Numerical analyses on shield-type inflatable dam

Numerical analyses on shield-type inflatable dam | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Numerical analyses on shield-type inflatable dam Min WANG, Qing YE, Lei DAI, Wei GUO, Guoyao GAO This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8381076/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The shield-type inflatable dam, integrating the steel shield and inflatable dams, has been developed recently to overcome the water-retaining limitations of conventional inflatable dams. In this study, a series of numerical studies are conducted using FLAC 2D software to investigate the performance of the shield-type inflatable dam. Parametric studies are carried out to examine the influence of upstream water head, air pressure, dam perimeter, and the anchor distance on the cross-sectional configuration, water-retaining capacity, and circumferential tensile force distribution of the shield-type inflatable dam. It is suggested to design the shield-type inflatable dam using the optimal normalized parameters with an air pressure p 0 = 0.6 γL , a cross-sectional perimeter L = 2 L 0 , and an anchor distance D = 0.05 L 0, where L and L 0 are the length of the inflatable dam and steel shield, γ is the unit weight of water. Designed using these parameters, the shield-type inflatable dam increases the critical water-retaining height by 34.4% and reduces the maximum tensile force by 13.9% compared to the conventional inflatable dam. These findings provide new insights into the structural behavior and contribute to the practical design of the shield-type inflatable dam. Dam rubber dam Shield-type inflatable dam numerical analyses 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 The low-height river barriers constructed using steel gate, concrete or rock, are characterized by their high resource consumption, large carbon emissions, and low cost-effectiveness. The inflatable dam is a greener alternative in low-head and large-span barrier which is constructed using inflatable dams anchored onto a concrete rigid foundation as shown in Fig. 1(a) (Plaut and Suherman, 1998 ; Guo et al., 2013 ). The inflatable dams have been widely used for irrigation, flood control and urban landscaping purposes due to its cost-effectiveness, aesthetic appeal, and ecological adaptability (Chanson, 1997 ; Tam and Zhang, 1999 ; Saleh and Mondal, 2001 ; Zhang et al., 2002 ; Kumar and Islam, 2019). However, the water-retaining capacity of the inflatable dam is often restrained by the strength of the geosynthetic materials (Tam, 1998 ; Guo et al., 2015 ). A shield-type inflatable dam was reported recently by Zhuang et al. ( 2025 ), with its sketch shown in Fig. 1(b). The shield-type inflatable dam consists of a steel shield gate, an inflatable dam, an air compression device, and an intelligent control system. The structure uses the flexible inflatable dam to support the steel shield, which significantly improves its water-retaining capacity and structural stability. The steel gate could be raised or lowered by inflating or deflating the inflatable dam, enabling precise control of the upstream water level. Two projects have been reported in literature: 1) the Villers-Devant-Mouzon dam in France, which utilizes three 5.87-m-wide inflatable dams to support a 2-m-high and 16-mm-thick and 2.5-ton-mass steel shield (Stéphanie and Moreira, 2007 ); 2) the 8-m-high and 60-m-wide shield-type inflatable dam constructed on the Nanming River dam in Guiyang City, China. For conventional inflatable dams, many analytical and numerical models have been developed to investigate their water-retaining capacities and circumferential tensile forces. The analytical solutions are usually based on the assumptions that the long inflatable dam is in a plane strain condition (Watson et al., 1999 ; Ghavanloo and Daneshmand 2010 ; Cheraghi-Shirazi et al., 2014 ; Streeter et al., 2015 ). For water-inflated inflatable dams, the theoretical solution of the cross-sectional shape of the upstream side is in a circular arc, while that of the downstream side requires elliptic integrals (Harrison, 1970 ; Binnie, 1973 ; Alhamati et al., 2005 ). For air-inflated inflatable dams, the theoretical solution of the cross-sectional shape of the upstream side requires elliptic integrals, while that of the downstream side is in a circular arc (Watson et al., 1985; Ghavanloo and Daneshmand, 2010 ; Streeter et al., 2015 ). The numerical studies using the finite element method usually simulate the inflatable dam using a shell element, which influences the accuracy of the results due to the bending stiffness of the shell elements (Mysore et al., 1998 ; Lowery and Liapis, 1999 ; Cheraghi-Shirazi et al., 2014 ; Gurt et al., 2015 ). The finite difference method has been proven effective in modeling inflatable dams, including scenarios when they rested on both rigid and deformable foundations (Huong et al., 2002 ; Kim et al., 2004 ; Kim et al., 2005a ; Kim et al., 2005b ; Guo et al., 2016 ; Gao et al., 2023 ). The discrete element method provides an alternative numerical approach to simulate inflatable dams using balls and interconnected by a contact-bond model, which effectively reduces the bending resistance between ball elements (Sun et al., 2017 , 2019 ; Gao et al., 2022b ). While these approaches provide powerful tools for analyzing the behaviors of inflexible membranes, their applications are only confined to the conventional inflatable dams. Systematic numerical investigations are required to investigate the performance of the more complex shield-type inflatable dam. In this paper, numerical studies were conducted to investigate the performance of the shield-type inflatable dam using FLAC 2D software. The accuracy of the proposed numerical model was verified by comparing its results with the large-scale model tests conducted by Zhuang et al. ( 2025 ). Parametric studies were conducted to investigate the effects of upstream water head, inflatable air pressure, cross-sectional perimeter of the inflatable dam, and the anchor distance on cross-sectional configurations, water-retaining capacity, and tensile force distributions of the shield-type inflatable dam. Comparison with a conventional inflatable dam was also conducted to highlight the advantage of the shield-type inflatable dam under optimized design conditions. 2. Numerical model The numerical analysis is conducted to simulate the cross-sectional configuration and tensile force distribution of the shield-type inflatable dam using commercial software FLAC 2D . It is assumed the shield-type inflatable dam is in a plane strain condition because the changes in cross-sectional shape are negligible compared to its length. The numerical model to analyze the shield-type inflatable dam is shown in Fig. 2. The inflatable dam with a cross-sectional perimeter of L is anchored in the rigid foundation with a distance of D from that of the steel shield with a length of L 0 . The inflatable dam, inflated by air pressure of p 0 has a height of H , a width of B , a contact width with the foundation of b , and a cross-sectional area of A . The top height of the steel shield is denoted as H b . The retained upstream water with unit weight of γ has a water head of H r , while the influence of the downstream water level is not considered in this study. When the upstream water reaches its limit and flows over the dam, the retained upstream water is in a critical state, with its height defined as the critical water-retaining height H cr . As no pressure can be applied directly onto the beam element in FLAC 2D , a converted point load method was adopted during the calculation. More details of the calculation method can be further referred to Huong et al. ( 2002 ), Kim et al. ( 2004 ), Guo et al. ( 2015 ) and Gao et al. ( 2023 ). The internal air pressure p 0 was applied to the internal side of the nodes. The hydraulic pressure was applied to the left-hand side of the shield steel, which was also modelled using beam elements. The anchoring points of the shield steel and inflatable dam are fixed to restrict their movements in all directions during the numerical analyses. The numerical analysis follows a two-step procedure: (1) an initial model state is built in a vertical standing steel shield and inflatable dam in sausage shape as shown in Fig. 2(a); (2) external hydrostatic pressures and internal air pressure are applied to the beam elements of the shield steel and inflatable dam, respectively. The “Whilestepping” command is invoked in step (2) to update the nodal positions and forces at every computational time step. The equilibrium of the system is controlled by the criterion that the height of the inflatable dam on the calculation cycle varies less than a tolerance of 10 − 6 . An example of the force-equilibrium state of the numerical model is shown in Fig. 2(b). 