Abstract
The earth pressure acting on retaining walls due to creep and consolidation is under limited equilibrium conditions (limited displacement). Linear elastic constitutive theory can be applied to determine earth pressure distribution along retaining walls under limited displacement condition. In addition, tangent modulus in Duncan-Chang nonlinear elastic model was introduced to reflect the variations of soil modulus with confining pressure, and boundary strains were derived from Rankine active earth pressure, Rankine passive earth pressure, static earth pressure and principal stress direction deflection. According to the above four boundary strains, earth pressure on retaining walls was divided into five state zones. By comparing the calculation results obtained from the equations proposed in this paper with those of experimental tests, the following conclusions can be drawn: earth pressure distribution was always nonlinear along retaining walls for translation displacement (T mode), rotation displacement around wall base (RB mode), and translation + rotation displacement around wall base (RBT mode). Also, calculated earth pressure distributions along with the depth of wall were found to be consistent with measured values under three displacement modes. Additionally, a parametric study was carried out to evaluate the effects of internal friction angle and backfill soil cohesion on earth pressure. It could be seen from the above series of studies that the earth pressure equations derived in this work could be well applied in practical engineering in designing retaining walls.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahmad MS, Choudhury D (2010) Seismic rotational stability of waterfront retaining wall using pseudo dynamic method. Int J Geomech 10(1): 45–52. https://doi.org/10.1061/(ASCE)1532-3641(2010)10:1(45)
Antão AN, Santana TG, Silva MVD, et al. (2016) Three-dimensional active earth pressure coefficients by upper bound numerical limit analysis. Comput Geotech 79: 96–104. https://doi.org/10.1016/j.compgeo.2016.05.022
Chang MF (1997) Lateral earth pressures behind rotating walls. Can Geotech J 34(4): 498–509. https://doi.org/10.1139/t97-016
Choudhury D, Nimbalkar S (2007) Seismic rotational displacement of gravity walls by pseudo- dynamic method: Passive case. Soil Dyn Earthq Eng 27: 242–249. https://doi.org/10.1016/j.soildyn.2006.06.009
Cao WG, Liu T, Xu Z (2019) Estimation of active earth pressure on inclined retaining wall based on simplified principal stress trajectory method. Int J Geomech 19(7): 06019011. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001447
Chehade HA, Dias D, Sadek M, et al. (2019) Seismic analysis of geosynthetic-reinforced retaining wall in cohesive soils. Geotext Geomembranes 47(3): 315–326. https://doi.org/10.1016/j.geotexmem.2019.02.003
Chu SC (1991) Rankine’s Analysis of Active and Passive Pressure in Dry Sands. Soils Found 31 (4): 115–120. https://doi.org/10.3208/sandf1972.31.4_115
Dave T, Dasaka S (2012) Transition of earth pressure on rigid retaining walls subjected to surcharge loading. Int J Geomech 6:427–436. https://doi.org/10.3328/IJGE.2012.06.04.427-435
Du DC, Dias D, Yang XL (2018) Analysis of earth pressure for shallow square tunnels in anisotropic and nonhomogeneous soils. Comput Geotech 104: 226–236. https://doi.org/10.1016/j.compgeo.2018.08.022
Fang YS, Chen TJ, Wu BF (1994). Passive earth pressures with various wall movements. J Geotech Eng 120 (8): 1307–1323. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:8(1307)
Fang YS, Ishibashi I (1986) Static earth pressures with various wall movements. J Geotech Eng 112 (3): 317–333. https://doi.org/10.1061/(ASCE)0733-9410(1986)112:3(317)
Fang YS, Yang YC, Chen TJ (2003) Retaining walls damaged in the Chi-Chi earthquake. Can Geotech J 40 (6): 1142–1153. https://doi.org/10.1139/t03-055
Fan CC, Fang YS (2010) Numerical solution of active earth pressures on rigid retaining walls built near rock faces. Comput Geotech 37: 1023–1029. https://doi.org/10.1016/j.compgeo.2010.08.004
Goel S, Patra NR (2008) Effect of arching on active earth pressure for rigid retaining walls considering translation mode. Int J Geomech 8(2): 123–133. https://doi.org/10.1061/(ASCE)1532-3641(2008)8:2(123)
Hu Z, Yang ZX, Wilkinson SP (2017) Active earth pressure acting on retaining wall considering anisotropic seepage effect. J Mt Sci 14(6): 1202–1211. https://doi.org/10.1007/s11629-016-4014-3
Iskander M, Chen ZB, Omidvar M, et al. (2013) Rankine pseudo-static earth pressure for c-φ soils. Mech Res Commun 51: 51–55. https://doi.org/10.1016/j.mechrescom.2013.04.010
