Abstract Free fall projectiles have been used in offshore engineering to determine in-situ undrained shear strength profiles of near-surface soft soils from accelerations recorded during penetrating. In doing so, however, only the equation of motion in the vertical direction has been formulated with the vertical acceleration by assuming vertical impact and penetration. In this study, the governing equations of curvilinear penetration of a sphere projectile are established with consideration of an angle of impact with soil surface. By treating the penetration process as an initial value problem, an algorithm is proposed for computing the trajectory, velocity and linear acceleration of penetration. The effects of impact angle, impact velocity and soil strength non-homogeneity on the penetration behavior are analyzed using a set of parameters reported in literature. The computed results of the final embedment depth and linear acceleration of sphere are shown to be in reasonably good agreement with published field data. Moreover, a new explicit equation is derived for determining the undrained shear strength of soil based on both vertical and horizontal linear accelerations. The accuracy of the undrained shear strength estimated by assuming vertical penetration is assessed. The impact angle is shown to have important influence on soil strength determination.

中文翻译：

---

自由落体球体弹丸在软土中曲线穿透的简化分析

摘要 自由落体弹丸已被用于海上工程，根据穿透过程中记录的加速度确定近地表软土的原位不排水剪切强度剖面。然而，在这样做时，通过假设垂直冲击和穿透，只有垂直方向的运动方程与垂直加速度一起被公式化。在本研究中，考虑与土壤表面的撞击角度，建立了球形弹丸的曲线穿透控制方程。将穿透过程视为初值问题，提出了一种计算穿透轨迹、速度和线加速度的算法。冲击角度的影响，使用文献中报告的一组参数分析了冲击速度和土壤强度对穿透行为的非均匀性。球体的最终嵌入深度和线性加速度的计算结果与公布的现场数据相当吻合。此外，推导出了一个新的显式方程，用于基于垂直和水平线性加速度确定土壤的不排水剪切强度。评估通过假设垂直穿透估计的不排水剪切强度的准确性。研究表明，冲击角度对土壤强度的测定有重要影响。推导出了一个新的显式方程，用于根据垂直和水平线性加速度确定土壤的不排水剪切强度。评估通过假设垂直穿透估计的不排水剪切强度的准确性。研究表明，冲击角度对土壤强度的测定有重要影响。推导出了一个新的显式方程，用于根据垂直和水平线性加速度确定土壤的不排水剪切强度。评估通过假设垂直穿透估计的不排水剪切强度的准确性。研究表明，冲击角度对土壤强度的测定有重要影响。