3. Verification of the numerical model A large-scale laboratory model tests were conducted by Zhuang et al. ( 2025 ) to investigate the performance of the shield-type inflatable dam. The large-scale model tests were conducted in a concrete tank with a height of 9.0 m, a width of 2.8 m, and a depth of 1.8 m. The steel shield, with dimensions of 8.3 m in width and 1 m in height, was fabricated by welding two 4.0 m and one 2.3 m steel plates, each with a thickness of 2 cm. The inflatable dams were made of a 0.6 mm-thick PVC membrane reinforced with bidirectional polyamide fabric. The anchorage featured a 4-cm-wide fold secured with screw nuts at 20-cm intervals, with the dam ends fixed to the side walls at a 60° angle to permit free deformation. The membrane exhibited average tensile strengths of 41.8 kN/m in longitudinal direction and 24.8 kN/m in latitudinal direction in the unfolded state, which reduced to 22 kN/m and 11.2 kN/m, respectively, in its folded state. These inflatable dams had varying cross-sectional perimeters (1.0, 1.5, 2.0, and 2.5 m) and were anchored to the concrete base at different distances (0.05, 0.1, 0.2, 0.3 m) from the hinge of the steel shield. A preinstalled port was used for air inflation. The upstream water levels were gradually raised until the system reached its equilibrium state. All the parameters used for the steel shield and the inflatable dam are listed in Table 1 . Table 1 Parameters used in FLAC 2D for model test simulation Type Parameters Value Steel shield Density ρ 1 7.9×10 3 kg/m 3 Length of element l 1 L 0 /50 Thickness of element h 1 2×10 − 3 Cross-sectional area a 1 2×10 − 3 Moment of inertia I 1 0.67×10 − 9 m 4 Elastic modulus E 1 2.06×10 8 kN/m 2 Contact normal stiffness K n1 2.5×10 5 kN/m 2 Contact shear stiffness K s1 0.89×10 5 kN/m 2 Friction coefficient between inflatable dam / shield steel f 1 0.3 Inflatable dam Density ρ 2 1.1×10 3 kg/m 3 Length of element l 2 L /100 Thickness of element h 2 6×10 − 4 m Cross-sectional area a 2 6×10 − 4 m 2 Moment of inertia I 2 1.8×10 − 11 m 4 Elastic modulus E 2 2.5×10 5 kN/m 2 Contact normal stiffness K n1 2.5×10 5 kN/m 2 Contact shear stiffness K s1 0.89×10 5 kN/m 2 Friction coefficient between inflatable dam / rigid base f 2 0.3 To compare the cross-sectional profiles obtained from model tests and numerical simulations, parameters are normalized by the unit weight of water and the steel shield width, which are similar to those used in literature (Freeman, 2002 ; Kim et al., 2004 ; Plaut and Stephens, 2012). The normalized upstream water level H r , the circumference of the inflatable dam L , the anchor distance D , the height of the steel shield H b , and the critical water-retaining height H cr are normalized by the width of the steel shield as H r / L 0 , L / L 0 , D / L 0 , H b / L 0 , and H cr / L 0 , respectively. The internal air pressure p 0 and tensile force T are normalized by the circumference of the inflatable dam L and unit weight of water γ as p 0 / γL , and T / γL 2 , respectively. Taking the model test of the circumference of the inflatable dam with L = 2.0 m, inflated by the air pressure p 0 = 8 kPa, anchored with the anchor distance D = 0.1 m, and acted by upstream water levels of H r = 0.6 m for example, the numerical analysis was conducted using p 0 = 8, L = 2.0, D = 0.1, H r =0.6, as the height of the steel shield L 0 = 1.0 m and unit weight of the water γ = 10 kN/m 3 . The cross-sectional profiles obtained from model tests and numerical simulations are shown in Fig. 3. The effects of upstream water levels, internal air pressure, the anchor distance, and the cross-section perimeter of the inflatable dam on the cross-sectional profiles of the shield-type inflatable dam were investigated and compared. Generally, the heights of the steel shields obtained from two sets of results agree well with each other, with the maximum difference of less than 1.2%. The circumferential tensile forces along the inflatable dam were measured using strain gauges, which were attached to the middle of the longitudinal direction of the inflatable dam. More details of the measuring method were described by Zhuang et al. ( 2025 ). The cross-sectional tensile forces of the inflatable dam with the anchor distance of D/L 0 = 0.1, dam perimeter of L / L 0 = 2.0 inflated by air pressure p 0 / γL ranging from 0.3 to 0.6 and obtained from the numerical modeling and the experimental studies are shown in Fig. 4. It can be observed that the measured tensile forces on the contact edge with the rigid foundation are smaller than those on other areas which are due to the contact friction between them. Generally, the circumferential tensile forces obtained from numerical studies fairly agree with those from laboratory model tests, except those on the contact edge, which are larger than those from laboratory model tests. One possible reason for this mismatch may because the frictions between the inflatable dam and rigid base were linearly distributed in the numerical model. 4. Parametric studies To investigate the effect of air pressure on the deformation characteristics and water-retaining performance of the shield-type inflatable dam, parametric studies were conducted using a steel shield with a width of L 0 = 1.0 m supported by an inflatable dam with perimetric length L / L 0 = 2.0, inflated by air pressure p 0 / γL ranging from 0.4 to 1.0, and anchored with the anchor distance D/L 0 ranging from 0.05 to 0.3. The calculated cross-sectional profiles of the shield-type inflatable dam under critical water-retaining head are presented in Fig. 5. It can be found that increasing the air pressure progressively raises the inflatable dam which causes the steel shield to rotate toward the upstream side. The normalized contact width between the inflatable dam and rigid base b / L and the width of the inflatable dam B / L slightly decrease, while the normalized height of the inflatable dam H / L increases with the increase of inflated air pressures. It can also be found that increasing the anchor distances lowers the critical water-retaining heights of the steel shield inflatable dam. The magnitudes of the critical water-retaining height H cr / L 0 of the inflatable dam in Fig. 5 were taken and replotted in Fig. 6. It can be observed that the critical water-retaining height H cr / L 0 nonlinearly increases with the increase of the inflated air pressure. For p 0 / γL ranging from 0.3 to 0.6, the rate of increase was relatively slow, but was more pronounced for p 0 / γL ranging from 0.6 to 1.0. Parametric studies were conducted to investigate the effect of cross-sectional perimeters of the inflatable dam on the critical water-retaining capacity of the shield-type inflatable dam using an inflatable dam with a cross-sectional perimeter of L / L 0 ranging from 1.5 to 2.5, inflated by air pressure p 0 / γL = 0.6, and anchored with the anchor distance D/L 0 ranging from 0.05 to 0.3. The calculated geometry profiles of the shield-type inflatable dams under the critical water-retaining heights are shown in Fig. 7. It can be found that the supports of the inflatable dam to the steel shield dam increase with the increase of the perimeters of the inflatable dams. Under the air pressure p 0 / γL = 0.6, the larger the perimeters of the inflatable dam, the larger the critical water-retaining heights of the shield-type inflatable dam. The critical water-retaining heights in Fig. 8 are taken out and replotted with respect to the perimeter of the inflatable dam L / L 0 for further analyses. It can be observed that the critical water-retaining height H cr / L 0 nonlinearly increases with the increase of the cross-sectional perimeters of the inflatable dams. For L / L 0 ranging from 1.5 to 2.0, the rate of increase was relatively slow, but was more pronounced for L / L 0 larger than 2.0. The effects of the anchor distance of the inflatable dam on the profiles and water-retaining capacity of the shield-type inflatable dam are investigated. The cross-sectional profiles of the shield-type inflatable dam under the critical water-retaining height using an inflatable dam with a cross-sectional perimeter of L / L 0 = 2.0, inflated by air pressure p 0 / γL = 0.6, and anchored with the anchor distance D/L 0 ranging from 0.05 to 0.3 are shown in Fig. 9. It is observed that the larger the anchor distance, the lower the critical water-retaining height of the shield-type inflatable dams. The normalized critical water-retaining height H cr /L 0 versus the normalized anchor distance D/L 0 curves of the shield-type inflatable dams are replotted in Fig. 10. It can be found that H cr / L 0 decreases approximately linearly with respect to D / L 0 . The tensile forces along the cross-section of the inflatable dam with cross-sectional perimeter of L / L 0 = 2.0, inflated by air pressure p 0 / γL ranging from 0.4 to 1.0, and anchored with the anchor distance D/L 0 = 0.05 are shown in Fig. 11. It can be found that the max normalized tensile forces T max /γL ² increase with the increase of the normalized air pressure p 0 / γL. It can be observed that the tensile forces on the contact areas with the rigid foundation and steel shield are smaller than those on other areas, which are due to the contact friction between them. The tensile forces are smallest on the left corner of the shield-type inflatable dam, while they are largest on its right corners. The maximum normalized tensile force T max /γL 2 ·( L / L 0 ) along the inflatable dams is taken and