Full Text:   <902>

Summary:  <557>

Suppl. Mater.: 

CLC number: 

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2023-04-25

Cited: 0

Clicked: 1232

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Shiguo XIAO

https://orcid.org/0000-0003-4648-5149

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2023 Vol.24 No.5 P.432-449

http://doi.org/10.1631/jzus.A2200340


General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off


Author(s):  Shiguo XIAO, Yuan QI, Pan XIA

Affiliation(s):  Key Laboratory of High-Speed Railway Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, China; more

Corresponding email(s):   xiaoshiguo@swjtu.cn

Key Words:  Active earth pressure, Tensile strength cut-off, Variational calculus method, Pseudo-static method, Strip surcharge


Shiguo XIAO, Yuan QI, Pan XIA. General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off[J]. Journal of Zhejiang University Science A, 2023, 24(5): 432-449.

@article{title="General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off",
author="Shiguo XIAO, Yuan QI, Pan XIA",
journal="Journal of Zhejiang University Science A",
volume="24",
number="5",
pages="432-449",
year="2023",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A2200340"
}

%0 Journal Article
%T General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off
%A Shiguo XIAO
%A Yuan QI
%A Pan XIA
%J Journal of Zhejiang University SCIENCE A
%V 24
%N 5
%P 432-449
%@ 1673-565X
%D 2023
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2200340

TY - JOUR
T1 - General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off
A1 - Shiguo XIAO
A1 - Yuan QI
A1 - Pan XIA
J0 - Journal of Zhejiang University Science A
VL - 24
IS - 5
SP - 432
EP - 449
%@ 1673-565X
Y1 - 2023
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2200340


Abstract: 
According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach, a general closed-form solution to seismic and static active earth pressure on the walls, which considers shear and tension failure of the retained soil, is put forward using a variational calculus method. The application point of the active resultant force specified in the proposed method is explained with a clear physical meaning related to possible movement modes of the walls. In respect of the derived nine dependent equations reflecting the functional characteristics of the earth pressure, the proposed method can be performed easily via an implicit strategy. There are 13 basic factors related to the retained soils, walls, and external loads to be involved in the proposed method. The tension crack segment of the slip surface is obviously influenced by these parameters, apart from vertical seismic coefficient and geometric bounds of the surcharge, but the shear slip segment maintains an approximately planar shape almost uninfluenced by these parameters. Noticeably, the proposed method quantitatively reflects that the resultant of the active earth pressure is always within a limited range under different possible movements of the same wall.

考虑土体抗拉强度的刚性挡土墙地震和静态主动土压力的一般变分解

作者:肖世国1,2,齐远2,夏攀3
机构:1西南交通大学,高速铁路线路工程教育部重点实验室,中国成都,610031;2西南交通大学,土木工程学院,中国成都,610031;3西南交通大学,地质工程系,中国成都,610031
目的:传统的主动土压力计算方法在考虑土体抗拉强度时的假设不合理,具有明显的局限性。本文考虑土体剪切屈服和拉伸破坏准则,不假设滑裂面形态,并基于墙后填土主动极限平衡条件与变分极值原理,提出刚性挡土墙的地震和静态主动土压力的一般解析解,确定相应于墙体可能运动模式的主动土压力合力值及其作用点的变化范围。
创新点:1.采用变分法,建立同时考虑土体剪切和拉伸破坏的刚性挡土墙地震和静态主动土压力的紧凑解析解;2.确立相应于墙体平动和转动复合运动模式的刚性挡土墙主动土压力的可能变化范围,以及其合力作用点的合理范围;3.揭示13个基本参数对主动土压力的影响规律,并定量确定剪切-拉裂复合模式的滑裂面形态以及作用于滑裂面上的法向应力。
方法:1.基于刚性挡土墙后侧土体的主动极限平衡状态,通过拟静力法引入等效地震力,并根据拉格朗日乘子法和变分极值原理,建立考虑土体剪切与拉裂破坏的地震(含静态)主动土压力的隐式求解方程;2.运用MATLAB中的fsolve函数,通过叠代计算与精度控制,得到主动土压力的计算结果。
结论:1.所提方法算得的地震和静态主动土压力,与试验及理论结果具有较好的一致性,且本方法的适用性更为广泛;2.同一刚性挡土墙在不同的运动模式下,墙后主动土压力有所不同,但其总是在有限范围内变化;3.随着土压力合力作用点在其合理变化范围内逐渐升高,滑裂面剪切段的形态逐渐由平面向曲面发展;4.墙后土体表层的张拉裂隙深度受竖向地震系数、条形荷载分布宽度及其距墙顶水平距离的影响均很小,但受其余10个参数的影响较大。

关键词:主动土压力;抗拉强度;变分法;拟静力法;条形超载

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]BakerR, GarberM, 1978. Theoretical analysis of the stability of slopes. Géotechnique, 28(4):395-411.

[2]BellAL, 1915. The lateral pressure and resistance of clay and the supporting power of clay foundations. Minutes of the Proceedings of the Institution of Civil Engineers, 199(1915):233-272.

