Abstract
A new methodology for the rotational stability analysis of a gravity retaining wall supporting inclined backfill under earthquake and heavy rainfall conditions has been presented. According to the movement mode of retaining wall and the characteristics of backfill sliding and rainwater infiltration, a sliding model of the infinite soil strip and rainwater infiltration model were established respectively. By calculating the internal energy dissipation rate and external loads power of the wall-soil system mechanism, a formula to calculate seismic yield acceleration coefficient under coupling conditions of earthquakes and rainfall was deduced. The results revealed a large effect size of infiltration depth of rainwater and the backfill inclination on the seismic yield acceleration coefficient. When the rainwater reaches 1/5 the height of the retaining wall and the backfill inclination exceeds 15°, the seismic yield acceleration coefficient will decrease rapidly. Moreover, the results obtained in this paper showed good consistency with those obtained by numerical simulation.
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Abbreviations
- B :
-
Width of the wall
- dA 1 :
-
Area of a rigid water strip when
- θ :
-
θ2 in Fig. 8
- dA 2 :
-
Area of a rigid water strip when
- θ :
-
θ1 in Fig. 8
- H :
-
Height of the wall
- h :
-
Height of the point g in Fig. 2
- i :
-
Hydraulic gradient
- J :
-
Seepage force
- k cr :
-
Yield acceleration coefficient
- k h :
-
Horizontal seismic yield acceleration coefficient
- n :
-
The porosity of soil mass
- O :
-
Toe of the wall
- P dyn :
-
Hydrodynamic pressure on the wall
- P stat :
-
Hydrostatic pressure on the wall
- r u :
-
Pore water pressure ratio
- V p :
-
Velocity of point P in Figs. 5 and 6
- V ps :
-
Relative velocity between Vs and Vp
- V s :
-
Velocities of the rigid adjacent to point P in Figs. 5 and 6
- Ẇ eg :
-
Rate of work done by the soil wedge
- Ẇ D :
-
Rate of work done by water on soil wedge
- Ẇ D1 :
-
The work done by the water pressure on soil wedge when
- θ :
-
θ1 in Fig. 8
- Ẇ D2 :
-
The work done by the water pressure on soil wedge when
- θ :
-
θ2 in Fig. 8
- Ẇ dyn :
-
Rate of work done by hydrostatic pressure on the wall
- Ẇ ec :
-
Rate of work done by horizontal inertial force of the wall
- Ẇ es :
-
Rate of work done by horizontal inertial force of soil wedge
- Ẇ stat :
-
Rate of work done by hydrodynamic pressure
- Ẇ wg :
-
Rate of work done by the wall weight
- w :
-
Backfill moisture content
- Δy 1 :
-
The midpoint depth of a rigid water strip when
- θ :
-
θ1 in Fig. 8
- Δy 2 :
-
The midpoint depth of a rigid water strip when
- θ :
-
θ2 in Fig. 8
- Δu(z):
-
Excess pore water pressure
- ± :
-
The wall front inclination
- β :
-
Inclination angle of rupture
- β cr :
-
β corresponding to kcr
- \(\bar{\gamma}\) :
-
Equivalent unit weight of the soil
- γ c :
-
Unit weight of the retaining wall
- γ d :
-
Unit weight of dry soil
- γ s :
-
Unit weight of soil
- γ stst :
-
Saturated unit weight of soil
- γ w :
-
Unit weight of water
- γ we :
-
The modified unit weights of water
- δ :
-
Wall-soil friction angle
- η :
-
The backfill inclination
- λ :
-
Arctan (h/B)
- θ :
-
Inclination angle of line OP in Fig. 3
- \(\sigma_{V}^{\prime}(z)\) :
-
The initial vertical effective stress
- ϕ :
-
Arctan (H/B)
- φ :
-
Internal friction angle
- ω :
-
Angular velocity of the wall about toe
References
Ahmad SM, Choudhury D (2010) Seismic rotational stability of waterfront retaining wall using pseudodynamic method. International Journal of Geomechanics 10(1):45–52, DOI: https://doi.org/10.1061/(ASCE)1532-3641(2010)10:1(45)
Augusto Filho O, Fernandes MA (2019) Landslide analysis of unsaturated soil slopes based on rainfall and matric suction data. Bulletin of Engineering Geology and the Environment 78(6):4167–4185, DOI: https://doi.org/10.1007/s10064-018-1392-5
Bo A, Chun Z, Kuiming L, Sitong L, Zhigang T, Haipeng L, Haoran Y (2019) The influence of rainfall on landslide stability of an open-pit mine: The case of Haizhou open-pit min. Geotechnical and Geological Engineering 37(4):3367–3378, DOI: https://doi.org/10.1007/s10706-019-00851-y
Capparelli G, Damiano E, Greco R, Olivares L, Spolverino G (2020) Physical modeling investigation of rainfall infiltration in steep layered volcanoclastic slopes. Journal of Hydrology 580:124199, DOI: https://doi.org/10.1016/j.jhydrol.2019.124199
Chakraborty D, Choudhury D (2014a) Sliding stability of non-vertical waterfront retaining wall supporting inclined backfill subjected to pseudo-dynamic earthquake forces. Applied Ocean Research 47: 174–182, DOI: https://doi.org/10.1016/j.apor.2014.05.004
Chakraborty D, Choudhury D (2014b) Stability of non-vertical waterfront retaining wall supporting inclined backfill under earthquake and tsunami. Ocean Engineering 78: 1–10, DOI: https://doi.org/10.1016/j.oceaneng.2013.11.024
