刚性挡墙位移土压力的数学拟合公式研究综述

在研究土压力与挡墙位移关系时，可采用数学拟合方法表征土压力随挡墙位移的变化规律。数学拟合方法常以静止土压力、主/被动土压力为基础，通过构造数学函数来描述挡墙位移土压力，但所采用的数学函数形式各不相同。将挡墙位移土压力的数学拟合公式按函数形式分为：三角函数、指数函数、双曲线函数、幂函数、S型函数以及其他函数等6大类，总结了位移土压力数学拟合公式的特点与不足，并指出需进一步研究的方向。结果表明：数学拟合公式的主要差异在于函数形式选择和待定参数及取值不同，导致了数学拟合公式的多样性与研究的广泛性。合理实用的位移土压力数学拟合公式需具备3方面特征：边界条件与初值满足、参数含义明确以及能反映挡墙与土体之间的相互作用。在试验方面，应持续对挡墙不同位移模式开展针对性研究，并进行黏性土、非饱和土、湿陷性黄土、膨胀土等的土压力试验；在理论计算方面，应加强位移土压力数学拟合公式间对比分析，探究各自的合理性及适用性，揭示土压力与挡墙位移关系的内在机理。拓展对非饱和土挡墙的位移土压力研究，完善参数选择、模型验证，以加快工程应用进程。

State-of-the-art review on displacement-dependent earth pressure formulations of rigid retaining walls via mathematical fitting functions

Variation laws of earth pressure accounting for the displacement of a retaining wall can be well described by mathematical fitting, which is usually based on the earth pressure at rest or the active and passive earth pressures to illustrate the displacement-earth pressure of retaining walls through constructing various mathematical functions. This study subdivides displacement-dependent earth pressure formulations into six categories according to different functional forms, including trigonometric, exponential, hyperbolic, power, sigmoid and other functions. Characteristics and deficiencies of displacement-dependent earth pressure formulations are summarized, and future researches are provided. The findings of this study show that main differences of mathematical fitting are attributed to determination of function forms as well as undetermined parameters as well as their magnitudes, which results in the uncertainty of mathematical fitting and the generallity of research. A reasonable and practical mathematical fitting function has three features:boundary condition and initial value satisfied, parameters with clear meaning and representing the interaction between a retaining wall and soils. In terms of test studies, it is necessary to perform targeted research on different movement modes of a retaining wall, and model tests of earth pressure are conducted on clay, unsaturated soil, collapsible loess, expansive soil, among others. In terms of theoretical calculations, displacement-dependent earth pressure formulations using different mathematical fitting functions are compared to explore their rationality and applicability as well as to reveal intrinsic mechanisms between earth pressure of a retaining wall and its displacement. Displacement-dependent earth pressure of a retaining wall in unsaturated soil needs to be paid more attention. The choice and measurement of different parameters are improved and validated by model tests in order to accelerate the process of engineering applications for mathematical fitting functions.