剛性擋墻位移土壓力的數學擬合公式研究綜述

張常光 單冶鵬 高本賢 吳凱

摘 要：在研究土壓力與擋墻位移關系時，可采用數學擬合方法表征土壓力隨擋墻位移的變化規律。數學擬合方法常以靜止土壓力、主/被動土壓力為基礎，通過構造數學函數來描述擋墻位移土壓力，但所采用的數學函數形式各不相同。將擋墻位移土壓力的數學擬合公式按函數形式分為：三角函數、指數函數、雙曲線函數、冪函數、S型函數以及其他函數等6大類，總結了位移土壓力數學擬合公式的特點與不足，并指出需進一步研究的方向。結果表明：數學擬合公式的主要差異在于函數形式選擇和待定參數及取值不同，導致了數學擬合公式的多樣性與研究的廣泛性。合理實用的位移土壓力數學擬合公式需具備3方面特征：邊界條件與初值滿足、參數含義明確以及能反映擋墻與土體之間的相互作用。在試驗方面，應持續對擋墻不同位移模式開展針對性研究，并進行黏性土、非飽和土、濕陷性黃土、膨脹土等的土壓力試驗;在理論計算方面，應加強位移土壓力數學擬合公式間對比分析，探究各自的合理性及適用性，揭示土壓力與擋墻位移關系的內在機理。拓展對非飽和土擋墻的位移土壓力研究，完善參數選擇、模型驗證，以加快工程應用進程。

關鍵詞：擋墻位移;位移土壓力;數學擬合公式;位移模式;非飽和土

中圖分類號：TU432 文獻標志碼：R 文章編號：2096-6717（2020）06-0019-12

Abstract： 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.

Keywords：displacement of retaining walls; displacement-dependent earth pressure; mathematical fitting; movement mode; unsaturated soil

土壓力大小及其分布在擋墻和地下設施設計中占有十分重要的地位，Coulomb、Rankine基于擋墻平移極限狀態建立了土壓力公式并形成兩類經典極限土壓力理論，文獻[1-4]對經典極限土壓力理論進行了擴展研究。……