确定前期固结压力的一个简单数学模型

前期固结压力是判断土应力历史的最常用指标。为能够更加准确地确定前期固结压力，首先将超固结土压缩线上曲率最大时所对应的竖向应力引入到单对数坐标中，建立正常固结土和超固结土统一的一维压缩线方程。然后，基于该方程严格推导出前期固结压力的计算式。该计算式是一个显式函数，无需采用编程计算，且只需土的压缩指数Cc及一维压缩线的渐进线在单对数坐标中的纵轴截距N两个常见参数，便于工程师应用。最后，通过两个算例验证所提数学模型的合理性。

A simple mathematic model for determining preconsolidation pressure

Preconsolidation pressure is a common index of stress history. In order to determine the preconsolidation pressure accurately, an expression of one-dimensional compression line was proposed firstly by introducing the vertical stress corresponding to the maximum curvature in the single logarithmic coordinate. The new expression is a unified expression of soil because it can describe the compression lines of both normal consolidated soil and overconsolidated soil. Secondly, an explicit formulation of preconsolidation pressure was derived based on the new expression. The new explicit formulation requires only two parameters, and so can be easily used by engineers. Finally, comparisons with the experimental results illustrate that the mathematical model can accurately determine the preconsolidation pressure of soil.