo; represents a large vehicle with a weight of 5.0 tons. The former numbers in the legend, such as 30 km/h, 45 km/h, and 60 km/h, represent the velocity of the vehicle. The latter numbers in the legend, such as 9 and 11.8, represent the monitoring position. To better demonstrate the settlement and lateral displacement of the reinforced soil abutment at 11.8 m in the X-direction, the deformation of the reinforced soil abutment under dynamic loadings of 47.5 km/h and 52.5 km/h was added.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e5.1 GRS-IBS Settlement analysis\u003c/h2\u003e \u003cp\u003eTo investigate the effect of velocity on the settlement of the GRS abutment, the results are summarised in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e show the settlement comparison curves of the GRS abutment under different small and large vehicle dynamic loadings, respectively. The solid and dotted lines indicate the settlement of the GRS abutment monitored at X\u0026thinsp;=\u0026thinsp;9 m and X\u0026thinsp;=\u0026thinsp;11.8 m, respectively. Differential settlements exist between the two monitoring points (i.e., X\u0026thinsp;=\u0026thinsp;9 m and X\u0026thinsp;=\u0026thinsp;11.8).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDifferential settlement ((\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|\\varDelta\\:s\\right|/H\\)\u003c/span\u003e\u003c/span\u003e)%) between X\u0026thinsp;=\u0026thinsp;9 m and X\u0026thinsp;=\u0026thinsp;11.8m\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMonitor height(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30km/h\u003c/p\u003e \u003cp\u003e(S)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e45km/h\u003c/p\u003e \u003cp\u003e(S)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e60km/h\u003c/p\u003e \u003cp\u003e(S)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30km/h\u003c/p\u003e \u003cp\u003e(L)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e45km/h\u003c/p\u003e \u003cp\u003e(L)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e60km/h\u003c/p\u003e \u003cp\u003e(L)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eNote: s refers to the monitored settlement(mm); H refers to the totall height of the Abutment(m).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, the settlements of the geosynthetic-reinforced soil abutment present similar trends along with the elevation of the GRS abutment. Under the same dynamic loading conditions, larger vehicles cause greater maximum settlement values (e.g., 5.11 mm, 4.97 mm, and 4.5 mm) than do smaller vehicles (e.g., 4.83 mm, 4.78 mm, and 4.6 mm). This comparison indicates that heavier vehicles exert greater dynamic forces on the abutments, leading to more considerable deformation.\u003c/p\u003e \u003cp\u003eAt locations farther from the loading point (e.g., X\u0026thinsp;=\u0026thinsp;9 m), the settlement values decrease with increasing vehicle speed. This decrease is observed because higher speeds reduce the duration of the dynamic load acting on the abutment, thereby minimizing cumulative deformation. However, at locations closer to the loading point (e.g., X\u0026thinsp;=\u0026thinsp;11.8 m), the settlement behaviour exhibited a nonmonotonic trend. The settlement values tend to be greater at the extremes (30 km/h and 60 km/h) and lower at intermediate speeds (45 km/h). This nonlinear behaviour is likely due to the vehicle‒bridge coupling effect becoming more pronounced at higher speeds, which alters the dynamic response of the abutment.\u003c/p\u003e \u003cp\u003eAs depicted in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e to \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, it can be inferred that the differential settlement between the points at X\u0026thinsp;=\u0026thinsp;9 m and X\u0026thinsp;=\u0026thinsp;11.8 m was negligible, even though the maximum value reached approximately 0.5% of the total height of the GRS abutment. The GRS abutment demonstrated commendable deformation performance under various dynamic vehicle loadings.\u003c/p\u003e \u003cp\u003eAccording to the above analysis, it can be concluded that the settlement behaviour of GRS abutments is considerably influenced by vehicle speed and weight. Lower speeds and heavier vehicles generally result in larger settlements, whereas higher speeds can reduce settlement due to shorter load application durations. However, the interaction between these factors is complex and highly dependent on the monitoring location. Long-term monitoring and predictive modelling are crucial for managing settlement behaviour and ensuring the long-term stability and safety of GRS abutments.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Analysis of the lateral displacement at the face wall\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the lateral displacement curve of the reinforced soil abutment at 11.8 m in the X-direction under dynamic loading. The solid line represents the lateral displacement under small vehicle loading, whereas the dotted line corresponds to large vehicle loading. The trend in lateral displacement at the monitoring points is similar for small and large vehicle loading conditions. As the height of the abutment increases, the lateral displacement also increases, converging between 3.5 m and 4 m. This trend aligns closely with the settlement behaviour observed at the same location, indicating a strong correlation between lateral displacement and settlement.