二次抛物线型强度准则下黄土主动土压力计算

关晓迪 曹周阳 马迪 朱勇锋 何盛东

摘 要：为了解决基于Mohr-Coulomb强度理论求解出的黄土主动土压力往往偏离实际的问题，本文基于二次抛物线型强度准则，通过对墙后填土展开主动极限平衡状态分析，推导了基于二次抛物线准则的黄土主动土压力解析解。研究结果表明：基于二次抛物线型强度准则的黄土主动土压力呈非线性分布，在填土拉张区其主动土压力值小于朗肯主动土压力值，且基于二次抛物线型强度准则的填土拉张区开裂深度明显小于基于Mohr-Coulomb理论的拉张区开裂深度;在填土压剪区，填土深度越大则其所受围压越大，基于二次抛物线型强度准则的主动土压力明显大于朗肯主动土压力。因此，在应力水平较大或负应力水平时，基于二次抛物线型强度准则的黄土主动土压力更贴近实际。

关键词：黄土;抗拉强度;内摩擦角;二次抛物线型强度准则

中图分类号：TU43     文献标识码：A     文章编号：1003-5168（2021）21-0071-03

Calculation of Active Earth Pressure of Loess based On Quadratic Parabolic Strength Criterion

GUAN Xiaodi1    CAO Zhouyang2    MA Di1    ZHU Yongfeng3    HE Shengdong2

（1. Institute of Geotechnical Engineering， Xi'an University of Technology， Xi'an Shaanxi 710048;

2. School of Civil Engineering and Architecture， Zhengzhou University of Aviation Industry Management， Zhengzhou Henan 50046;3. School of Geoengineering and Surveying and Mapping， Chang'an University， Xi 'an Shaanxi 710048）

Abstract： In order to solve the problem that the active earth pressure of loess calculated based on Mohr-Coulom strength theory often deviates from the reality. In this paper， based on the quadratic parabolic strength criterion， the analytical solution of the active earth pressure of loess based on the quadratic parabolic criterion is derived by analyzing the active limit equilibrium state of the backfill. The results show that the active earth pressure of the loess is non- linear based on the quadratic parabolic strength criterion. The active earth pressure is less than that of Rankine in the filling tension area. The crack depth based on quadratic parabolic strength criterion is obviously smaller than that based on Mohr-Coulomb theory. In the compression and shear zone of filling， the greater filling depth is， the greater the confining pressure is， and the active earth pressure based on the quadratic parabolic strength criterion is obvious- ly greater than the active earth pressure of Rankine. Therefore， when the stress level is large or negative， the active earth pressure of loess based on the quadratic parabolic strength criterion is more practical.

Keywords： loess; tensile strength; angle of internal friction; quadratic parabolic strength criterion

擋土墙土压力计算是支护结构设计的主要依据之一[1]。基于不同强度理论的挡土结构的土压力计算也是不同的，应用最为广泛的经典土压力理论是基于Mohr-Coulomb强度理论得出的，然而采用Mohr-Coulomb强度理论对工程案例中土压力进行研究往往有其局限性，使得土压力的计算结果偏离实际。因此，现阶段土压力理论的相关研究仍然是岩土工程的热门问题。

蒋莼秋[2]基于卡岗的研究成果，推导出挡土墙后填土面为水平、墙背坡度取随机值时的土压力非线性解。谢群丹等[3]通过对挡土结构与土进行空间相互作用分析，推导了黏性土与无黏性土的主动与被动土压力统一解。范文等[4]通过采用塑性极限上限分析法，推导了基于统一强度理论的土压力计算公式。张常光等[5]合理考虑中间主应力效应，推导了非饱和土双应力状态变量抗剪强度统一解。马林等[6]提出了结构性对黄土力学和变形特性影响的适用表达式。上述研究基于不同的强度理论，发展和完善了挡土结构土压力计算。