Iskander M, Chen ZB, Omidvar M, et al. (2015) Active static and seismic earth pressure for c-φ soils. Soils Found 53(5): 639–652. https://doi.org/10.1016/j.sandf.2013.08.003
Jia JB, Wang YS, Leng YG (2019) Unloading creep characteristics of frozen clay subjected to long-term high-pressure Ko consolidation before freezing. Adv in Civ Eng 2019: 7192845–1–7192845–18. https://doi.org/10.1155/2019/7192845
Khosravi MH, Pipatpongsa T, Takemura J (2013) Experimental analysis of earth pressure against rigid retaining walls under translation mode. Geótechnique 63(12): 1020–1028. https://doi.org/10.1680/geot.12.P.021
Keykhosropour L, Lemnitzer A (2019) Experimental studies of seismic soil pressures on vertical flexible, underground structures and analytical comparisons. Soil Dyn Earthq Eng 118: 166–178. https://doi.org/10.1016/j.soildyn.2018.12.012
Li XG, Liu WN (2005) Study on measurements of earth pressure and water-soil pressure acting on retaining wall. Chinese J Rock Mech Eng 24(12): 2149–2154. (In Chinese) https://doi.org/10.3321/j.issn:1000-6915.2005.12.024
Lu KL, Yang Y (2010) Preliminary study of active earth pressure under nonlimit state. Rock Soil Mech 31(2): 615–619. (In Chinese) https://doi.org/10.16285/j.rsm.2010.02.032
Li JP, Wang M (2014) Simplified method for calculating active earth pressure on rigid retaining walls considering the arching effect under translational mode. Int J Geomech 14(2): 282–290. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000313
Li ZW, Yang XL (2019) Active earth pressure for retaining structures in cohesive backfills with tensile strength cut-off. Comput Geotech 110: 242–250. https://doi.org/10.1016/j.compgeo.2019.02.023
Ma P, Qing SQ, Qian HT (2008) Calculation of active earth pressure for limited soils. Chin J Rock Mech Eng 27(Supp. 1): 3070–3074. (In Chinese)
Nadukuru SS, Michalowski RL (2012) Arching in distribution of active load on retaining walls. J Geotech Geoenviron Eng 138(5): 575–584. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000617
Ouyang C, Xu Q, He S, et al. (2013) A generalized limit equilibrium method for the solution of active earth pressure on a retaining wall. J Mt Sci 10(6):1018–1027. https://doi.org/10.1007/s11629-013-2576-x
Paik KH, Salgado R (2003) Estimation of active earth pressure against rigid retaining walls considering arching effects. Geotechnique 53(7): 643–653. https://doi.org/10.1680/geot.2003.53.7.643
Pain A, Choudhury D, Bhattacharyya SK (2016) Seismic rotational displacement of retaining walls: a pseudo-dynamic approach. Innov Infrastruct Solut 1(1):22. https://doi.org/10.1007/s41062-016-0023-x
Pain A, Choudhury D, Bhattacharyya SK (2017) Seismic rotational stability of gravity retaining walls by modified pseudo-dynamic method. Soil Dyn Earthq Eng 94:244–253. https://doi.org/10.1016/j.soildyn.2017.01.016
Patel S, Deb K (2020) Study of active earth pressure behind a vertical retaining wall subjected to rotation about the Base. Int J Geomech 20 (4): 04020028. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001639
Qian ZH, Zou JF, Tian J, et al. (2020) Estimations of active and passive earth thrusts of non-homogeneous frictional soils using a discretisation technique. Comput Geotech 119: 103366. https://doi.org/10.1016/j.compgeo.2019.103366
Rao PP, Chen QS, Zhou YT, et al. (2016) Determination of active earth pressure on rigid retaining wall considering arching effect in cohesive backfill soil. Int J Geomech 16 (3): 04015082. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000589
Ramakrishna VSA, Pain A (2021) Finite element modeling (FEM) vs simplified force-based methods for rigid retaining walls under earthquake excitation. J Earthq Tsunami 2020: 2150020. https://doi.org/10.1142/S1793431121500202
Shi JY, Lei GH, Ai YB, et al. (2005) Stress path controlled triaxial experimental study of lateral earth pressure behaviour. Rock Soil Mech 26(11): 1700–1704. (In Chinese) https://doi.org/10.1007/s11769-005-0030-x
Shamsabadi A, Xu SY, Taciroglu E (2013) A generalized log-spiral-Rankine limit equilibrium model for seismic earth pressure analysis. Soil Dyn Earthq Eng 49: 197–209. https://doi.org/10.1016/j.soildyn.2013.02.020
Santolo ASD, Evangelista A (2011) Dynamic active earth pressure on cantilever retaining walls. Comput Geotech 38: 1041–1051. https://doi.org/10.1016/j.compgeo.2011.07.015
Seo M, Im JC, Kim C, et al. (2016) Study on the applicability of a retaining wall using batter piles in clay. Can Geotech J 53 (8): 1195–1212. https://doi.org/10.1139/cgj-2014-0264
Terazghi K (1934) Large retaining wall tests I—pressure of dry sand. ENR 112(1): 136–140.