replotted versus the inflated air pressure p 0 / γL ·( L / L 0 ) in Fig. 12. Generally, they are in a linear relationship with the curve fitting equations and R 2 = 0.9749, and shown as follows, $$\frac{{{T_{\hbox{max} }}}}{{\gamma {L^2}}}=0.1489\frac{{{p_0}}}{{\gamma L}} - 0.0272\frac{{{L_0}}}{L}$$ 1 5. Discussion It is found from the numerical studies that the shield-type inflatable dam can be designed using the optimal cross-sectional perimeter of L = 2 L 0 , inflated by air pressures p 0 = 0.6 γL and anchored with distance D = 0.05 L 0 , where L 0 is the height of the shield steel. The corresponding shield-type inflatable dam has a critical water-retaining height of H cr = 0.814 L 0 , and maximum tensile forces of T max = 0.767 γL 2 , and inclined with an angle between the steel shield and rigid base of 60°. It has to be pointed out that a safety restraint belt is often installed in practice, as shown in Fig. 1(b), to prevent the risk of anticlockwise overturning of the steel shields. The cross-sectional profile and tensile force of the shield-type inflatable dam designed using the optimal design parameters are compared with those of a conventional inflatable dam. To compare their performances, a same cross-sectional perimeter of L = 1.0 m is used for the two inflatable dams, which are inflated by normalized air pressures of p 0 / γL = 0.6, or p 0 = 6 kPa because γ = 10 kN/m 3 . The height of the steel shield is derived using their optimal ratio L / L 0 = 2.0 which gives its magnitude L 0 = 0.5 m. The anchor distance used in the shield-type inflatable dam is then calculated as D = 0.05 L 0 = 0.025 m. The cross-sectional profiles of the two types of inflatable dams under critical water-retaining height are shown in Fig. 13. It can be found that the critical water-retaining height H cr of the shield-type inflatable dam is 0.407 m which is 34.4% higher than the conventional inflatable dam with its critical water-retaining height of 0.3028 m. The corresponding maximum cross-sectional tensile force T max along the shield-type inflatable dam 0.767 kN/m or 13.9% lower than that of the conventional inflatable dam with its magnitude of 0.891 kN/m. Generally, the shield-type inflatable dam can not only effectively increase the critical water-retaining height but also reduce the tension forces along the inflatable dam. However, it has to be pointed out that the material cost of the shield steel is another consumption of the shield-type inflatable dam. 6. Conclusions Numerical analyses are conducted in this paper to investigate the performance of the shield-type inflatable dam. The accuracy of the numerical model was validated by comparing its results with those from laboratory model tests. Parametric studies were carried out to identify the influence of some key factors on the cross-sectional profile and tensile force of the structure to provide references for practical engineering design. The following conclusions can be drawn through this study: 1) The shield-type inflatable dam can be designed using the optimal cross-sectional perimeter of L = 2 L 0 , inflated by air pressures p 0 = 0.6 γL , anchored with anchor distance D = 0.05 L 0 , where L 0 is the height of the shield steel. The corresponding shield-type inflatable dam has a critical water-retaining height of H cr = 0.814 L 0 , maximum tensile forces of T max = 0.0767 γL 2 , with its inclined angle between the steel shield and rigid base of 60°. 2) The designed shield-type inflatable dam using optimal parameters could increase the critical water-retaining height by 34.4% and reduce the maximum tensile force by 13.9% compared to the conventional inflatable dam under the same conditions. However, the material cost of the shield steel increases the total cost of the shield-type inflatable dam. Declarations Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Contribution **Min WANG** : Software, Validation, Writing – original draft. **Qing YE** : Software, Writing – original draft. **Lei DAI** : Formal analysis, Writing – original draft. **Wei GUO** : Methodology, Supervision, Writing – review & editing. **Guoyao GAO** : Writing – review & editing. Acknowledgments The financial support from the National Natural Science Foundation of China (Grant No. 52171273, 52578422) are gratefully acknowledged. Data Availability Statement All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. References Alhamati, A. A. N., Mohammed, T. A. & Norzaie, J., Ghazali, A.H., Al-Jumaily, K. K. (2005). Behavior of inflatable dams under hydrostatic conditions. Suranaree Journal of Science and Technology , 12 , No. 1, 1–18. Binnie, A. M. (1973). The theory of flexible dams inflated by water pressure. Journal of Hydraulic Research , 11 , No 1, 61–68. Chanson, H. (1997). Use of Rubber Dams for Flood Mitigation in Hong Kong. Journal of Irrigation and Drainage Engineering , 124 , No. 3, 73–78. Cheraghi-Shirazi, N., Kabiri-Samani, A. R. & Boroomand, B. (2014). Numerical analysis of rubber dams using fluid-structure interactions. Flow Measurement and Instrumentation , 40 , 91–98. Freeman, M. (2002). Experiments and analysis of water-filled tubes used as temporary flood barriers. Master Thesis . Virginia Polytechnical Institute and State University, Blacksburg. Gao X., Guo W., Dai L., Guo W. & Ren Y. (2022a), Experimental study on air- and water-inflated double-rubber dam, Journal of Irrigation and Drainage Engineering , 149 , No. 9, 04023021. Gao, X., Guo W., Ren Y., & Zeng W. (2022b). Numerical analysis of a double layer rubber dam. Geotextile and Geomembrane . 50 , No. 2, 249–261. Gao, X., Guo, W., Guo, W. F., Ren, Y. & Dai, L. (2023). Large-scale model test studies on a double-layer rubber dam. Geosynthetics International , 30 , No. 5, 545–560. Ghavanloo, E. & Daneshmand, F. (2010). Analytical analysis of the static interaction of fluid and cylindrical membrane structures. European Journal of Mechanics - A/Solids . 29 , No. 4, 600–610. Guo, W., Chu, J., Yan, S. (2015). Simplified analytical solution for geosynthetic tube resting on deformable foundation soil. Geotextiles and Geomembranes , 43 , No. 5, 432–439. Guo, W., Chu, J. & Yan, S. (2013). Recent studies of geosynthetic tubes and geosynthetic mats: an overview. Geotechnical and Geological Engineering, An International Journal , 44 , No. 4, 115–124. Guo, W., Kou, H., Zhou, B., Nie, W. & Chu, J. (2016). Simplified methods to analyze geosynthetic mattress resting on deformable foundation soil. Marine Georesources & Geotechnology. 35 , No. 3, 339–345. Gurt, R., Deutscher, M. & Gebhardt, M. (2015). Design and analysis of reinforced rubber membranes for inflatable dams. Proceedings of the 7th International Conference on Textile Composites and Inflatable Structures, Structural Membranes , Oñate, E., Bletzinger, K.-U. and Kröplin, B., Editors, International Center for Numerical Methods in Engineering Publishing, Barcelona, Spain, pp. 306–317. Harrison, H. B. (1970). The analysis and behavior of the inflatable membrane dams under static loading. Proceedings of the Institution of Civil Engineers , 45 , No. 4, 661–676. Huong, T. C., Plaut, R. H. & Filz, G. M. (2002). Wedged geomembrane tubes as temporary flood-fighting devices. Thin-Walled Structures , 40 , No. 11, 913–923. Kim, M., Filz, G. M. & Plaut, R. H. (2005a). Two-chambered waterfilled geomembrane tubes used as water barriers: experiments and analysis. Geosynthetics International, 12 , No. 3, 127–133. Kim, M., Freeman, M., FitzPatrick, B. T., Nevius, D. B., Plaut, R. H. & Filz, G. M. (2004). Use of an apron to stabilize geomembrane tubes for fighting floods. Geotextiles and Geomembranes , 22 , No. 4, 239–254. Kim, M., Moler, M., Freeman, M., Filz, G. M. & Plaut, R. H. (2005b). Stacked geomembrane tubes for flood control: experiments and analysis. Geosynthetics International , 12 , No. 5, 253–259. Kumar, A. &Islam, S. U. (2019). Ch 6: Inflation and deflation of rubber dam. In Hydraulic Rubber Dam , Thomas, S., Rane, A. V., Abitha, V. K., Kanny, K. and Dutta, A., Editors, William Andrew Publishing, Norwich, NY, USA, pp. 67–98. Lowery, K. & Liapis, S. (1999). Dynamic analysis of an inflatable dam subjected to a flood. Computational Mechanics , 24 , No. 1, 52–64. Mysore, G. V., Liapis, S. I. & Plaut, R. H. (1998). Dynamic analysis of single-anchor inflatable dams. Journal of Sound and Vibration , 215 , No. 2, 251–272. Plaut, R. H. & Suherman, S. (1998). Two-dimensional analysis of geosynthetic tubes. Acta Mechanica , 129 , No. 3, 207–218. Saleh, A. F. M. & Mondal, M. S. (2001). Performance evaluation of rubber dam projects of Bangladesh in irrigation development. Irrigation and Drainage , 50 , No. 3, 237–248. Stéphanie, P. & Moreira, S. (2007). The French experiment of an inflatable weir with steel gates. In: Mitteilungsblatt der Bundesanstalt für Wasserbau . Karlsruhe:Bundesanstalt für Wasserbau. 