Abstract
This paper offers an extension of Cauchy’s first law of motion to deformable bodies with internal resistance with application to earth pressures. In this respect, a unified continuum mechanics approach for deriving earth pressure coefficients for all soil states, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions is proposed. Adopting Jaky’s (1944) sand heap hypothesis, modified suitably to accommodate the needs of the present research, the analysis led to generalized, yet remarkably simple in form, expressions for the “at rest”, active and passive earth pressure coefficients. The validity of the proposed coefficients is strongly supported by the fact that, under static conditions they are transformed into the well-known Rankine’s expressions for cohesive-frictional soils for the active and passive state. Comparisons with widely used solutions (e.g., Rankine’s and Mononobe–Okabe’s), design code practices (Eurocode 8-5; AASHTO), and results from centrifuge tests further support the validity of the proposed coefficients. In the framework of the present work, analytical expressions for the calculation of the depth of neutral zone in the state “at rest”, the depth of tension crack in the active state, the required wall movement for the mobilization of the active or passive state, as well as the mobilized shear strength of soil (for all states) are also given. Finally, following the proposed approach, the earth pressure can be calculated for any intermediate state between the state “at rest” and the active or passive state when the allowable wall movement is known.
Highlights
The earth pressure problem dates from the beginning of the 18th century, when Gautier [1] listed five areas requiring research, one of which was the dimensions of gravity-retaining walls needed to hold back soil
From the purely theoretical point of view, the very simple 1 − sin φ0 formula, works ideally for the two extreme values of φ0, where for φ0 = 0o it gives Ko = 1 referring to hydrostatic conditions and for φ0 = 90o it gives Ko = 0 referring to a frictional material that can stand vertically without support, exerting no lateral pressure
Re-evaluating the above expression, the procedure for the active case will have as follows: first, σh,Finn is replaced by Equation (10) and the term (μ/(1 − μ))γz by Equation (16); solving as for ∆x, the required displacement for the active state to fully develop at depth z will be:
Summary
The earth pressure problem dates from the beginning of the 18th century, when Gautier [1] listed five areas requiring research, one of which was the dimensions of gravity-retaining walls needed to hold back soil. Except for the above widely adopted solutions, numerous other evidential, closed-form, limit analysis, limit equilibrium, discrete spring model, and continuum model approaches have been proposed by various researchers for the calculation of the active and passive earth pressure. The present paper offers an extension of Cauchy’s first law of motion to deformable bodies with internal resistance with application to earth pressures In this respect, a unified continuum mechanics approach for deriving earth pressure coefficients for all soil states, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions is proposed. A unified continuum mechanics approach for deriving earth pressure coefficients for all soil states, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions is proposed In this framework, Jaky’s [11]. Soil heap hypothesis will be adopted, for the derivation of generalized coefficients of earth pressure for all soil states, i.e., at rest, active, and passive
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