二次拋物線型強度準則下黃土主動土壓力計算

關曉迪 曹周陽 馬迪 朱勇鋒 何盛東

摘 要：為了解決基于Mohr-Coulomb強度理論求解出的黃土主動土壓力往往偏離實際的問題，本文基于二次拋物線型強度準則，通過對墻后填土展開主動極限平衡狀態分析，推導了基于二次拋物線準則的黃土主動土壓力解析解。研究結果表明：基于二次拋物線型強度準則的黃土主動土壓力呈非線性分布，在填土拉張區其主動土壓力值小于朗肯主動土壓力值，且基于二次拋物線型強度準則的填土拉張區開裂深度明顯小于基于Mohr-Coulomb理論的拉張區開裂深度;在填土壓剪區，填土深度越大則其所受圍壓越大，基于二次拋物線型強度準則的主動土壓力明顯大于朗肯主動土壓力。因此，在應力水平較大或負應力水平時，基于二次拋物線型強度準則的黃土主動土壓力更貼近實際。

關鍵詞：黃土;抗拉強度;內摩擦角;二次拋物線型強度準則

中圖分類號：TU43 ? ? 文獻標識碼：A ? ? 文章編號：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

擋土墻土壓力計算是支護結構設計的主要依據之一[1]。基于不同強度理論的擋土結構的土壓力計算也是不同的，應用最為廣泛的經典土壓力理論是基于Mohr-Coulomb強度理論得出的，然而采用Mohr-Coulomb強度理論對工程案例中土壓力進行研究往往有其局限性，使得土壓力的計算結果偏離實際。因此，現階段土壓力理論的相關研究仍然是巖土工程的熱門問題。

蔣莼秋[2]基于卡崗的研究成果，推導出擋土墻后填土面為水平、墻背坡度取隨機值時的土壓力非線性解。謝群丹等[3]通過對擋土結構與土進行空間相互作用分析，推導了黏性土與無黏性土的主動與被動土壓力統一解。范文等[4]通過采用塑性極限上限分析法，推導了基于統一強度理論的土壓力計算公式。張常光等[5]合理考慮中間主應力效應，推導了非飽和土雙應力狀態變量抗剪強度統一解。馬林等[6]提出了結構性對黃土力學和變形特性影響的適用表達式。上述研究基于不同的強度理論，發展和完善了擋土結構土壓力計算。