Abstract
In the area of high seismic intensity, there were few methods for calculating active earth pressure (Ea). Especially for the cantilever retaining wall with long relief shelf (CRW-LRS), the theoretical method lags behind the practical engineering. The seismic active earth pressure (ES) of the CRW-LRS subject to translational mode was researched. By finite element method (FEM), the failure mode of the active limit state under seismic load was evaluated. The results show that the backfill behind the wall generates the first sliding surface at the wall heel bottom, the second at the wall heel top, and the third at the relief shelf top. The calculation formula of ES under long relief shelf failure mode was proposed using the limit analysis method of a horizontal differential layer. The calculation results were compared with the FEM results to prove the rationality and reliability of the theoretical solution. The effects of relief shelf relative length (l) and position (m), wall heel length (n), internal frictional angle of the backfill (φ), seismic horizontal acceleration (ah), and seismic vertical acceleration (aV) on ES were studied.
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Abbreviations
- a h :
-
Horizontal seismic acceleration (m2/s)
- a v :
-
Vertical seismic acceleration (m2/s)
- b :
-
Length of relief shelf (m)
- b 1 :
-
Length of wall toe bottom plate (m)
- b 2 :
-
Thickness of vertical arm (m)
- b 3 :
-
Length of wall heel (m)
- c :
-
Cohesion of backfilled soil (kPa)
- C F :
-
Cohesion of foundation soil (kPa)
- dw :
-
Self-weight of horizontal differential element (kN)
- E :
-
Earth pressure resultant force of retaining wall (kN)
- E a :
-
Active earth pressure
- E F :
-
Compression modulus of foundation soil (MPa)
- E s :
-
Seismic active earth pressure
- E S :
-
Compression modulus of backfilled soil (MPa)
- e w :
-
Elastic modulus of retaining wall (MPa)
- H :
-
Height of retaining wall (m)
- H′:
-
Height of retaining wall vertical arm (m)
- H 1 :
-
Location of relief shelf (m)
- H 4 :
-
Thickness of wall heel (m)
- k 1 :
-
Coefficient of normal earth pressure on region I
- k 2 :
-
Coefficient of normal earth pressure on region II
- k 3 :
-
Coefficient of normal earth pressure on region III
- k h :
-
Horizontal seismic acceleration coefficient
- k v :
-
Vertical seismic acceleration coefficient
- l :
-
Relative length of relief shelf
- m :
-
Relative height of upper wall
- n :
-
Relative length of wall heel
- q′:
-
Upper additional load on region III (kPa)
- v :
-
Poisson’s ratio of backfilled soil
- V F :
-
Poisson’s ratio of foundation soil
- V W :
-
Poisson’s ratio of retaining wall
- Z 1 :
-
Unloading effect’s influence range (m)
- Z E :
-
Distance between the operating point of the earth pressure resultant force and the wall top (m)
- α 1 :
-
First sliding surface inclination (°)
- α 2 :
-
Second sliding surface inclination (°)
- α 3 :
-
Third sliding surface inclination (°)
- δ :
-
Friction of the soil–wall interface (°)
- γ :
-
Unti weight of backfilled soil (kN/m3)
- γ F :
-
Unti weight of foundation soil (kN/m3)
- γ W :
-
Unti weight of retaining wall (kN/m3)
- φ :
-
Internal friction angle of backfilled soil (°)
- φ F :
-
Internal friction angle of foundation soil (°)
- σ r :
-
Normal stresses of first sliding surface (kPa)
- σ s1 :
-
Normal stresses of third sliding surface (kPa)
- σ v :
-
Vertical stress (kPa)
- σ v1 :
-
Vertical stress on region I (kPa)
- σ ′v1 :
-
Vertical stress imposed by region I on region II (kPa)
- σ v2 :
-
Vertical stress on region II (kPa)
- σ ′v2 :
-
Vertical stress imposed by region II on region III (kPa)
- σ v3 :
-
Vertical stress on region III (kPa)
- σ ′v3 :
-
Vertical stress imposed by region III on region IV (kPa)
- σ v31 :
-
Vertical stress in unloading effect’s influence range (kPa)
- σ v4 :
-
Vertical stress on region IV (kPa)
- σ w1 :
-
Horizontal stress on region I (kPa)
- σ w2 :
-
Horizontal stress on region II (kPa)
- σ v31 :
-
Horizontal stress in unloading effect’s influence range (kPa)
- σ w3 :
-
Horizontal stress on region III (kPa)
- σ w4 :
-
Horizontal stress on region IV (kPa)
- τ s1 :
-
Tangential stresses of third sliding surface (kPa)
- τ w2 :
-
Tangential stresses on region II (kPa)
- τ r :
-
Tangential stresses of first sliding surface (kPa)
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Que, Y., Long, Cc. & Chen, Fq. Seismic Active Earth Pressure of Infinite Width Backfilled Soil on Cantilever Retaining Wall with Long Relief Shelf under Translational Mode. KSCE J Civ Eng 27, 3285–3299 (2023). https://doi.org/10.1007/s12205-023-1194-6
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DOI: https://doi.org/10.1007/s12205-023-1194-6