Abstract
To solve the Earth pressure problems in practical engineering, such as retaining walls and foundation pits, we derive active and passive Earth pressure formulas in accordance with the relationship between intermediate principal stress and excavation under three-dimensional stress states. The formulas are derived on the basis of the Mohr–Coulomb, spatially mobilized plane (SMP), σ 3 SMP, Lade–Duncan, axisymmetric compression- (AC-) SMP strength, and generalized Mises (Gen-Mises) criteria and then extended to clay. We also compare the calculated Earth pressure with the measured data. Results indicate that the Earth pressure considering medium principal stress contribution under a three-dimensional stress state is consistent with the actual engineering. The calculated active Earth pressure in the Mohr–Coulomb strength criterion is larger, and the passive Earth pressure is smaller than the practical one because the intermediate principal stress effect is not considered. The calculated results of the SMP, σ 3 SMP, Lade–Duncan, AC-SMP strength, and Gen-Mises criteria are close to the measured data, among which the result of the Gen-Mises criterion is closer. The Earth pressure calculated using the Lade–Duncan criterion is no longer appropriate to describe the Earth pressure under medium principal stress condition in this study. The results of this study have theoretical significance for retaining structure design under a three-dimensional stress state.
Highlights
The Earth pressure problems of retaining walls and vertical excavation of foundation pits are usually in a three-dimensional stress state. e classical Rankine Earth pressure theory is based on the Mohr–Coulomb strength criterion, only considering the influence of large and small principal stresses on strength and ignoring the contribution of intermediate principal stress. is limitation leads to underrating Earth pressure, which has been confirmed by many experimental results [1]
Most research focuses on the Earth pressure under static load, which can be divided into two categories. e first one regards the retaining structure as a plane strain problem, the intermediate principal stress condition is obtained on the basis of a specific strength criterion in accordance with the deformation conditions and elastic-plastic theory [6,7,8,9], and the general stress state strength theory is introduced into the Earth pressure calculation
We propose the design formulas of active and passive Earth pressures for cohesionless and cohesive soils under three-dimensional stress states. e calculated results are compared with the measured data of sand and clay soil to verify the precision and applicability of the formulas
Summary
The Earth pressure problems of retaining walls and vertical excavation of foundation pits are usually in a three-dimensional stress state. e classical Rankine Earth pressure theory is based on the Mohr–Coulomb strength criterion, only considering the influence of large and small principal stresses on strength and ignoring the contribution of intermediate principal stress. is limitation leads to underrating Earth pressure, which has been confirmed by many experimental results [1]. E second one obtains the Earth pressure under a specific strength criterion in accordance with the empirical or assumed intermediate principal stress conditions under three-dimensional stress states [11,12,13,14,15]. Erefore, a calculation method for Earth pressure in a three-dimensional stress state, considering the contribution of intermediate principal stress and revealing the differences of the results based on various strength criteria, should be established, and its applicability should be studied. 3. Active and Passive Soil Pressures of Cohesive Soils with Various Strength Criteria under a Three-Dimensional Stress State e classical Rankine Earth pressure theory is based on the Mohr–Coulomb strength criterion, disregarding the contribution of intermediate principal stress. En, the result should be integrated into the strength criteria of each three-dimensional stress state, and the relationship between large and small principal stresses of the failure soil can be obtained. Where Ka−SMP (−1 − 3k2 − k22 + k2KSMP − C)/2 + 2k2. e passive Earth pressure is σ3 Ka−SMP cz
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