Application of the material point method in the modeling of arching effects behind retaining walls with active movements

Document Type : Research


1 Department of Civil Engineering, Maragheh Branch, Islamic Azad University, Maragheh, Iran

2 Department of Civil Engineering, bonab Branch, Islamic Azad University


Numerical modeling of problems with large deformations is one of the main challenges in computational mechanics. Conventional numerical approaches cannot accurately model large deformations. Recently, the material point method (MPM), which comprises advantages of Eulerian and Lagrangian descriptions of movement, has been developed to solve complicated numerical problems such as large deformations. In this paper, the MPM method is employed to model the behavior of a soil mass behind a rigid retaining wall during active movement. It is the first time that the accuracy of the MPM method has been evaluated in the modeling of retaining walls with active movements. The accuracy and efficiency of the MPM are measured using two small-scale physical modeling tests and an analytical approach (for translational motion). In addition, a comparison between the results of the MPM and conventional FEM is provided. It is shown that the MPM can model the arching effect in the soil media better than the FEM; however, the material point method leads to smaller stresses on the wall compared to experimental results. It is demonstrated that the employed MPM can accurately model arching effects on the soil media behind the retaining walls with active movement. For transitional movement, arching effects lead to the upward movement of the resultant horizontal force on the wall, which occurs higher than 1/3H (H is the height of the wall). The achieved results indicate that the traditional methods can lead to overestimated designs without considering arching effects.


