This work presents a spherical cavity expansion solution aimed at linking soil constitutive behavior with quantities that bear direct engineering meanings for practicing engineers (e.g., foundation bearing capacity). For this purpose, we derive the solution based on the state-dependent, critical state constitutive model proposed by Li and Dafalias (Geotechnique 50(4): 449–460, 2000), whose ability to realistically represent the actual mechanical behavior of sand has been extensively verified in the literature. To ensure the reliability of the solution, we verify it against an independent finite element analysis of spherical cavity expansion in solid governed by the same constitutive model. In this validation, we also highlight the dependence of cavity expansion response on the current state of granular materials relative to critical state. The application of the proposed solution in solving engineering problems is demonstrated in predicting the resistance of cone penetration and the ground movements associated with static pipe bursting in sand. We show that, based on the soil parameters determined from laboratory triaxial tests, the proposed solution can reasonably represent the dependence of cone penetration resistance on the density and pressure level of sand, as revealed from centrifuge testing. By comparing with finite element analysis, we demonstrate that the proposed solution can provide useful estimations for soil displacements caused by pipe bursting operation. These archetypal examples suggest that the proposed cavity expansion solution can form a theoretical basis for linking fundamental soil properties with quantities that have direct implications for geotechnical engineering practice.

这项工作提出了一种球形空腔扩张解决方案，旨在将土壤的本构行为与对工程实践工程师具有直接工程意义（例如，地基承载力）的量联系起来。为此，我们基于Li和Dafalias提出的状态相关的临界状态本构模型（Geotechnique 50（4）：449–460，2000）推导了该解决方案，该模型能够真实地表示砂子的实际力学行为，在文献中得到了广泛的验证。为了确保该解决方案的可靠性，我们针对由相同本构模型控制的固体中球形腔膨胀的独立有限元分析进行了验证。在此验证中，我们还强调了相对于临界状态，腔体膨胀响应对颗粒状材料当前状态的依赖性。通过预测锥体渗透的阻力以及与沙子中的静态管道破裂有关的地面运动，证明了所提出的解决方案在解决工程问题中的应用。我们表明，根据实验室三轴试验确定的土壤参数，拟议的解决方案可以合理地代表锥形渗透阻力对沙子密度和压力水平的依赖性，如离心试验所示。通过与有限元分析进行比较，我们证明了所提出的解决方案可以为爆破操作引起的土壤位移提供有用的估计。