Chandrasekaran SS, Sayed Owaise R, Ashwin S, Jain RM, Prasanth S, Venugopalan RB (2013) Investigation on infrastructural damages by rainfall-induced landslides during November 2009 in Nilgiris, India. Natural Hazards 65(3):1535–1557, DOI: https://doi.org/10.1007/s11069-012-0432-x
Chen WF, Liu XL (1990) Limit analysis in soil mechanics. Elsevier, Amsterdam, The Netherlands
Choudhury D, Ahmad SM (2007) Stability of waterfront retaining wall subjected to pseudo-static earthquake forces. Ocean Engineering 34(14–15):1947–1954, DOI: https://doi.org/10.1016/j.oceaneng.2007.03.005
Drucker DC, Prager W, Greenberg HJ (1952) Extended limit design theorems for continuous media. Quarterly of Applied Mathematics 9(4):381–389, DOI: https://doi.org/10.1090/qam/45573
Ebeling RM, Morrison EE (1992) The seismic design of waterfront retaining structures. US Army Corps of Engineers, Washington DC, USA
Green WH, Ampt GA (1911) Studies of soil physics, Part I — The flow of air and water through soils. Journal of Agricultual Science 4:1–24, DOI: https://doi.org/10.1017/S0021859600001441
Huang D, Liu J (2016) Upper-bound limit analysis on seismic rotational stability of retaining wall. KSCE Journal of Civil Engineering 20(11):2664–2669, DOI: https://doi.org/10.1007/s12205-016-0471-z
Iverson RM (2000) Landslide triggering by rain infiltration. Water Resources Research 36(7):1897–1910, DOI: https://doi.org/10.1029/2000WR900090
Jo S-B, Ha J-G, Lee J-S, Kim D-S (2017) Evaluation of the seismic earth pressure for inverted T-shape stiff retaining wall in cohesionless soils via dynamic centrifuge. Soil Dynamics and Earthquake Engineering 92:345–357, DOI: https://doi.org/10.1016/j.soildyn.2016.10.009
Leshchinsky D, Ebrahimi S, Vahedifard F, Zhu F (2012) Extension of Mononobe-Okabe approach to unstable slopes. Soils and Foundations 52(2):239–256, DOI: https://doi.org/10.1016/j.sandf.2012.02.004
Li X, Su L, Wu Y, He S (2015) Seismic Stability of gravity retaining walls under combined horizontal and vertical accelerations. Geotechnical and Geological Engineering 33(1):161–166, DOI: https://doi.org/10.1007/s10706-014-9815-y
Li X, Wu Y, He S (2010) Seismic stability analysis of gravity retaining walls. Soil Dynamics and Earthquake Engineering 30(10):875–878, DOI: https://doi.org/10.1016/j.soildyn.2010.04.005
Mononobe N, Matsuo H (1929) On the determination of earth pressure during earthquake. Proceedings of the World Engineering Conference, 177–185
Okabe S (1924) General theory on earth pressure and seismic stability of retaining wall and dam. Journal of Japan Society of Civil Engineers 10(6):1277–1323
Pain A, Choudhury D, Bhattacharyya SK (2017) Seismic rotational stability of gravity retaining walls by modified pseudo-dynamic method. Soil Dynamics and Earthquake Engineering 94:244–253, DOI: https://doi.org/10.1016/j.soildyn.2017.01.016
Ren F, Huang Q, Wang G (2020) Shaking table tests on reinforced soil retaining walls subjected to the combined effects of rainfall and earthquakes. Engineering Geology 267:105475, DOI: https://doi.org/10.1016/j.enggeo.2020.105475
Song J, Fan Q, Feng T, Chen Z, Chen J, Gao Y (2019) A multi-block sliding approach to calculate the permanent seismic displacement of slopes. Engineering Geology 255:48–58, DOI: https://doi.org/10.1016/j.enggeo.2019.04.012
Wilson P, Elgamal A (2015) Shake table lateral earth pressure testing with dense c-ϕ backfill. Soil Dynamics and Earthquake Engineering 71:13–26, DOI: https://doi.org/10.1016/j.soildyn.2014.12.009
Xie M, Esaki T, Cai M (2004) A time-space based approach for mapping rainfall-induced shallow landslide hazard. Environmental Geology 46(6–7):840–850, DOI: https://doi.org/10.1007/s00254-004-1069-1
Yeh P-T, Lee KZ-Z, Chang K-T (2020) 3D effects of permeability and strength anisotropy on the stability of weakly cemented rock slopes subjected to rainfall infiltration. Engineering Geology 266:105459, DOI: https://doi.org/10.1016/j.enggeo.2019.105459
Zeng X, Steedman RS (2000) Rotating block method for seismic displacement of gravity walls. Journal of Geotechnical and Geoenvironmental Engineering 126(8):709–717, DOI: https://doi.org/10.1061/(ASCE)1090-0241(2000)126:8(709)
Zhang C, Chen X, Fan W (2016) Overturning stability of a rigid retaining wall for foundation pits in unsaturated soils. International Journal of Geomechanics 16(4), DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000613
Zhang G, Qian Y, Wang Z, Zhao B (2014) Analysis of rainfall infiltration law in unsaturated soil slope. The Scientific World Journal 2014:1–7, DOI: https://doi.org/10.1155/2014/567250
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Li, X., Liu, J. Seismic Rotational Stability Analysis of Gravity Retaining Wall under Heavy Rainfall. KSCE J Civ Eng 25, 4575–4584 (2021). https://doi.org/10.1007/s12205-021-1623-3
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DOI: https://doi.org/10.1007/s12205-021-1623-3