AASHTO’s ad hoc method (AAM) for predicting free-field soil stress under a rectangular loading area is a simple and very useful tool for the analysis of buried culverts subject to vehicular wheel loads. AAM assumes the surface load spreads with soil depth into an ever-increasing rectangular area whose dimensions are controlled by a constant spread angle θ usually taken as 30°, denoted as AAM-30°. Both simplified and comprehensive culvert analysis procedures utilize AAM predictions for adjusting pressure distributions acting on the culvert periphery. Also, AAM-30° is routinely used to determine the two-wheel soil interaction depth, in which the combined effect of both axial wheels need to be considered. To date, a thorough accuracy analysis of AAM-30° has not been published in the open literature. This paper provides a unique and rigorous evaluation of AAM-30° using an exact solution from an elasticity-based model (EBM) of a homogeneous half-space with rectangular surface load. One key discovery is the depth parameter called y*, which is the soil depth at which AAM-30° peak-stress prediction exactly matches the exact EBM solution. Moreover, it is shown that y* may be determined by a simple, yet accurate formula that only depends on the square root of the load area. However, the investigation reveals that AAM-30° significantly underestimates peak stress in the shallow-depth zone 0 < y < ½y* by as much as 31.3% of the applied surface pressure. As this is a large nonconservative error it cannot be ignored. Accordingly, a very simple modification is introduced called AAM-θ*, in which θ* is a spread angle that linearly increases to 30° at soil depth ½y* and thereafter θ* remains constant at 30°. An accuracy evaluation of AAM-θ* reveals an order of magnitude increase in accuracy in which the small residual error is conservative, not nonconservative. The paper concludes with discussions on applying AAM-θ* to the analysis of buried culverts when using either simple or finite element model solution procedures.

AASHTO 用于预测矩形加载区域下自由场土壤应力的特别方法 (AAM) 是一种简单且非常有用的工具，可用于分析受车辆车轮载荷影响的埋地涵洞。AAM 假设表面载荷随着土壤深度扩展到一个不断增加的矩形区域，其尺寸由恒定的扩展角 θ 控制，通常取为 30°，表示为 AAM-30°。简化和全面的涵洞分析程序都利用 AAM 预测来调整作用在涵洞外围的压力分布。此外，AAM-30°通常用于确定双轮土壤相互作用深度，其中需要考虑两个轴向轮的综合影响。迄今为止，尚未在公开文献中发表对 AAM-30° 的全面准确度分析。本文使用来自具有矩形表面载荷的均匀半空间的基于弹性的模型 (EBM) 的精确解，对 AAM-30° 进行了独特而严格的评估。一个关键发现是称为深度参数y *，这是 AAM-30° 峰值应力预测与精确 EBM 解完全匹配的土壤深度。此外，还表明y * 可以通过一个简单而准确的公式确定，该公式仅取决于负载面积的平方根。然而，调查显示 AAM-30° 显着低估了浅层深度区域 0 < y  < ½ y *中的峰值应力，最多低估 了所施加表面压力的 31.3%。由于这是一个很大的非保守性错误，因此不能忽略。因此，引入了一个非常简单的修改，称为 AAM-θ*，其中 θ* 是在土壤深度 ½ y处线性增加到 30° 的扩展角* 之后 θ* 保持恒定在 30°。AAM-θ* 的准确度评估揭示了准确度的数量级增加，其中小残差是保守的，而不是非保守的。本文最后讨论了在使用简单或有限元模型求解程序时将 AAM-θ* 应用于埋地涵洞分析的讨论。