[3]FranzG, 1983. Beton Kalender. Verlag von Wilhelm Ernst and Sohn, Munich, Germany (in German).

[4]CernicaJN, 1995. Geotechnical Engineering: Foundation Design. John Wiley & Sons, Inc., New York, USA.

[5]ChangMF, 1997. Lateral earth pressures behind rotating walls. Canadian Geotechnical Journal, 34(4):498-509.

[6]ChenJG, YangY, ChenYH, et al., 2020. Calculation of active earth pressure of cohesive soil behind retaining wall considering soil tensile strength. Rock and Soil Mechanics, 41(6):1829-1835 (in Chinese).

[7]ChenWF, 1975. Limit Analysis and Soil Plasticity. Elsevier, Amsterdam, The Netherlands.

[8]ChoudhuryD, SinghS, 2006. New approach for estimation of static and seismic active earth pressure. Geotechnical & Geological Engineering, 24(1):117-127.

[9]CoulombCA, 1776. Essai sur une application des règles de maximis & minimis à quelques problèmes de statique, relatifs à l’architecture microform. In: Mémoires de Mathématique et de Physique. de l’Imprimerie Royale, Paris, France, p.343-382 (in French).

[10]de Josselin de Jong G, 1980. Application of the calculus of variations to the vertical cut off cohesive frictionless soil. Géotechnique, 30(1):1-16.

[11]FangYS, IshibashiI, 1986. Static earth pressures with various wall movements. Journal of Geotechnical Engineering, 112(3):317-333.

[12]FangYS, ChenTJ, 1995. Modification of Mononobe-Okabe theory. Géotechnique, 45(1):165-167.

[13]FarzanehO, AskariF, FatemiJ, 2014. Active earth pressure induced by strip loads on a backfill. International Journal of Civil Engineering, 12(4):281-291.

[14]GiaquintaM, HildebrandtS, 2004. Calculus of Variations I. Springer, Berlin, Germany.

[15]GrecoVR, 2006. Lateral earth pressure due to backfill subject to a strip of surcharge. Geotechnical and Geological Engineering, 24(3):615-636.

[16]HanS, GongJX, ZhangYQ, 2016. Earth pressure of layered soil on retaining structures. Soil Dynamics and Earthquake Engineering, 83:33-52.

[17]HazarikaH, MatsuzawaH, 1996. Wall displacement modes dependent active earth pressure analyses using smeared shear band method with two bands. Computers and Geotechnics, 19(3):193-219.

[18]HouGX, ShuSZ, 2019. Trial wedge approach to determine lateral earth pressures. International Journal of Geomechanics, 19(1):06018035.

[19]IskanderM, ChenZB, OmidvarM, et al., 2013. Active static and seismic earth pressure for cφ soils. Soils and Foundations, 53(5):639-652.

[20]KhosraviMH, PipatpongsaT, TakemuraJ, 2013. Experimental analysis of earth pressure against rigid retaining walls under translation mode. Géotechnique, 63(12):1020-1028.

[21]KimJS, BarkerRM, 2002. Effect of live load surcharge on retaining walls and abutments. Journal of Geotechnical and Geoenvironmental Engineering, 128(10):803-813.

[22]KopáscyJ, 1957. Three-dimensional stress distribution and slip surfaces in earth works at rupture. Proceedings of the 4th International Conference on Soil Mechanics and Foundations Engineering, p.339-342.

[23]KrabbenhoftK, 2018. Static and seismic earth pressure coefficients for vertical walls with horizontal backfill. Soil Dynamics and Earthquake Engineering, 104:403-407.

[24]LiJP, WangM, 2014. Simplified method for calculating active earth pressure on rigid retaining walls considering the arching effect under translational mode. International Journal of Geomechanics, 14(2):282-290.

[25]LiXG, LiuWN, 2010. Study on the action of the active earth pressure by variational limit equilibrium method. International Journal for Numerical and Analytical Methods in Geomechanics, 34(10):991-1008.

[26]LiXP, ZhaoSX, HeSM, et al., 2019. Seismic stability analysis of gravity retaining wall supporting cφ soil with cracks. Soils and Foundations, 59(4):1103-1111.

[27]LiZW, YangXL, 2019. Active earth pressure for retaining structures in cohesive backfills with tensile strength cut-off. Computers and Geotechnics, 110:242-250.

[28]LuanMT, NogamiT, 1997. Variational analysis of earth pressure on a rigid earth-retaining wall. Journal of Engineering Mechanics, 123(5):524-530.

[29]MatsuzawaH, HazarikaH, 1996. Analyses of active earth pressure against rigid retaining wall subjected to different modes of movement. Soils and Foundations, 36(3):51-65.

[30]MazindraniZH, GanjaliMH, 1997. Lateral earth pressure problem of cohesive backfill with inclined surface. Journal of Geotechnical and Geoenvironmental Engineering, 123(2):110-112.

[31]MichalowskiRL, 2017. Stability of intact slopes with tensile strength cut-off. Géotechnique, 67(8):720-727.