Tu BX, Jia JQ (2012) Research on active earth pressure behind rigid retaining wall from clayey backfill considering soil arching effects. Chinese J Rock Mech Eng 31(5): 1064–1070. (In Chinese) https://doi.org/10.3969/j.issn.1000-6915.2012.05.025
Tu BX, Jia JQ (2013) Active earth pressure from c-φ soil backfill. Geotech Eng 167 (GE3): 270–280. https://doi.org/10.1680/geng.12.00008
Tang Y, Li JP, Yuan M (2018) Lateral earth pressure considering the displacement of a rigid retaining wall. Int J Geomech 18 (11): 06018031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001284
Watanabe K, Koseki J, Tateyama M (2011) Seismic earth pressure exerted on retaining walls under a large seismic load. Soil Found 51(3): 379–394. https://doi.org/10.3208/sandf.51.379
Wan T, Li PF, Zheng H, et al. (2019) An analytical model of loosening earth pressure in front of tunnel face for deep-buried shield tunnels in sand. Comput Geotech 115: 103170. https://doi.org/10.1016/j.compgeo.2019.103170
Xu RQ, Chen YK, Yang ZX, et al. (2002) Experimental research on the passive earth pressure acting on a rigid wall. Chinese J Geotech Eng 24(5): 569–575. (In Chinese) https://doi.org/10.1016/j.compgeo.2019.103170
Xia JW, Dou GT, Su Q, et al. (2019) An experiment study on the non-limit passive earth pressure of clay under different displacement modes. J Southwest Jiaotong Univ 54(4): 769–777. (In Chinese) https://doi.org/10.3969/j.issn.0258-2724.20170343
Ying HW, Huang D, Xie XY (2011) Study of active earth pressure on retaining wall subject to translation mode considering lateral pressure on adjacent existing basement exterior wall. Chinese J Rock Mech Eng 30(Supp. 1): 2970–2978. (In Chinese)
Ying HW, Zhang JH, Wang XG, et al. (2016) Experimental analysis of passive earth pressure against rigid retaining wall under translation mode for finite soils. Chin J Geotech Eng 38(6): 978–986. (In Chinese) https://doi.org/10.11779/CJGE201606002
Yang MH, Dai XB, Zhao MH, et al. (2017) Calculation of active earth pressure for limited soils with curved sliding surface. Rock Soil Mech 38(7): 2029–2035. (In Chinese) https://doi.org/10.16285/j.rsm.2017.07.024
Yan ZY, Li G, Zhang JL, et al. (2019) Study on the creep behaviors of interactive marine-terrestrial deposit soils. Adv Civ Eng 2019: 6042893. https://doi.org/10.1155/2019/6042893
Yang C, Carter JP, Sheng DC, et al. (2016) An isotach elastoplastic constitutive model for natural soft clays. Comput Geotech 77: 134–155. https://doi.org/10.1016/j.compgeo.2016.04.011
Zhou YY, Ren ML (1990) An experimental study on active earth pressure behind rigid retaining wall. Chin J Geotech Eng 12(2): 19–26. (In Chinese)
Zhang YX, Chen L (2011) Active earth pressure on retaining walls in non-limit state. China Civil Eng J 44(4): 112–119. (In Chinese) https://doi.org/10.15951/j.tmgcxb.2011.04.002
Zhang JJ, Gao GY, Fu BJ, et al. (2020) A universal multifractal approach to assessment of spatiotemporal extreme precipitation over the Loess Plateau of China. Hydrol Earth Syst Sci 24(2): 809–826. https://doi.org/10.5194/hess-24-809-2020
Zhuang Y, Xing AG, Cheng QG, et al. (2019) Characteristics and numerical modeling of a catastrophic loess flow slide triggered by the 2013 Minxian-Zhangxian earthquake in Yongguang village, Minxian, Gansu, China. B Eng Geol Environ 79: 439–449. https://doi.org/10.1007/s10064-019-01542-x
Zhan JW, Wang Q, Zhang W, et al. (2019) Soil-engineering properties and failure mechanisms of shallow landslides in soft-rock materials. Catena 181: 104093. https://doi.org/10.1016/j.catena.2019.104093
Zhou YT (2018) Active earth pressure against rigid retaining wall considering effects of wall-soil friction and inclinations. KSCE J Civ Eng 22(12): 4901–4908. https://doi.org/10.1007/s12205-018-1984-4
Acknowledgments
This study was funded by the National Natural Science Foundation of China (No. 51979225, 51679199), the Special Funds for Public Industry Research Projects of the Ministry of Water Resources (No. 201501034-04), the Key Laboratory for Science and Technology Coordination & Innovation Projects of Shaanxi Province (No. 2014SZS15-Z01) and the Natural Science Foundation of Shaanxi Province (No. 2020JQ-584).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, L., Dang, Fn., Wang, X. et al. Estimation of earth pressure against retaining walls with different limited displacement modes based on elastic theory. J. Mt. Sci. 19, 289–304 (2022). https://doi.org/10.1007/s11629-021-6844-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11629-021-6844-x