91 , S.93-98 Streeter, M., Rhode-Barbarigos, L. & Adriaenssens, S. (2015). Form finding and analysis of inflatable dams using dynamic relaxation. Applied Mathematics and Computation , 267 , 742–749. Sun, L., Qi, Y.., Gao, X., Guo, W. & Zhang, N. (2019). Stability of supported geomembrane tube flood barriers of novel design. Journal of Flood Risk Management , 13 , No. 1, 1–10. Sun, L., Yue, C., Guo, W. & Ren, Y. X. (2017). Lateral stability analysis of wedged geomembrane tubes using PFC2D. Marine Georesources and Geotechnology , 35 , No. 5, 730–737. Tam, P. W. M. (1998). Application of inflatable dam technology problems and countermeasures. Canadian Journal of Civil Engineering , 25 , No. 2, 383–388. Tam, P. W. M. & Zhang, X. Q. (1999). Management of rubber dams in Hong Kong. Canadian Journal of Civil Engineering , 26 , No. 2, 123–134. Watson, R. (1985). A note on the shapes of flexible dams. Journal of Hydraulic Research , 23(2), 179–194. https://doi.org/10.1080/00221688509499364 Watson, L. T., Suherman, S. & Plaut, R. H. (1999). Two-dimensional elastic analysis of equilibrium shapes of single-anchor inflatable dams. International Journal of Solids and Structures , 36 , No. 9, 1383–1398. Zhang, X., Tam, P. W. M. & Zheng, W. (2002). Construction, operation, and maintenance of rubber dams. Canadian Journal of Civil Engineering , 29 , No. 3, 409–420. Zhuang, D., Ye, Q., Dai, L., Wang, M., Guo, W. & Gao, G. (2025). Large-scale model test on shield-type rubber dam. International Journal of Geosynthetics and Ground Engineering , 11 , 63. 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12","display":"","copyAsset":false,"role":"figure","size":236217,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8381076/v1/70a9f483c385fe2bf3c64db5.png"},{"id":99313399,"identity":"ca141b5d-1d82-41d0-961b-7480aec6611f","added_by":"auto","created_at":"2025-12-31 16:20:07","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":295819,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8381076/v1/9824cf1c8ff005a70e2aaaaf.png"},{"id":99787928,"identity":"45bf8bda-e7e2-4b4b-ac5e-a2e1f2c99b93","added_by":"auto","created_at":"2026-01-08 12:41:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7237565,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8381076/v1/6863ac1e-d273-499d-a6da-2c79a5948c9c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical analyses on shield-type inflatable dam","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe low-height river barriers constructed using steel gate, concrete or rock, are characterized by their high resource consumption, large carbon emissions, and low cost-effectiveness. The inflatable dam is a greener alternative in low-head and large-span barrier which is constructed using inflatable dams anchored onto a concrete rigid foundation as shown in Fig.\u0026nbsp;1(a) (Plaut and Suherman, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Guo et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The inflatable dams have been widely used for irrigation, flood control and urban landscaping purposes due to its cost-effectiveness, aesthetic appeal, and ecological adaptability (Chanson, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Tam and Zhang, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Saleh and Mondal, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Kumar and Islam, 2019). However, the water-retaining capacity of the inflatable dam is often restrained by the strength of the geosynthetic materials (Tam, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Guo et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eA shield-type inflatable dam was reported recently by Zhuang et al. (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), with its sketch shown in Fig.\u0026nbsp;1(b). The shield-type inflatable dam consists of a steel shield gate, an inflatable dam, an air compression device, and an intelligent control system. The structure uses the flexible inflatable dam to support the steel shield, which significantly improves its water-retaining capacity and structural stability. The steel gate could be raised or lowered by inflating or deflating the inflatable dam, enabling precise control of the upstream water level. Two projects have been reported in literature: 1) the Villers-Devant-Mouzon dam in France, which utilizes three 5.87-m-wide inflatable dams to support a 2-m-high and 16-mm-thick and 2.5-ton-mass steel shield (St\u0026eacute;phanie and Moreira, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2007\u003c/span\u003e); 2) the 8-m-high and 60-m-wide shield-type inflatable dam constructed on the Nanming River dam in Guiyang City, China.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor conventional inflatable dams, many analytical and numerical models have been developed to investigate their water-retaining capacities and circumferential tensile forces. The analytical solutions are usually based on the assumptions that the long inflatable dam is in a plane strain condition (Watson et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Ghavanloo and Daneshmand \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Cheraghi-Shirazi et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Streeter et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). For water-inflated inflatable dams, the theoretical solution of the cross-sectional shape of the upstream side is in a circular arc, while that of the downstream side requires elliptic integrals (Harrison, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1970\u003c/span\u003e; Binnie, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1973\u003c/span\u003e; Alhamati et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). For air-inflated inflatable dams, the theoretical solution of the cross-sectional shape of the upstream side requires elliptic integrals, while that of the downstream side is in a circular arc (Watson et al., 1985; Ghavanloo and Daneshmand, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Streeter et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe numerical studies using the finite element method usually simulate the inflatable dam using a shell element, which influences the accuracy of the results due to the bending stiffness of the shell elements (Mysore et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Lowery and Liapis, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Cheraghi-Shirazi et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Gurt et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The finite difference method has been proven effective in modeling inflatable dams, including scenarios when they rested on both rigid and deformable foundations (Huong et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Kim et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Kim et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2005a\u003c/span\u003e; Kim et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2005b\u003c/span\u003e; Guo et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Gao et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The discrete element method provides an alternative numerical approach to simulate inflatable dams using balls and interconnected by a contact-bond model, which effectively reduces the bending resistance between ball elements (Sun et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Gao et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022b\u003c/span\u003e). While these approaches provide powerful tools for analyzing the behaviors of inflexible membranes, their applications are only confined to the conventional inflatable dams. Systematic numerical investigations are required to investigate the performance of the more complex shield-type inflatable dam.\u003c/p\u003e \u003cp\u003eIn this paper, numerical studies were conducted to investigate the performance of the shield-type inflatable dam using FLAC\u003csup\u003e2D\u003c/sup\u003e software. The accuracy of the proposed numerical model was verified by comparing its results with the large-scale model tests conducted by Zhuang et al. (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Parametric studies were conducted to investigate the effects of upstream water head, inflatable air pressure, cross-sectional perimeter of the inflatable dam, and the anchor distance on cross-sectional configurations, water-retaining capacity, and tensile force distributions of the shield-type inflatable dam. Comparison with a conventional inflatable dam was also conducted to highlight the advantage of the shield-type inflatable dam under optimized design conditions.\u003c/p\u003e"},{"header":"2. Numerical model","content":"\u003cp\u003eThe numerical analysis is conducted to simulate the cross-sectional configuration and tensile force distribution of the shield-type inflatable dam using commercial software FLAC\u003csup\u003e2D\u003c/sup\u003e. It is assumed the shield-type inflatable dam is in a plane strain condition because the changes in cross-sectional shape are negligible compared to its length. The numerical model to analyze the shield-type inflatable dam is shown in Fig.