Abstract In a centrifuged model, the centrifugal acceleration increases radially outward from the axis of rotation. The variations in the magnitude and direction of the centrifugal acceleration will inevitably result in a distortion of the stress field of the model compared with its desired prototype counterpart. This distortion alone is generally considered to be slight and negligible, but the extent of its impact on the accuracy of the centrifuge modeling of the soil slope instability is yet unknown. To answer this question, analytical solutions for a generally shaped critical slip surface and its normal stress distribution are derived for a plane-strain model slope by using a variational limiting equilibrium approach, without a need for arbitrary kinematic and static assumptions. Their validities are verified by comparing the extreme cases of the proposed solutions with available analytical solutions for the slope instability under the Earth's gravity condition. The proposed solutions are also validated by a well-documented centrifuge study of the slope instability with slip surface measurements, and reasonably good agreement is obtained. A parametric study is carried out by using the proposed solutions. The computed results for the model slopes are compared with those for the corresponding prototype slopes. The comparison shows that when the cross section of the model slope is radially oriented to the axis of rotation, the variation in the magnitude of the centrifugal acceleration alone has a negligible influence on the slope instability. When the cross section of the model slope is tangentially oriented to the circumference of the rotation of the centrifuge, however, the radial acceleration is shown to have a potentially important influence on the similitude of the slope instability. An optimum location of a model slope in a model container for the minimal effect of the radial acceleration can be determined by using the proposed solutions.

中文翻译：

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径向加速度对边坡失稳离心建模影响的理论分析

摘要 在离心模型中，离心加速度从旋转轴径向向外增加。离心加速度的大小和方向的变化将不可避免地导致模型的应力场与其所需的原型对应物相比发生畸变。这种畸变通常被认为是轻微的和可以忽略不计的，但其对土坡失稳离心建模精度的影响程度尚不清楚。为了回答这个问题，通过使用变分极限平衡方法，无需任意的运动学和静态假设，就可以为平面应变模型斜率推导出一般形状的临界滑移面及其法向应力分布的解析解。通过将所提出的解的极端情况与地球重力条件下边坡失稳的可用解析解进行比较，验证了它们的有效性。所提出的解决方案也通过滑面测量的边坡不稳定性离心机研究得到验证，并且获得了相当好的一致性。使用所提出的解决方案进行参数研究。将模型斜率的计算结果与相应原型斜率的计算结果进行比较。比较表明，当模型斜坡的横截面沿径向朝向旋转轴时，仅离心加速度大小的变化对斜坡失稳的影响可以忽略不计。然而，当模型斜坡的横截面与离心机旋转的圆周相切时，径向加速度显示出对斜坡不稳定性的相似性具有潜在的重要影响。通过使用所提出的解决方案，可以确定模型容器中模型斜率在径向加速度影响最小的最佳位置。