[32]MOHURD (Ministry of Housing and Urban-Rural Development of the People’s Republic of China), 2013. Technical Code for Building Slope Engineering, GB 50330-2013. National Standards of the People’s Republic of China(in Chinese).

[33]MononobeN, 1924. Considerations into earthquake vibrations and vibration theories. Journal of the Japan Society of Civil Engineers, 10(5):1063-1094.

[34]NianTK, HanJ, 2013. Analytical solution for Rankine’s seismic active earth pressure in c-ϕ soil with infinite slope. Journal of Geotechnical and Geoenvironmental Engineering, 139(9):1611-1616.

[35]NiedostatkiewiczM, LesniewskaD, TejchmanJ, 2011. Experimental analysis of shear zone patterns in cohesionless for earth pressure problems using particle image velocimetry. Strain, 47(S2):218-231.

[36]OkabeS, MemberCE, 1924. General theory on earth pressure and seismic stability of retaining wall and dam. Journal of the Japan Society of Civil Engineers, 10(6):1277-1323.

[37]PaikKH, SalgadoR, 2003. Estimation of active earth pressure against rigid retaining walls considering arching effects. Géotechnique, 53(7):643-653.

[38]ParkD, MichalowskiRL, 2017. Three-dimensional stability analysis of slopes in hard soil/soft rock with tensile strength cut-off. Engineering Geology, 229:73-84.

[39]PaulB, 1961. A modification of the Coulomb-Mohr theory of fracture. Journal of Applied Mechanics, 28(2):‍259-268.

[40]PengMX, ChenJ, 2013. Slip-line solution to active earth pressure on retaining walls. Géotechnique, 63(12):1008-1019.

[41]PułaO, PułaW, WolnyA, 2005. On the variational solution of a limiting equilibrium problem involving an anchored wall. Computers and Geotechnics, 32(2):107-121.

[42]RankineWJM, 1857. II. On the stability of loose earth. Philosophical Transactions, 147:9-27.

[43]RaoPP, ChenQS, ZhouYT, et al., 2016. Determination of active earth pressure on rigid retaining wall considering arching effect in cohesive backfill soil. International Journal of Geomechanics, 16(3):04015082.

[44]RichardsR, ShiX, 1994. Seismic lateral pressures in soils with cohesion. Journal of Geotechnical Engineering, 120(7):1230-1251.

[45]SaranS, PrakashS, 1968. Dimensionless parameters for static and dynamic earth pressures behind retaining walls. Indian Geotechnical Journal, 7(3):295-310.

[46]ShuklaSK, GuptaSK, SivakuganN, 2009. Active earth pressure on retaining wall for c-ϕ soil backfill under seismic loading condition. Journal of Geotechnical and Geoenvironmental Engineering, 135(5):690-696.

[47]SokolovskiiVV, 1965. Statics of Granular Media. Pergamon Press, Oxford, UK.

[48]SoubraAH, MacuhB, 2002. Active and passive earth pressure coefficients by a kinematical approach. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 155(2):119-131.

[49]SpencerE, 1968. Effect of tension on stability of embankments. Journal of the Soil Mechanics and Foundations Division, 94(5):1159-1173.

[50]TangZC, PengYZ, SongJW, 1988. Centrifuge model test of a rigid wall used to retain cohesionless soil. Journal of Chongqing Jiaotong University, 7(2):48-57 (in Chinese).

[51]MathWorksThe, Inc., 2018. Global Optimization Toolbox: User’s Guide (R2018b). The MathWorks, Inc., Natick, USA. https://www.mathworks.com/help/

[52]TsagareliZV, 1965. Experimental investigation of the pressure of a loose medium on retaining walls with a vertical back face and horizontal backfill surface. Soil Mechanics and Foundation Engineering, 2(4):197-200.

[53]UtiliS, 2013. Investigation by limit analysis on the stability of slopes with cracks. Géotechnique, 63(2):140-154.

[54]WangYZ, 2000. Distribution of earth pressure on a retaining wall. Géotechnique, 50(1):83-88.

[55]WeiM, LuoQ, FengGS, et al., 2022. Shaking table tests on a cantilever retaining wall with reinforced and unreinforced backfill. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 23(11):900-916.

[56]XiaoSG, YanYP, XiaP, 2021. General solution for active earth pressure on rigid walls under strip surcharge on retained soils using variational method. International Journal of Civil Engineering, 19(8):881-896.

[57]XieY, LeshchinskyB, 2016. Active earth pressures from a log-spiral slip surface with arching effects. Géotechnique Letters, 6(2):149-155.

[58]YangXL, ZhangS, 2019. Seismic active earth pressure for soils with tension cracks. International Journal of Geomechanics, 19(6):06019009.

[59]ZhangF, LeshchinskyD, BakerR, et al., 2016. Implications of variationally derived 3D failure mechanism. International Journal for Numerical and Analytical Methods in Geomechanics, 40(18):2514-2531.

[60]ZhouYT, ChenQS, ChenFQ, et al., 2018. Active earth pressure on translating rigid retaining structures considering soil arching effect. European Journal of Environmental and Civil Engineering, 22(8):910-926.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE