The Generalized Coefficients of Earth Pressure: A Unified Approach

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.

Multi-Criteria Parametric Verifications for Stability Diagnosis of Rammed-Earth Historic Urban Ramparts Working as Retaining Walls

“…Checking the lateral pressure from the backfill, two methods have been considered among the possibilities currently available [27]: the Coulomb method (Figure 1a), in case of static conditions, and the Mononobe-Okabe method (Figure 1b) for dynamic conditions from seismic events.…”

An Analytical Random Field Solution for the Reliability of Axially Loaded Piles in the Ultimate Limit State Considering the Effect of Soil Sampling

“…The soil is assumed to be normally consolidated. For the sake of simplicity, the effect of the (mobilized) cohesion of soil on the at rest earth pressure coefficient (see Pantelidis [28]) has been neglected, although for axially loaded piles this effect is unfavorable. The adhesion factor is usually mentioned in the literature in the undrained type of analysis (e.g., Das [29]), however, in the present paper, it is mentioned in the general case.…”

“…Now, if PF refers to the optimal sampling point, the F PF (that is, the safety factor for a given level of failure probability) can be calculated in terms of the parameters Θ, Λ, and cov u . One should recall that the optimal depth is given by Equation (28). Then, F PF is the minimum required safety factor to achieve the desired probability of failure (optimal safety factor value for the given probability of failure).…”

“…It is also mentioned that the internal mechanics of the body of the soil away from the pile is neglected; this is a widely used assumption, especially when the problem is investigated from the 1D numerical point of view (e.g., [25][26][27]). Although this assumption looks crude, it is rather valid as, as shown by Pantelidis [28], the active earth pressure and the at rest earth pressure on a retaining structure are exerted from the same soil wedge; as known, the at rest state of soil is commonly used for the calculation of the shaft resistance of piles due to friction. In addition, Christodoulou et al [3] showed numerically that the optimal sampling location in the case of retaining walls in the active state is at zero distance from the wall face (the same authors [4] showed that the optimal sampling distance in the problem of retaining walls in the passive state is half wall height away from the wall face).…”

“…Λ versus z s /L chart for different Θ values; chart drawn using Equation(28), while Λ has been defined in Equation(7).…”