Mmax values versus x1 / H, φ and Ls.

The behavior of a sheet pile wall constructed on saturated sand soil and exposed to a distant surcharge load with a finite length at the top of the backfill soil is examined in this study. For this aim, various internal friction angles (φ), and natural ground surface for the groundwater level are considered. Furthermore, it is considered that the sheet pile wall acts as cantilevered and supports a six-meter-high (H) excavation. The simple “45° distribution” (AP) and uniform distribution of “Beton Kalender distribution” (BK) methods are examined with Coulomb’s and Rankine’s earth pressure theories in analytical solutions, while the finite element method (FEM) is used as a numerical method. The present research has two primary goals: a) determining the best analytical approach that provides the maximum bending moment (Mmax) values that are more comparable to those of the FEM b) examining the behavior of the sheet pile wall considering several effects of load scenarios, depth (D) and section type (ST) of the wall, and the soil properties together. In this context, parametrical analyses are performed. Consequently, it is found that the distance of the surcharge load (x1) has a pronounced effect than the intensity (q) and length (Ls) of the surcharge load on the behavior of the sheet pile, and this effect vanishes for the large values of x1. Furthermore, Coulomb theory provides more convenient values with FEM for Mmax than those obtained from Rankine theory. The Mmax values obtained from FEM are generally less than those from BK, while they are greater than those from APC.本研究针对饱和砂土（saturated sand soil）中修建、回填土（backfill soil）顶部受有限长度远端附加荷载（surcharge load）作用的板桩墙（sheet pile wall）的受力性状展开分析。为此，本研究考虑了多种内摩擦角（internal friction angle，φ）以及对应不同地下水位的天然地表工况。此外，假定该板桩墙为悬臂式结构，支撑6米高（H）的开挖基坑。解析解层面，分别采用库仑（Coulomb）与朗肯（Rankine）土压力理论，对简化的“45°分布法（AP）”与“Beton Kalender分布法（BK）”两种均布荷载分布模式进行验证；数值解法则采用有限元法（Finite Element Method, FEM）。本研究的核心目标有二：其一，筛选出可给出与有限元法结果最为匹配的最大弯矩（maximum bending moment, Mmax）值的最优解析方法；其二，综合考量荷载工况、墙体埋深（depth, D）与截面类型（section type, ST）以及土体特性等多因素，探究板桩墙的受力性状。为此，本研究开展了参数化分析（parametrical analyses）。研究结果表明：附加荷载的作用距离（x₁）对板桩墙受力性状的影响显著大于荷载强度（q）与荷载长度（Ls），且当x₁取值较大时，该影响会逐渐消失。此外，相较于朗肯土压力理论，库仑土压力理论得到的最大弯矩值与有限元法的结果更为吻合。有限元法得到的最大弯矩值整体上小于Beton Kalender分布法的计算结果，却大于“45°分布法（APC）”的计算结果。