Three-Dimensional Active Earth Pressures for Unsaturated Backfills with Cracks Considering Steady Seepage
Publication: International Journal of Geomechanics
Volume 23, Issue 2
Abstract
Traditional analyses for active earth pressures considered soils dry or saturated by the application of a two-dimensional (2D) failure pattern. However, soils are usually unsaturated in nature, and the collapse of backfills presents a three-dimensional (3D) characteristic. The extant studies proved that the existence of cracks and seepage flow encountered in backfills would impact active earth pressures but are still limited to 2D conditions. To this end, this study developed an analytical framework to evaluate the 3D active earth pressure considering the presence of cracks and steady-infiltration effects within unsaturated backfills. Based on the kinematic approach of limit analysis, a suction-induced effective method is introduced into a 3D failure mechanism to characterize the collapse of unsaturated backfills. By means of the work rate balance equation, the most adverse location of cracks and the explicit expression of active thrust under steady seepage conditions can be obtained through the incorporation of the suction stress profile. The presented method is verified by comparison with the exact cases in previous studies and comparison with the results of numerical simulation. A systematic parametric study is conducted to reveal the impacts of width-to-height ratio, air-entry value, pore-size distribution, vertical discharge, and cracks on the active earth pressure variations. The results show that considering 3D effects is significant because it leads to a lower economic cost for the design of retaining walls; the presence of cracks and the effect of steady infiltration encountered in unsaturated backfills would increase the lateral force of earthen structures. This study presented a more realistic understanding of the service state behavior of retaining walls and a useful strategy for evaluating the 3D active earth pressure.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request, including the following:
1.
The detailed data of Figs. 2 and 7–11;
2.
The MATLAB code of the proposed procedure.
Notation
The following symbols are used in this paper:
- A
- loaded boundary;
- Ar
- stressed area imposed by active earth pressure;
- B
- width of the retaining wall;
- B/H
- width-to-height ratio;
- Be
- equivalent width;
- maximum width of the rotational mechanism;
- b
- width of the plane insert portion;
- capp
- apparent cohesion;
- c′
- effective cohesion;
- c′/γH
- normalized soil cohesion;
- Dc
- internal dissipated energy due to the soil effective cohesion;
- internal dissipated energy due to the apparent cohesion;
- , , , , ,
- D is the internal dissipated energy. The subscript c′ represents the work rates generated by the effective cohesion; 3D and insert represent different portions of the failure mechanism, respectively. The superscripts represent the area of the slip surface;
- d1
- distance between the rotation center with the slip surface;
- Fi
- vector of body force;
- , , ,
- dimensionless functions;
- H
- wall height;
- Ka
- active earth pressure coefficient;
- ks
- saturated hydraulic conductivity;
- L
- length of AD;
- L′
- length of AB;
- n
- pore-size distribution;
- O
- rotation center;
- Pa
- active earth pressure;
- q
- vertical specific discharge;
- R
- radius of the curvilinear cone mechanism;
- r0
- length of OA;
- length of OA′;
- rm
- distance from the axis of a curvilinear cone to a rotation point;
- Ti
- vector of the surface force;
- ua
- pore-air pressure;
- uw
- pore-water pressure;
- ua − uw
- matric suction;
- velocity vector;
- V
- volume;
- external work rates generated by the active earth pressure;
- external work rates generated by the soil weight;
- Wγ−3D, , , Wγ−insert, ,
- W is the external work rate. The subscript γ represents the work rates generated by the soil unit weight; 3D and insert represent different portions of the failure mechanism, respectively. The superscripts represent the volume of failure block;
- z0
- interval between the base and the water table;
- z
- vertical interval above the water table;
- 1/α
- air-entry value;
- β
- inclination angle of the wall back;
- χ
- degree of saturation (0–1);
- δ
- general angle to specify the slip surface in the rotational plane, as illustrated in Fig. 3;
- δw
- wall interface friction angle;
- δ1, δ2
- boundary of the general angle δ;
- strain rate;
- γ
- soil unit weight;
- γw
- unit weight of water;
- γH/c
- normalized critical height;
- ω
- angular velocity;
- φ′
- effective internal frication angle;
- σs
- suction stress;
- σ′
- effective stress;
- σ
- total stress;
- (σ − ua)
- net normal stress;
- stress tensor;
- τ
- shear strength;
- θ
- general angle between θ0 and θh; and
- θ0, θh, θB, θC, θD
- angles to describe the 3D failure mechanism, which are illustrated in Fig. 3.
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History
Received: Jan 5, 2022
Accepted: Aug 29, 2022
Published online: Nov 16, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 16, 2023
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