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe data indicate that the lateral displacement values are considerably greater under large vehicle loading than under small vehicle loading. For example, under 30 km/h dynamic loading, the lateral displacement is 7.57 mm for large vehicles but 3.03 mm for small vehicles. This comparison suggests that vehicle weight is a predominant factor influencing lateral displacement, akin to its impact on settlement. The data further reveal that the maximum lateral displacement under dynamic loading ranging from 30 km/h to 60 km/h is minimal at 45 km/h and increases at the extremes (30 km/h and 60 km/h). This trend aligns with the previously observed settlement behaviour, as the lateral restraint provided by the panel results in displacement increasing in conjunction with the abutment's settlement value.\u003c/p\u003e \u003cp\u003eOn the basis of the analysis, it can be concluded that the lateral displacement values are more sensitive to dynamic loading conditions than the settlement values are, making them critical parameters for assessing structural integrity. These findings emphasise the need for robust design, long-term monitoring, and effective traffic management strategies to ensure the stability and safety of reinforced soil abutments.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Geogrid deformation analysis\u003c/h2\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e and 11 present the settlement and lateral displacement of the geogrid within the GRS abutment under dynamic vehicle loading conditions. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, the maximum settlement of the geogrid occurs at elevations between 3 m and 4 m in the Z-direction of the abutment, particularly in areas with relatively high geogrid densities. This finding suggests that the deformation of the geogrid is concentrated in the regions where it is most densely packed, likely due to the redistribution of stresses in these areas. The settlement values under large vehicle loading are considerably greater than those under small vehicle loading. With increasing dynamic vehicle loading, the settlement value of the geogrid correspondingly increases. This trend is consistent across small and large vehicle loadings, indicating that the magnitude of the applied load directly influences the deformation of the geogrid.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;11 reveals that the lateral displacement of the geogrid is approximately half of the lateral displacement observed at 11.8 m in the X-direction of the GRS abutment. The maximum lateral displacement of the geogrid occurs under a dynamic loading rate of 30 km/h, mainly in areas with relatively high geogrid intensities. In addition, as the height of the abutment increases, the lateral displacement of the geogrid also increases, indicating that the upper sections of the geogrid are more susceptible to deformation under dynamic loading.\u003c/p\u003e \u003cp\u003eThe analysis of Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e and 11 reveals that the vehicle speed, weight, and geogrid density influence the settlement and lateral displacement of the geogrid. Although the settlement of the geogrid increases with vehicle speed, the lateral displacement exhibits a nonmonotonic trend, with the maximum value occurring at 30 km/h and the minimum occurring at 45 km/h. This discrepancy confirms that vehicle speed primarily influences lateral displacement through its effect on settlement. The geogrid's ability to redistribute stresses plays a critical role in mitigating lateral deformation, particularly at intermediate speeds.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Stress analysis of the GRS abutment\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;12 presents the cloud map of the maximum shear stress in the GRS abutment under various dynamic vehicle loading conditions. This figure shows that the maximum shear stress under large vehicle dynamic loading is approximately twice that observed under small vehicle loading. Notably, the shear stress under a dynamic load of 60 km/h is the smallest among the loading conditions. This comparison suggests that higher speeds reduce shear stress due to shorter loading duration, which limits stress propagation and accumulation in the soil-abutment system. The stress concentration is evident on both sides of the beam seat, where the dynamic vehicle loading is applied. Additionally, the shear stress decreases with increasing vehicle speed and is more pronounced in the lower part of the abutment. This distribution pattern indicates that the lower sections of the abutment bear a considerable portion of the load, emphasizing the importance of reinforcing these areas.