Theoretical Analysis of Pressure-Dependent K₀ for Normally Consolidated Clays Using Critical State Soil Models

The coefficient of earth pressure at rest (K0) for normally consolidated clays increases nonlinearly with increasing consolidation pressure toward a steady value under high pressure rather than remaining constant. Analytical expressions for evaluating pressure-dependent K0 were derived from three representative critical state soil models: modified Cam-clay model (MCC), original Cam-clay model (OCC), and clay and sand model (CASM). In formulations, the authors relaxed a well-adopted assumption that stress ratio is kept constant during one-dimensional (1D) compression. It is found that the constant stress ratio, corresponding to the well-adopted assumption, is essentially a limit value of the stress ratio as predicted by MCC and CASM under high pressure during 1D compression. The predicted relationship between K0 and consolidation pressure is significantly affected by the critical state stress ratio. Without considering the effect of high pressure, the value of K0 may be considerably underestimated. The results predicted by the proposed formula based on CASM agree well with experimental data, showing the capability of this formula for predicting pressure-dependent K0.