\u0026nbsp;2. The inflatable dam with a cross-sectional perimeter of \u003cem\u003eL\u003c/em\u003e is anchored in the rigid foundation with a distance of \u003cem\u003eD\u003c/em\u003e from that of the steel shield with a length of \u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e. The inflatable dam, inflated by air pressure of \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e has a height of \u003cem\u003eH\u003c/em\u003e, a width of \u003cem\u003eB\u003c/em\u003e, a contact width with the foundation of \u003cem\u003eb\u003c/em\u003e, and a cross-sectional area of \u003cem\u003eA\u003c/em\u003e. The top height of the steel shield is denoted as \u003cem\u003eH\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e. The retained upstream water with unit weight of \u003cem\u003eγ\u003c/em\u003e has a water head of \u003cem\u003eH\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e, while the influence of the downstream water level is not considered in this study. When the upstream water reaches its limit and flows over the dam, the retained upstream water is in a critical state, with its height defined as the critical water-retaining height \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs no pressure can be applied directly onto the beam element in FLAC\u003csup\u003e2D\u003c/sup\u003e, a converted point load method was adopted during the calculation. More details of the calculation method can be further referred to Huong et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), Kim et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), Guo et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and Gao et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The internal air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e was applied to the internal side of the nodes. The hydraulic pressure was applied to the left-hand side of the shield steel, which was also modelled using beam elements. The anchoring points of the shield steel and inflatable dam are fixed to restrict their movements in all directions during the numerical analyses.\u003c/p\u003e \u003cp\u003eThe numerical analysis follows a two-step procedure: (1) an initial model state is built in a vertical standing steel shield and inflatable dam in sausage shape as shown in Fig.\u0026nbsp;2(a); (2) external hydrostatic pressures and internal air pressure are applied to the beam elements of the shield steel and inflatable dam, respectively. The \u0026ldquo;Whilestepping\u0026rdquo; command is invoked in step (2) to update the nodal positions and forces at every computational time step. The equilibrium of the system is controlled by the criterion that the height of the inflatable dam on the calculation cycle varies less than a tolerance of 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e. An example of the force-equilibrium state of the numerical model is shown in Fig.\u0026nbsp;2(b).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Verification of the numerical model","content":"\u003cp\u003eA large-scale laboratory model tests were conducted by Zhuang et al. (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) to investigate the performance of the shield-type inflatable dam. The large-scale model tests were conducted in a concrete tank with a height of 9.0 m, a width of 2.8 m, and a depth of 1.8 m. The steel shield, with dimensions of 8.3 m in width and 1 m in height, was fabricated by welding two 4.0 m and one 2.3 m steel plates, each with a thickness of 2 cm. The inflatable dams were made of a 0.6 mm-thick PVC membrane reinforced with bidirectional polyamide fabric. The anchorage featured a 4-cm-wide fold secured with screw nuts at 20-cm intervals, with the dam ends fixed to the side walls at a 60\u0026deg; angle to permit free deformation. The membrane exhibited average tensile strengths of 41.8 kN/m in longitudinal direction and 24.8 kN/m in latitudinal direction in the unfolded state, which reduced to 22 kN/m and 11.2 kN/m, respectively, in its folded state. These inflatable dams had varying cross-sectional perimeters (1.0, 1.5, 2.0, and 2.5 m) and were anchored to the concrete base at different distances (0.05, 0.1, 0.2, 0.3 m) from the hinge of the steel shield. A preinstalled port was used for air inflation. The upstream water levels were gradually raised until the system reached its equilibrium state. All the parameters used for the steel shield and the inflatable dam are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters used in FLAC\u003csup\u003e2D\u003c/sup\u003e for model test simulation\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eType\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"8\" rowspan=\"9\"\u003e \u003cp\u003eSteel shield\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.9\u0026times;10\u003csup\u003e3\u003c/sup\u003e kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLength of element \u003cem\u003el\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThickness of element \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCross-sectional area \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMoment of inertia \u003cem\u003eI\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.67\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eElastic modulus \u003cem\u003eE\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.06\u0026times;10\u003csup\u003e8\u003c/sup\u003e kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eContact normal stiffness \u003cem\u003eK\u003c/em\u003e\u003csub\u003en1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.5\u0026times;10\u003csup\u003e5\u003c/sup\u003e kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eContact shear stiffness \u003cem\u003eK\u003c/em\u003e\u003csub\u003es1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.89\u0026times;10\u003csup\u003e5\u003c/sup\u003e kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFriction coefficient between inflatable dam / shield steel \u003cem\u003ef\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"8\" rowspan=\"9\"\u003e \u003cp\u003eInflatable dam\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.1\u0026times;10\u003csup\u003e3\u003c/sup\u003e kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLength of element \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e/100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThickness of element \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e \u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCross-sectional area \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e \u003cem\u003em\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMoment of inertia \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.8\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003e \u003cem\u003em\u003c/em\u003e\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eElastic modulus \u003cem\u003eE\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.5\u0026times;10\u003csup\u003e5\u003c/sup\u003e kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eContact normal stiffness \u003cem\u003eK\u003c/em\u003e\u003csub\u003en1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.5\u0026times;10\u003csup\u003e5\u003c/sup\u003e kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eContact shear stiffness \u003cem\u003eK\u003c/em\u003e\u003csub\u003es1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.89\u0026times;10\u003csup\u003e5\u003c/sup\u003e kN/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFriction coefficient between inflatable dam / rigid base \u003cem\u003ef\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo compare the cross-sectional profiles obtained from model tests and numerical simulations, parameters are normalized by the unit weight of water and the steel shield width, which are similar to those used in literature (Freeman, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Kim et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Plaut and Stephens, 2012). The normalized upstream water level \u003cem\u003eH\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e, the circumference of the inflatable dam \u003cem\u003eL\u003c/em\u003e, the anchor distance \u003cem\u003eD\u003c/em\u003e, the height of the steel shield \u003cem\u003eH\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, and the critical water-retaining height \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e are normalized by the width of the steel shield as \u003cem\u003eH\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003eD\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003eH\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, and \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, respectively. The internal air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e and tensile force \u003cem\u003eT\u003c/em\u003e are normalized by the circumference of the inflatable dam \u003cem\u003eL\u003c/em\u003e and unit weight of water \u003cem\u003eγ\u003c/em\u003e as \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e, and \u003cem\u003eT\u003c/em\u003e/\u003cem\u003eγL\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e, respectively. Taking the model test of the circumference of the inflatable dam with \u003cem\u003eL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.0 m, inflated by the air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8 kPa, anchored with the anchor distance \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.1 m, and acted by upstream water levels of \u003cem\u003eH\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e = 0.6 m for example, the numerical analysis was conducted using \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8, \u003cem\u003eL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.0, \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.1, \u003cem\u003eH\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e=0.6, as the height of the steel shield \u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0 m and unit weight of the water \u003cem\u003eγ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10 kN/m\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe cross-sectional profiles obtained from model tests and numerical simulations are shown in Fig.