Closed-Form Formulation for Continuous Prediction of At-Rest Coefficient for Saturated Soils


The at-rest lateral earth pressure coefficient, which is called the k0 coefficient, is an important parameter in geotechnical engineering. An accurate evaluation of k0 is of great significance in both theoretic analyses and practical geotechnical applications. Existing analytical formulations for k0 suffer one or more of the following limitations: (1) they have one or more unrealistic assumptions; (2) k0 is derived as a constant for the very high stress state only, but implicitly applied to the entire stress range; and (3) the k0 equation is often implicit and complicated, and it may require advanced mathematical and computational analysis. This paper provides a simple, explicit formulation to predict continuous changes of the at-rest earth pressure (k0) coefficient as a function of stress for any critical state constitutive model for saturated soils without any assumption. The modified Cam-clay (MCC) model is used as an example to demonstrate the application of the proposed formulation. Procedures are developed to calibrate the model parameters for the MCC model using experimental results from the literature. The continuous changes of the k0 coefficient are then computed during one-dimensional consolidation tests from which the effectiveness and simplicity of the proposed formulation are evaluated. Calculations indicate that a coefficient of determination around 99% is reached between the measured and predicted void ratios.


Civil, Architectural and Environmental Engineering

Research Center/Lab(s)

Center for Research in Energy and Environment (CREE)

Keywords and Phrases

At-rest coefficient; Constitutive modeling; Elastoplastic; Modified Cam-clay model (MCC); Odometer test; Stress path

International Standard Serial Number (ISSN)

1532-3641; 1943-5622

Document Type

Article - Journal

Document Version


File Type





© 2019 American Society of Civil Engineers (ASCE), All rights reserved.

Publication Date

01 Jul 2019