Main Subjects

[1] Terzaghi, Karl. Theoretical soil mechanics. John Wiley & sons  New York (1943): 11-15.
[2] Patel, S., & Deb, K. (2020). Study of active earth pressure behind a vertical retaining wall subjected to rotation about the base. International Journal of Geomechanics, 20(4), 04020028.
[3] Abbasnezhad, A., and Sadr, Karimi, J. (2008). An experimental investigation into the arching effect in fine sand.
[4] Li, Z. W., & Yang, X. L. (2018). Active earth pressure for soils with tension cracks under steady unsaturated flow conditions. Canadian Geotechnical Journal, 55(12), 1850-1859.
[5] Zhang, H., Chen, J., & Xu, M. (2022). The Determination of Rational Spacing of Anti-Slide Piles and Soil Pressure on Pile Sheet Based on Soil Arching Effect. Geotechnical and Geological Engineering, 40(5), 2857-2866.
[6] Janssen, H. A. (1895). Versuche uber getreidedruck in silozellen. Z. ver. deut. Ing., 39, 1045.
[7] Frydman, S., & Keissar, I. (1987). Earth pressure on retaining walls near rock faces. Journal of Geotechnical Engineering, 113(6), 586-599.
[8] Chenghua, W., Yongbo, C., & Lixiang, L. (2001). Soil arch mechanical character and suitable space between one another anti-sliding pile. Journal of Mountain Science, 19(6), 556-559.
[9] Paik, K. H., & Salgado, R. (2003). Estimation of active earth pressure against rigid retaining walls considering arching effects. Geotechnique, 53(7), 643-653.
[10] Spangler, M. G., & Handy, R. L. (1973). Soil engineering (No. 624.151 S6 1973).
[11] Goel, S., & Patra, N. R. (2008). Effect of arching on active earth pressure for rigid retaining walls considering translation mode. International Journal of Geomechanics, 8(2), 123-133.
[12] Pipatpongsa, T., & Heng, S. (2010). Granular arch shapes in storage silo determined by quasi-static analysis under uniform vertical pressure. Journal of Solid Mechanics and Materials Engineering, 4(8), 1237-1248.
[13] Dalvi, R. S., & Pise, P. J. (2012). Analysis of arching in soil-passive state. Indian Geotechnical Journal, 42(2), 106-112.
[14] Bahmani Tajani, S., Fathipour, H., Payan, M., Jamshidi Chenari, R., & Senetakis, K. (2022). Temperature-dependent lateral earth pressures in partially saturated backfills. European Journal of Environmental and Civil Engineering, 1-27.
[15] Deng, B., & Yang, M. (2019). Analysis of Passive Earth Pressure for Unsaturated Retaining Structures. International Journal of Geomechanics, 19(12), 06019016.
[16] Fathipour, H., Tajani, S. B., Payan, M., Chenari, R. J., & Senetakis, K. (2022). Influence of transient flow during infiltration and isotropic/anisotropic matric suction on the passive/active lateral earth pressures of partially saturated soils. Engineering Geology, 310, 106883.
[17] Fathipour, H., Payan, M., & Chenari, R. J. (2021). Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures using finite element and second-order cone programming. Computers and Geotechnics, 134, 104119.
[18] Shahrokhabadi, S., Vahedifard, F., Ghazanfari, E., & Foroutan, M. (2019). Earth pressure profiles in unsaturated soils under transient flow. Engineering Geology, 260, 105218.
[19] Liang, W. B., Zhao, J. H., Li, Y., Zhang, C. G., & Wang, S. (2012). Unified solution of Coulomb's active earth pressure for unsaturated soils without crack. In Applied Mechanics and Materials (Vol. 170, pp. 755-761). Trans Tech Publications.
[20] Stanier, S., & Tarantino, A. (2010). Active earth force in 'cohesionless' unsaturated soils using bound theorems of plasticity. In Proc. of 5th Int. conf. on Unsaturated Soils, Barcelona (pp. 1081-1086).
[21] Sahoo, J. P., & Ganesh, R. (2017). Active Earth Pressure on Retaining Walls with Unsaturated Soil Backfill. In International Congress and Exhibition" Sustainable Civil Infrastructures: Innovative Infrastructure Geotechnology" (pp. 1-19). Springer, Cham.
[22] Pufahl, D. E., Fredlund, D. G., & Rahardjo, H. (1983). Lateral earth pressures in expansive clay soils. Canadian Geotechnical Journal, 20(2), 228-241.
[23] Veiskarami, M., Chenari, R. J., & Jameei, A. A. (2019). A study on the static and seismic earth pressure problems in anisotropic granular media. Geotechnical and Geological Engineering, 37(3), 1987-2005.
[24] Mirmoazen, S. M., Lajevardi, S. H., Mirhosseini, S. M., Payan, M., & Jamshidi Chenari, R. (2022). Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures subjected to strip footing loading using finite element and second-order cone programming. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 46(4), 3181-3192.
[25] Payan, M., Fathipour, H., Hosseini, M., Chenari, R. J., & Shiau, J. S. (2022). Lower Bound Finite Element Limit Analysis of Geo-Structures with Non-Associated Flow Rule. Computers and Geotechnics, 147, 104803.
[26] Mirmoazen, S. M., Lajevardi, S. H., Mirhosseini, S. M., Payan, M., & Chenari, R. J. (2021). Active lateral earth pressure of geosynthetic-reinforced retaining walls with inherently anisotropic frictional backfills subjected to strip footing loading. Computers and Geotechnics, 137, 104302.
[27] Vahedifard, F., Leshchinsky, B. A., Mortezaei, K., & Lu, N. (2015). Active earth pressures for unsaturated retaining structures. Journal of Geotechnical and Geoenvironmental Engineering, 141(11), 04015048.
[28] Patki, M. A., Mandal, J. N., & Dewaikar, D. M. (2015). Determination of passive earth pressure coefficients using limit equilibrium approach coupled with the Kötter equation. Canadian Geotechnical Journal, 52(9), 1241-1254.