\u0026nbsp;3. The effects of upstream water levels, internal air pressure, the anchor distance, and the cross-section perimeter of the inflatable dam on the cross-sectional profiles of the shield-type inflatable dam were investigated and compared. Generally, the heights of the steel shields obtained from two sets of results agree well with each other, with the maximum difference of less than 1.2%.\u003c/p\u003e \u003cp\u003eThe circumferential tensile forces along the inflatable dam were measured using strain gauges, which were attached to the middle of the longitudinal direction of the inflatable dam. More details of the measuring method were described by Zhuang et al. (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The cross-sectional tensile forces of the inflatable dam with the anchor distance of \u003cem\u003eD/L\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1, dam perimeter of \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.0 inflated by air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e ranging from 0.3 to 0.6 and obtained from the numerical modeling and the experimental studies are shown in Fig.\u0026nbsp;4. It can be observed that the measured tensile forces on the contact edge with the rigid foundation are smaller than those on other areas which are due to the contact friction between them. Generally, the circumferential tensile forces obtained from numerical studies fairly agree with those from laboratory model tests, except those on the contact edge, which are larger than those from laboratory model tests. One possible reason for this mismatch may because the frictions between the inflatable dam and rigid base were linearly distributed in the numerical model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Parametric studies","content":"\u003cp\u003eTo investigate the effect of air pressure on the deformation characteristics and water-retaining performance of the shield-type inflatable dam, parametric studies were conducted using a steel shield with a width of \u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0 m supported by an inflatable dam with perimetric length \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.0, inflated by air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e ranging from 0.4 to 1.0, and anchored with the anchor distance \u003cem\u003eD/L\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e ranging from 0.05 to 0.3. The calculated cross-sectional profiles of the shield-type inflatable dam under critical water-retaining head are presented in Fig.\u0026nbsp;5. It can be found that increasing the air pressure progressively raises the inflatable dam which causes the steel shield to rotate toward the upstream side. The normalized contact width between the inflatable dam and rigid base \u003cem\u003eb\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e and the width of the inflatable dam \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e slightly decrease, while the normalized height of the inflatable dam \u003cem\u003eH\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e increases with the increase of inflated air pressures. It can also be found that increasing the anchor distances lowers the critical water-retaining heights of the steel shield inflatable dam. The magnitudes of the critical water-retaining height \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e of the inflatable dam in Fig.\u0026nbsp;5 were taken and replotted in Fig.\u0026nbsp;6. It can be observed that the critical water-retaining height \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e nonlinearly increases with the increase of the inflated air pressure. For \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e ranging from 0.3 to 0.6, the rate of increase was relatively slow, but was more pronounced for \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e ranging from 0.6 to 1.0.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eParametric studies were conducted to investigate the effect of cross-sectional perimeters of the inflatable dam on the critical water-retaining capacity of the shield-type inflatable dam using an inflatable dam with a cross-sectional perimeter of \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e ranging from 1.5 to 2.5, inflated by air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.6, and anchored with the anchor distance \u003cem\u003eD/L\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e ranging from 0.05 to 0.3. The calculated geometry profiles of the shield-type inflatable dams under the critical water-retaining heights are shown in Fig.\u0026nbsp;7. It can be found that the supports of the inflatable dam to the steel shield dam increase with the increase of the perimeters of the inflatable dams. Under the air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.6, the larger the perimeters of the inflatable dam, the larger the critical water-retaining heights of the shield-type inflatable dam. The critical water-retaining heights in Fig.\u0026nbsp;8 are taken out and replotted with respect to the perimeter of the inflatable dam \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e for further analyses. It can be observed that the critical water-retaining height \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e nonlinearly increases with the increase of the cross-sectional perimeters of the inflatable dams. For \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e ranging from 1.5 to 2.0, the rate of increase was relatively slow, but was more pronounced for \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e larger than 2.0.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe effects of the anchor distance of the inflatable dam on the profiles and water-retaining capacity of the shield-type inflatable dam are investigated. The cross-sectional profiles of the shield-type inflatable dam under the critical water-retaining height using an inflatable dam with a cross-sectional perimeter of \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.0, inflated by air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.6, and anchored with the anchor distance \u003cem\u003eD/L\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e ranging from 0.05 to 0.3 are shown in Fig.\u0026nbsp;9. It is observed that the larger the anchor distance, the lower the critical water-retaining height of the shield-type inflatable dams. The normalized critical water-retaining height \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e\u003cem\u003e/L\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e versus the normalized anchor distance \u003cem\u003eD/L\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e curves of the shield-type inflatable dams are replotted in Fig.\u0026nbsp;10. It can be found that \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e decreases approximately linearly with respect to \u003cem\u003eD\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe tensile forces along the cross-section of the inflatable dam with cross-sectional perimeter of \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.0, inflated by air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e ranging from 0.4 to 1.0, and anchored with the anchor distance \u003cem\u003eD/L\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;0.05 are shown in Fig.\u0026nbsp;11. It can be found that the max normalized tensile forces \u003cem\u003eT\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e\u003cem\u003e/γL\u003c/em\u003e\u0026sup2; increase with the increase of the normalized air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL.\u003c/em\u003e It can be observed that the tensile forces on the contact areas with the rigid foundation and steel shield are smaller than those on other areas, which are due to the contact friction between them. The tensile forces are smallest on the left corner of the shield-type inflatable dam, while they are largest on its right corners. The maximum normalized tensile force \u003cem\u003eT\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e\u003cem\u003e/γL\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026middot;(\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e) along the inflatable dams is taken and replotted versus the inflated air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e\u0026middot;(\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e) in Fig.