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;13 shows the maximum stress distribution within the geogrid under different vehicle dynamic loading scenarios. According to the theory of tensile membrane action, peak stress is influenced primarily by the overlying load. The top layer of the reinforced material helps offset some of the downwards stress, which in turn reduces settlement in the lower part. This reduction in settlement causes the lower reinforced material to experience tensile stress due to the upwards rotation of the panel foundation. However, in the current state, this tensile stress plays a relatively minor role, resulting in lower stress values in the tendon material.\u003c/p\u003e \u003cp\u003eFor small and large vehicles, the geogrid results in the lowest peak stress under a dynamic load of 45 km/h, the second-highest peak stress under a dynamic load of 60 km/h, and the highest peak stress under a dynamic load of 30 km/h. This finding indicates that the stress on the GRS abutment is minimised when the vehicle speed is approximately 45 km/h.\u003c/p\u003e \u003cp\u003eThe above analysis demonstrates that vehicle speed and weight influence the maximum shear stress and geogrid stress in reinforced soil abutments. The stress on the abutment and geogrid is minimised at a vehicle speed of approximately 45 km/h, highlighting the importance of optimal speed ranges in reducing dynamic effects. Vehicle weight considerably increases stress levels, emphasising the need to consider traffic composition in design. The geogrid's ability to redistribute stresses plays a critical role in mitigating deformation and enhancing structural stability.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eIn this study, the deformation of a GRS‒IBS under different dynamic vehicle loadings was simulated via FLAC 3D software. The results were analysed from five aspects: settlement, lateral displacement of the face wall, geogrid deformation, maximum shear stress of the GRS‒IBS, and geogrid stress. The following conclusions were drawn.\u003c/p\u003e \u003cp\u003e(1) The overall settlement of the reinforced soil abutment increases with increasing height of the abutment. For different vehicle dynamic loadings, the settlement increases with increasing dynamic load at X\u0026thinsp;=\u0026thinsp;9 m from the abutment. At X\u0026thinsp;=\u0026thinsp;11.8 m, near the loading position, the settlement is \"large on both sides, small in the middle\" under vehicle speeds ranging from 30 km/h to 60 km/h. This nonmonotonic behaviour is attributed to dynamic amplification effects caused by vehicle‒bridge coupling at intermediate speeds.\u003c/p\u003e \u003cp\u003e(2) The trend of lateral displacement at the GRS face wall is consistent with the trend of settlement, with larger values at the extremes and smaller values in the middle under vehicle dynamic loading. As the vehicle weight increases, the lateral displacement at the face wall also increases. The displacement converges at an elevation of approximately 4 m, indicating a stabilising effect in the upper sections of the abutment.\u003c/p\u003e \u003cp\u003e(3) The lateral displacement of the geogrid under dynamic vehicle loading is consistent with the overall settlement trend of the GRS‒IBS. Notably, the lateral displacement of the geogrid is half of the transverse displacement of the reinforced soil abutment panel at that location.\u003c/p\u003e \u003cp\u003e(4) As the vehicle dynamic loading increases, the maximum shear stress within the reinforced soil abutment and the maximum stress in the geogrid increase. The maximum stress value under large vehicle dynamic loading is approximately 2 to 3 times greater than that under small vehicle dynamic loading.\u003c/p\u003e \u003cp\u003e(5) Vehicle weight is identified as the primary factor affecting the deformation and stress behaviour of reinforced soil abutments. For the same vehicle weight, the vehicle speed considerably influences the abutment response. When the vehicle speed is approximately 45 km/h (within the range of 37.5 km/h to 52.5 km/h), the impact on all aspects of the reinforced soil abutment, including settlement, lateral displacement, and stress, is minimised.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eYan-li Dong provided the evolution of overarching research goals and aims and conducted a thorough review and final approval of the manuscript prior to submission. Hao-dong Zhang and Hao-ran Feng wrote the manuscript. Zhi-yi Zhao performed the data analysis. Jun Zhang performed the validation and format correction. All authors contributed to the writing and editing of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThis research is supported by the National Natural Science Foundation of China (grant 52278360), the Open Research Fund of Key Laboratory of Construction and Safety of Water Engineering of the Ministry of Water Resources, China Institute of Water Resources and Hydropower Research (Grant NO. 202202), and Fundamental Research Program of Shanxi Province (Grant NO. 202103021223211). These sponsorships are greatly appreciated.