[29] Vo, T., & Russell, A. R. (2014). Slip line theory applied to a retaining wall–unsaturated soil interaction problem. Computers and Geotechnics, 55, 416-428.
[30] Zhang, C. G., Zhu, D. H., Gao, Z., Xue, G. W., & Li, Z. (2012). Unified Solution of Passive Earth Pressure for Unsaturated Soils. In Advanced Materials Research (Vol. 594, pp. 430-433). Trans Tech Publications.
[31] Farajniya, R., Poursorkhabi, R. V., Zarean, A., & Dabiri, R. (2022). Investigation of the arching in rock-fill dam ten years after end construction using Numerical analysis and monitoring. Ferdowsi Civil Engineering, 35(1), 59-74.
[32] Zhao, L. H., Luo, Q., Li, L., Yang, F., & Yang, X. L. (2009). The upper bound calculation of passive earth pressure is based on the shear strength theory of unsaturated soil. In Slope Stability, Retaining Walls, and Foundations: Selected Papers from the 2009 GeoHunan International Conference (pp. 151-157).
[33] Soubra, A. H. (2000). Static and seismic passive earth pressure coefficients on rigid retaining structures. Canadian Geotechnical Journal, 37(2), 463-478.
[34] Fathipour, H., Siahmazgi, A. S., Payan, M., & Chenari, R. J. (2020). Evaluation of the lateral earth pressure in unsaturated soils with finite element limit analysis using second-order cone programming. Computers and Geotechnics, 125, 103587.
[35] Fathipour, H., Payan, M., Jamshidi Chenari, R., & Senetakis, K. (2021). Lower bound analysis of modified pseudo‐dynamic lateral earth pressures for retaining wall‐backfill system with depth‐varying damping using FEM‐Second order cone programming. International Journal for Numerical and Analytical Methods in Geomechanics, 45(16), 2371-2387.
[36] Li, X., Wu, Y., & He, S. (2010). Seismic stability analysis of gravity retaining walls. Soil Dynamics and Earthquake Engineering, 30(10), 875-878.
[37] Subba Rao, K. S., & Choudhury, D. (2005). Seismic passive earth pressures in soils. Journal of Geotechnical and Geoenvironmental Engineering, 131(1), 131-135.
[38] Aalami, M. T., Vafaeipoor, R., Naseri, A., & Mojtahedi, A. (2022). Experimental Analysis of the Effect of the Distance of a Submerged Berm in front of a Reshaping Rubble Mound Breakwater on Diminishing the Damage Parameter. Journal of Civil and Environmental Engineering, 52(107), 1-13.
[39] Nakai, T. (1985). Analysis of earth pressure problems considering the influence of wall friction and wall deflection. In International conference on numerical methods in geomechanics (pp. 765-772).
[40] Dasgupta, U. S., Chauhan, V. B., & Dasaka, S. M. (2017). Influence of spatially random soil on lateral thrust and failure surface in earth retaining walls. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 11(3), 247-256.
[41] Hajialilue-Bonab, M., & Tohidvand, H. R. (2015). A modified scaled boundary approach in frequency domain with diagonal coefficient matrices. Engineering Analysis with Boundary Elements, 50, 8-18.
[42] Hassanzadeh, M., Tohidvand, H. R., Hajialilue-Bonab, M., & Javadi, A. A. (2018). Scaled boundary point interpolation method for seismic soil-tunnel interaction analysis. Computers and Geotechnics, 101, 208-216.
[43] Morgun, A., & Balatiuk, A. (2013). STABILITY OF RETAINING WALLS BY BEM. Scientific Works of Vinnytsia National Technical University, (2).
[44] Harlow, F. H. (1964). The particle-in-cell computing method for fluid dynamics. Methods Comput. Phys., 3, 319-343.
[45] Sulsky, D., Chen, Z., & Schreyer, H. L. (1994). A particle method for history-dependent materials. Computer methods in applied mechanics and engineering, 118(1-2), 179-196.
[46] Higo, Y., Lee, C. W., Doi, T., Kinugawa, T., Kimura, M., Kimoto, S., & Oka, F. (2015). Study of dynamic stability of unsaturated embankments with different water contents by centrifugal model tests. Soils and Foundations, 55(1), 112-126.
[47] Wang, F., Li, X., Couples, G., Shi, J., Zhang, J., Tepinhi, Y., & Wu, L. (2015). Stress arching effect on stress sensitivity of permeability and gas well production in Sulige gas field. Journal of Petroleum Science and Engineering, 125, 234-246.
[48] Ceccato, F., Beuth, L., Vermeer, P. A., & Simonini, P. (2016). Two-phase material point method applied to the study of cone penetration. Computers and Geotechnics, 80, 440-452.
[49] Bolognin, M., Martinelli, M., Bakker, K. J., & Jonkman, S. N. (2017). Validation of material point method for soil fluidization analysis. Journal of Hydrodynamics, Ser. B, 29(3), 431-437.
[50] Kiriyama, T., Fukutake, K., & Higo, Y. (2018). Verification and validation of two-phase material point method simulation of pore water pressure rise and dissipation in earthquakes. In Physical Modelling in Geotechnics (pp. 215-220). CRC Press.
[51] Giridharan, S., Gowda, S., Stolle, D. F., & Moormann, C. (2020). Comparison of ubcsand and hypoplastic soil model predictions using the material point method. Soils and Foundations, 60(4), 989-1000.
[52] Tohidvand, H. R., Hajialilue-Bonab, M., Katebi, H., Nikvand, V., & Ebrahimi-Asl, M. (2022). Monotonic and post cyclic behavior of sands under different strain paths in direct simple shear tests. Engineering Geology, 302, 106639.
[53] Tohidvand, H. R., Hajialilue-Bonab, M., & Katebi, H. (2024). Evaluation of the Effects of Different Strain Paths on the Behavior of Sands Using Direct Simple Shear Tests. Journal of Testing and Evaluation, 52(1).
[54] Khosravi, M. H., Takemura, J., Pipatpongsa, T., & Amini, M. (2016). In-flight excavation of slopes with potential failure planes. Journal of Geotechnical and Geoenvironmental Engineering, 142(5), 06016001.