\u0026nbsp;12. Generally, they are in a linear relationship with the curve fitting equations and R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.9749, and shown as follows,\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\frac{{{T_{\\hbox{max} }}}}{{\\gamma {L^2}}}=0.1489\\frac{{{p_0}}}{{\\gamma L}} - 0.0272\\frac{{{L_0}}}{L}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Discussion","content":"\u003cp\u003eIt is found from the numerical studies that the shield-type inflatable dam can be designed using the optimal cross-sectional perimeter of \u003cem\u003eL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, inflated by air pressures \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003cem\u003eγL\u003c/em\u003e and anchored with distance \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.05\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, where \u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the height of the shield steel. The corresponding shield-type inflatable dam has a critical water-retaining height of \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e = 0.814\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, and maximum tensile forces of \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e = 0.767\u003cem\u003eγL\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e, and inclined with an angle between the steel shield and rigid base of 60\u0026deg;. It has to be pointed out that a safety restraint belt is often installed in practice, as shown in Fig.\u0026nbsp;1(b), to prevent the risk of anticlockwise overturning of the steel shields.\u003c/p\u003e \u003cp\u003eThe cross-sectional profile and tensile force of the shield-type inflatable dam designed using the optimal design parameters are compared with those of a conventional inflatable dam. To compare their performances, a same cross-sectional perimeter of \u003cem\u003eL\u0026thinsp;=\u003c/em\u003e\u0026thinsp;1.0 m is used for the two inflatable dams, which are inflated by normalized air pressures of \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eγL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.6, or \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;6 kPa because \u003cem\u003eγ\u0026thinsp;=\u003c/em\u003e\u0026thinsp;10 kN/m\u003csup\u003e3\u003c/sup\u003e. The height of the steel shield is derived using their optimal ratio \u003cem\u003eL\u003c/em\u003e/\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.0 which gives its magnitude \u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.5 m. The anchor distance used in the shield-type inflatable dam is then calculated as \u003cem\u003eD\u0026thinsp;=\u003c/em\u003e\u0026thinsp;0.05\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.025 m. The cross-sectional profiles of the two types of inflatable dams under critical water-retaining height are shown in Fig.\u0026nbsp;13. It can be found that the critical water-retaining height \u003cem\u003eH\u003c/em\u003e\u003csub\u003ecr\u003c/sub\u003e of the shield-type inflatable dam is 0.407 m which is 34.4% higher than the conventional inflatable dam with its critical water-retaining height of 0.3028 m. The corresponding maximum cross-sectional tensile force \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e along the shield-type inflatable dam 0.767 kN/m or 13.9% lower than that of the conventional inflatable dam with its magnitude of 0.891 kN/m. Generally, the shield-type inflatable dam can not only effectively increase the critical water-retaining height but also reduce the tension forces along the inflatable dam. However, it has to be pointed out that the material cost of the shield steel is another consumption of the shield-type inflatable dam.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eNumerical analyses are conducted in this paper to investigate the performance of the shield-type inflatable dam. The accuracy of the numerical model was validated by comparing its results with those from laboratory model tests. Parametric studies were carried out to identify the influence of some key factors on the cross-sectional profile and tensile force of the structure to provide references for practical engineering design. The following conclusions can be drawn through this study:\u003c/p\u003e \u003cp\u003e1) The shield-type inflatable dam can be designed using the optimal cross-sectional perimeter of \u003cem\u003eL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, inflated by air pressures \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003cem\u003eγL\u003c/em\u003e, anchored with anchor distance \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.05\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, where \u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the height of the shield steel. The corresponding shield-type inflatable dam has a critical water-retaining height of \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e = 0.814\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, maximum tensile forces of \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e = 0.0767\u003cem\u003eγL\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e, with its inclined angle between the steel shield and rigid base of 60\u0026deg;.\u003c/p\u003e \u003cp\u003e2) The designed shield-type inflatable dam using optimal parameters could increase the critical water-retaining height by 34.4% and reduce the maximum tensile force by 13.9% compared to the conventional inflatable dam under the same conditions. However, the material cost of the shield steel increases the total cost of the shield-type inflatable dam.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of Competing Interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003e**Min WANG** : Software, Validation, Writing \u0026ndash; original draft. **Qing YE** : Software, Writing \u0026ndash; original draft. **Lei DAI** : Formal analysis, Writing \u0026ndash; original draft. **Wei GUO** : Methodology, Supervision, Writing \u0026ndash; review \u0026amp;amp; editing. **Guoyao GAO** : Writing \u0026ndash; review \u0026amp;amp; editing.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe financial support from the National Natural Science Foundation of China (Grant No. 52171273, 52578422) are gratefully acknowledged.\u003c/p\u003e\u003ch2\u003eData Availability Statement\u003c/h2\u003e \u003cp\u003eAll data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003eAlhamati, A. A. N., Mohammed, T. A. \u0026amp; Norzaie, J., Ghazali, A.H., Al-Jumaily, K. K. (2005). Behavior of inflatable dams under hydrostatic conditions. \u003cem\u003eSuranaree Journal of Science and Technology\u003c/em\u003e, \u003cstrong\u003e12\u003c/strong\u003e, No. 1, 1\u0026ndash;18.\u003c/p\u003e\n\u003cp\u003eBinnie, A. M. (1973). The theory of flexible dams inflated by water pressure. \u003cem\u003eJournal of Hydraulic Research\u003c/em\u003e, \u003cstrong\u003e11\u003c/strong\u003e, No 1, 61\u0026ndash;68.\u003c/p\u003e\n\u003cp\u003eChanson, H. (1997). Use of Rubber Dams for Flood Mitigation in Hong Kong. \u003cem\u003eJournal of Irrigation and Drainage Engineering\u003c/em\u003e, \u003cstrong\u003e124\u003c/strong\u003e, No. 3, 73\u0026ndash;78.\u003c/p\u003e\n\u003cp\u003eCheraghi-Shirazi, N., Kabiri-Samani, A. R. \u0026amp; Boroomand, B. (2014). Numerical analysis of rubber dams using fluid-structure interactions. \u003cem\u003eFlow Measurement and Instrumentation\u003c/em\u003e, \u003cstrong\u003e40\u003c/strong\u003e, 91\u0026ndash;98. \u003c/p\u003e\n\u003cp\u003eFreeman, M. (2002). Experiments and analysis of water-filled tubes used as temporary flood barriers. \u003cem\u003eMaster Thesis\u003c/em\u003e. Virginia Polytechnical Institute and State University, Blacksburg.\u003c/p\u003e\n\u003cp\u003eGao X., Guo W., Dai L., Guo W. \u0026amp; Ren Y. (2022a), Experimental study on air- and water-inflated double-rubber dam, \u003cem\u003eJournal of Irrigation and Drainage Engineering\u003c/em\u003e, \u003cstrong\u003e149\u003c/strong\u003e, No. 9, 04023021. \u003c/p\u003e\n\u003cp\u003eGao, X., Guo W., Ren Y., \u0026amp; Zeng W. (2022b). Numerical analysis of a double layer rubber dam. \u003cem\u003eGeotextile and Geomembrane\u003c/em\u003e. \u003cstrong\u003e50\u003c/strong\u003e, No. 2, 249\u0026ndash;261. \u003c/p\u003e\n\u003cp\u003eGao, X., Guo, W., Guo, W. F., Ren, Y. \u0026amp; Dai, L. (2023). Large-scale model test studies on a double-layer rubber dam. \u003cem\u003eGeosynthetics International\u003c/em\u003e, \u003cstrong\u003e30\u003c/strong\u003e, No. 5, 545\u0026ndash;560.\u003c/p\u003e\n\u003cp\u003eGhavanloo, E. \u0026amp; Daneshmand, F. (2010). Analytical analysis of the static interaction of fluid and cylindrical membrane structures. \u003cem\u003eEuropean Journal of Mechanics - A/Solids\u003c/em\u003e. \u003cstrong\u003e29\u003c/strong\u003e, No. 4, 600\u0026ndash;610. \u003c/p\u003e\n\u003cp\u003eGuo, W., Chu, J., Yan, S. (2015). Simplified analytical solution for geosynthetic tube resting on deformable foundation soil. \u003cem\u003eGeotextiles and Geomembranes\u003c/em\u003e, \u003cstrong\u003e43\u003c/strong\u003e, No. 5, 432\u0026ndash;439. \u003c/p\u003e\n\u003cp\u003eGuo, W., Chu, J. \u0026amp; Yan, S. (2013). Recent studies of geosynthetic tubes and geosynthetic mats: an overview. \u003cem\u003eGeotechnical and Geological Engineering, An International Journal\u003c/em\u003e, \u003cstrong\u003e44\u003c/strong\u003e, No. 4, 115\u0026ndash;124. \u003c/p\u003e\n\u003cp\u003eGuo, W., Kou, H., Zhou, B., Nie, W. \u0026amp; Chu, J. (2016). Simplified methods to analyze geosynthetic mattress resting on deformable foundation soil. \u003cem\u003eMarine Georesources \u0026amp; Geotechnology.