Abstract

The ultimate bearing capacity of a ring footing on loose sand deposit, with an inclusion of a dense sand layer on its top, has been determined numerically in a bound form by following the finite element limit analysis (FELA). The friction angles ϕ₁ and ϕ₂ were varied from 40° to 46° and 30° to 36° for the top dense sand and the bottom loose sand respectively. The Mohr-Coulomb’s yield criterion has been assumed to be applicable. The bearing capacity has been found to increase quite extensively with an increase in the thickness $(H)$ of the dense sand layer thickness up to a certain optimal thickness ${(H}_{\mathrm{opt}})$ before attaining a constant value. The magnitude of $H_{\mathrm{opt}}/(r_{\mathrm{o}}-r_{\mathrm{i}})$ has been found to lie generally between 1.5 and 4.7, and the corresponding maximum value of the bearing capacity with an inclusion of the dense sand layer varies in a wide range of 2.32–82.45 times the corresponding value for an unimproved loose sand deposit; the parameters $r_{\mathrm{i}}$ and $r_{\mathrm{o}}$ refer to the inner and outer radii of the ring, respectively. Similar to a ring footing on homogeneous sand deposit, the bearing capacity for different chosen combinations of internal friction angles of the two sand layers, tends to become maximum generally for a value of ${r_{\mathrm{i}}/r}_{\mathrm{o}}$ closer to 0.25. For the validation, the results for a ring footing on two-layered sand deposit were also determined by using the displacements based elastoplastic finite element (EP-FE) method. The results from the FELA were found to compare well with (i) the obtained solutions based on the EP-FE method, and (ii) the published results by using experiments and the method of stress characteristics.

摘要

通过有限元极限分析(FELA)以绑定形式数值确定了松散砂层上环形基础的极限承载能力，其顶部包含致密砂层。顶部密砂和底部松砂的摩擦角φ ₁和φ ₂分别在 40° 到 46° 和 30° 到 36° 之间变化。假定 Mohr-Coulomb 屈服准则是适用的。已发现承载能力随着厚度的增加而大幅增加$(H)$致密砂层厚度达到一定的最佳厚度${(H}_{\mathrm{选择}})$在达到恒定值之前。的幅度$H_{\mathrm{选择}}/(r_{\mathrm{○}}-r_{\mathrm{一世}})$已发现一般在 1.5 和 4.7 之间，包含致密砂层的相应承载力最大值在未改良松砂层相应值的 2.32 至 82.45 倍范围内变化；参数$r_{\mathrm{一世}}$和$r_{\mathrm{○}}$分别指环的内半径和外半径。与均质砂层上的环形基础相似，两个砂层内摩擦角的不同选择组合的承载能力通常趋于最大值${r_{\mathrm{一世}}/r}_{\mathrm{○}}$接近 0.25。为进行验证，还使用基于位移的弹塑性有限元(EP-FE) 方法确定了两层砂层上环形基础的结果。发现 FELA 的结果与 (i) 基于 EP-FE 方法获得的解决方案以及 (ii) 通过使用实验和应力特性方法发布的结果进行了很好的比较。