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and/or analysed during the current study are not publicly available due to the data forms part of ongoing study but are available from the corresponding author on reasonable request. Data requests can be made to corresponding author via this email: [email protected].\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAdams, M., Nicks, J., Stabile, T., Schlatter, W., \u0026amp; Hartmann, J. (2012). \u003cem\u003eGeosynthetic reinforced soil integrated bridge system interim implementation guide \u003c/em\u003e(No. FHWA-HRT-11-026). Federal Highway Administration (US).\u003c/li\u003e\n\u003cli\u003eAdams, M., Nicks, J., Stabile, T., Wu, J. T., Schlatter, W., \u0026amp; Hartmann, J. (2011). \u003cem\u003eGeosynthetic reinforced soil integrated bridge system, synthesis report\u003c/em\u003e (No. FHWA-HRT-11-027). United States. Federal Highway Administration.\u003c/li\u003e\n\u003cli\u003eTalebi, M., Meehan, C. L., Cacciola, D. V., \u0026amp; Becker, M. L. (2014). 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Numerical investigation of the geosynthetic reinforced soil\u0026ndash;integrated bridge system under static loading. \u003cem\u003eJournal of Geotechnical and Geoenvironmental Engineering\u003c/em\u003e, 143(6), 04017008.\u003c/li\u003e\n\u003cli\u003eArdah, A., Abu-Farsakh, M. Y., \u0026amp; Voyiadjis, G. Z. (2018). Numerical evaluation of the effect of differential settlement on the performance of GRS-IBS. \u003cem\u003eGeosynthetics International\u003c/em\u003e, 25(4), 427-441.\u003c/li\u003e\n\u003cli\u003eAdams, M., \u0026amp; Nicks, J. (2018). \u003cem\u003eDesign and construction guidelines for geosynthetic reinforced soil abutments and integrated bridge systems \u003c/em\u003e(No. FHWA-HRT-17-080). United States. Federal Highway Administration.\u003c/li\u003e\n\u003cli\u003eZhang, X., Xu, C., Wang, QS., \u0026amp; Wu, WC. 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(in Chinese)\u003c/li\u003e\n\u003c/ol\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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"dynamic vehicle loading, reinforced soil abutment, geosynthetic reinforced soil, deformation analysis, geogrid stress","lastPublishedDoi":"10.21203/rs.3.rs-5657639/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5657639/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Geosynthetic Reinforced Soil-Integrated Bridge System (i.e. GRS-IBS) was developed to address the bumping issue from differential settlement at bridge abutments. This study focused on a Louisiana bridge abutment, using numerical simulation with the finite difference method to assess deformation and stress under dynamic loads. Results showed that deformation of the soil abutment and geogrid increased with the vehicle weight, with a more pronounced effect on lateral displacement than settlement. Settlement values initially decreased then rose with speeds between 30\u0026ndash;60 km/h, mirroring the trend in lateral displacement and geogrid deformation. The lateral displacement of the geogrid was roughly half that of the panel. Shear stress on the abutment at 5 tons was double that at 1.75 tons, and geogrid stress was triple. Analysis indicated that a vehicle speed of around 45 km/h had the least impact on the reinforced soil abutment. The findings offer valuable insights for the use and maintenance of reinforced earth bridge abutments.\u003c/p\u003e","manuscriptTitle":"Deformation and force analysis of reinforced soil bridge abutment under dynamic vehicle loading","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-09 11:10:03","doi":"10.21203/rs.3.rs-5657639/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-04-08T13:47:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-08T02:27:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"278535809552598165533799277140826344469","date":"2025-04-07T02:54:49+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-05T08:42:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"114761661820193775644228315874390028958","date":"2025-04-05T06:33:13+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-05T02:07:52+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-01T05:39:05+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-03-31T00:59:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"64865e69-a05c-4552-9eb3-9d8fd6198a84","owner":[],"postedDate":"April 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":46856977,"name":"Physical sciences/Engineering/Civil engineering"},{"id":46856978,"name":"Physical sciences/Engineering/Energy infrastructure"}],"tags":[],"updatedAt":"2025-04-28T16:03:59+00:00","versionOfRecord":{"articleIdentity":"rs-5657639","link":"https://doi.org/10.1038/s41598-025-97989-y","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-04-25 15:58:22","publishedOnDateReadable":"April 25th, 2025"},"versionCreatedAt":"2025-04-09 11:10:03","video":"","vorDoi":"10.1038/s41598-025-97989-y","vorDoiUrl":"https://doi.org/10.1038/s41598-025-97989-y","workflowStages":[]},"version":"v1","identity":"rs-5657639","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5657639","identity":"rs-5657639","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}