\u003c/em\u003e \u003cstrong\u003e35\u003c/strong\u003e, No. 3, 339\u0026ndash;345.\u003c/p\u003e\n\u003cp\u003eGurt, R., Deutscher, M. \u0026amp; Gebhardt, M. (2015). Design and analysis of reinforced rubber membranes for inflatable dams. \u003cem\u003eProceedings of the 7th International Conference on Textile Composites and Inflatable Structures, Structural Membranes\u003c/em\u003e, O\u0026ntilde;ate, E., Bletzinger, K.-U. and Kr\u0026ouml;plin, B., Editors, International Center for Numerical Methods in Engineering Publishing, Barcelona, Spain, pp. 306\u0026ndash;317.\u003c/p\u003e\n\u003cp\u003eHarrison, H. B. (1970). The analysis and behavior of the inflatable membrane dams under static loading. \u003cem\u003eProceedings of the Institution of Civil Engineers\u003c/em\u003e, \u003cstrong\u003e45\u003c/strong\u003e, No. 4, 661\u0026ndash;676.\u003c/p\u003e\n\u003cp\u003eHuong, T. C., Plaut, R. H. \u0026amp; Filz, G. M. (2002). Wedged geomembrane tubes as temporary flood-fighting devices. \u003cem\u003eThin-Walled Structures\u003c/em\u003e, \u003cstrong\u003e40\u003c/strong\u003e, No. 11, 913\u0026ndash;923.\u003c/p\u003e\n\u003cp\u003eKim, M., Filz, G. M. \u0026amp; Plaut, R. H. (2005a). Two-chambered waterfilled geomembrane tubes used as water barriers: experiments and analysis. Geosynthetics International, \u003cstrong\u003e12\u003c/strong\u003e, No. 3, 127\u0026ndash;133.\u003c/p\u003e\n\u003cp\u003eKim, M., Freeman, M., FitzPatrick, B. T., Nevius, D. B., Plaut, R. H. \u0026amp; Filz, G. M. (2004). Use of an apron to stabilize geomembrane tubes for fighting floods. \u003cem\u003eGeotextiles and Geomembranes\u003c/em\u003e, \u003cstrong\u003e22\u003c/strong\u003e, No. 4, 239\u0026ndash;254.\u003c/p\u003e\n\u003cp\u003eKim, M., Moler, M., Freeman, M., Filz, G. M. \u0026amp; Plaut, R. H. (2005b). Stacked geomembrane tubes for flood control: experiments and analysis. \u003cem\u003eGeosynthetics International\u003c/em\u003e, \u003cstrong\u003e12\u003c/strong\u003e, No. 5, 253\u0026ndash;259.\u003c/p\u003e\n\u003cp\u003eKumar, A. \u0026amp;Islam, S. U. (2019). Ch 6: Inflation and deflation of rubber dam. In \u003cem\u003eHydraulic Rubber Dam\u003c/em\u003e, Thomas, S., Rane, A. V., Abitha, V. K., Kanny, K. and Dutta, A., Editors, William Andrew Publishing, Norwich, NY, USA, pp. 67\u0026ndash;98.\u003c/p\u003e\n\u003cp\u003eLowery, K. \u0026amp; Liapis, S. (1999). Dynamic analysis of an inflatable dam subjected to a flood. \u003cem\u003eComputational Mechanics\u003c/em\u003e, \u003cstrong\u003e24\u003c/strong\u003e, No. 1, 52\u0026ndash;64.\u003c/p\u003e\n\u003cp\u003eMysore, G. V., Liapis, S. I. \u0026amp; Plaut, R. H. (1998). Dynamic analysis of single-anchor inflatable dams. \u003cem\u003eJournal of Sound and Vibration\u003c/em\u003e, \u003cstrong\u003e215\u003c/strong\u003e, No. 2, 251\u0026ndash;272.\u003c/p\u003e\n\u003cp\u003ePlaut, R. H. \u0026amp; Suherman, S. (1998). Two-dimensional analysis of geosynthetic tubes. \u003cem\u003eActa Mechanica\u003c/em\u003e, \u003cstrong\u003e129\u003c/strong\u003e, No. 3, 207\u0026ndash;218.\u003c/p\u003e\n\u003cp\u003eSaleh, A. F. M. \u0026amp; Mondal, M. S. (2001). Performance evaluation of rubber dam projects of Bangladesh in irrigation development. \u003cem\u003eIrrigation and Drainage\u003c/em\u003e, \u003cstrong\u003e50\u003c/strong\u003e, No. 3, 237\u0026ndash;248.\u003c/p\u003e\n\u003cp\u003eSt\u0026eacute;phanie, P. \u0026amp; Moreira, S. (2007). The French experiment of an inflatable weir with steel gates. In: \u003cem\u003eMitteilungsblatt der Bundesanstalt f\u0026uuml;r Wasserbau\u003c/em\u003e. Karlsruhe:Bundesanstalt f\u0026uuml;r Wasserbau. \u003cstrong\u003e91\u003c/strong\u003e, S.93-98\u003c/p\u003e\n\u003cp\u003eStreeter, M., Rhode-Barbarigos, L. \u0026amp; Adriaenssens, S. (2015). Form finding and analysis of inflatable dams using dynamic relaxation. \u003cem\u003eApplied Mathematics and Computation\u003c/em\u003e, \u003cstrong\u003e267\u003c/strong\u003e, 742\u0026ndash;749.\u003c/p\u003e\n\u003cp\u003eSun, L., Qi, Y.., Gao, X., Guo, W. \u0026amp; Zhang, N. (2019). Stability of supported geomembrane tube flood barriers of novel design. \u003cem\u003eJournal of Flood Risk Management\u003c/em\u003e, \u003cstrong\u003e13\u003c/strong\u003e, No. 1, 1\u0026ndash;10.\u003c/p\u003e\n\u003cp\u003eSun, L., Yue, C., Guo, W. \u0026amp; Ren, Y. X. (2017). Lateral stability analysis of wedged geomembrane tubes using PFC2D. \u003cem\u003eMarine Georesources and Geotechnology\u003c/em\u003e, \u003cstrong\u003e35\u003c/strong\u003e, No. 5, 730\u0026ndash;737.\u003c/p\u003e\n\u003cp\u003eTam, P. W. M. (1998). Application of inflatable dam technology problems and countermeasures. \u003cem\u003eCanadian Journal of Civil Engineering\u003c/em\u003e, \u003cstrong\u003e25\u003c/strong\u003e, No. 2, 383\u0026ndash;388.\u003c/p\u003e\n\u003cp\u003eTam, P. W. M. \u0026amp; Zhang, X. Q. (1999). Management of rubber dams in Hong Kong. \u003cem\u003eCanadian Journal of Civil Engineering\u003c/em\u003e, \u003cstrong\u003e26\u003c/strong\u003e, No. 2, 123\u0026ndash;134.\u003c/p\u003e\n\u003cp\u003eWatson, R. (1985). A note on the shapes of flexible dams. \u003cem\u003eJournal of Hydraulic Research\u003c/em\u003e, 23(2), 179\u0026ndash;194. https://doi.org/10.1080/00221688509499364\u003c/p\u003e\n\u003cp\u003eWatson, L. T., Suherman, S. \u0026amp; Plaut, R. H. (1999). Two-dimensional elastic analysis of equilibrium shapes of single-anchor inflatable dams. \u003cem\u003eInternational Journal of Solids and Structures\u003c/em\u003e, \u003cstrong\u003e36\u003c/strong\u003e, No. 9, 1383\u0026ndash;1398.\u003c/p\u003e\n\u003cp\u003eZhang, X., Tam, P. W. M. \u0026amp; Zheng, W. (2002). Construction, operation, and maintenance of rubber dams. \u003cem\u003eCanadian Journal of Civil Engineering\u003c/em\u003e, \u003cstrong\u003e29\u003c/strong\u003e, No. 3, 409\u0026ndash;420.\u003c/p\u003e\n\u003cp\u003eZhuang, D., Ye, Q., Dai, L., Wang, M., Guo, W. \u0026amp; Gao, G. (2025). Large-scale model test on shield-type rubber dam. \u003cem\u003eInternational Journal of Geosynthetics and Ground Engineering\u003c/em\u003e, \u003cstrong\u003e11\u003c/strong\u003e, 63.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Dam, rubber dam, Shield-type inflatable dam, numerical analyses","lastPublishedDoi":"10.21203/rs.3.rs-8381076/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8381076/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe shield-type inflatable dam, integrating the steel shield and inflatable dams, has been developed recently to overcome the water-retaining limitations of conventional inflatable dams. In this study, a series of numerical studies are conducted using FLAC\u003csup\u003e2D\u003c/sup\u003e software to investigate the performance of the shield-type inflatable dam. Parametric studies are carried out to examine the influence of upstream water head, air pressure, dam perimeter, and the anchor distance on the cross-sectional configuration, water-retaining capacity, and circumferential tensile force distribution of the shield-type inflatable dam. It is suggested to design the shield-type inflatable dam using the optimal normalized parameters with an air pressure \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.6\u003cem\u003eγL\u003c/em\u003e, a cross-sectional perimeter \u003cem\u003eL\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, and an anchor distance \u003cem\u003eD\u0026thinsp;=\u003c/em\u003e\u0026thinsp;0.05\u003cem\u003eL\u003c/em\u003e\u003csub\u003e0,\u003c/sub\u003e where \u003cem\u003eL\u003c/em\u003e and \u003cem\u003eL\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e are the length of the inflatable dam and steel shield, \u003cem\u003eγ\u003c/em\u003e is the unit weight of water. Designed using these parameters, the shield-type inflatable dam increases the critical water-retaining height by 34.4% and reduces the maximum tensile force by 13.9% compared to the conventional inflatable dam. These findings provide new insights into the structural behavior and contribute to the practical design of the shield-type inflatable dam.\u003c/p\u003e","manuscriptTitle":"Numerical analyses on shield-type inflatable dam","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-26 06:24:26","doi":"10.21203/rs.3.rs-8381076/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b1ce8aaf-9d68-4141-9cbf-d48e777f4f16","owner":[],"postedDate":"December 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-26T01:24:27+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-26 06:24:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8381076","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8381076","identity":"rs-8381076","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}