椭球形空洞地基稳定性分析

为了分析地基中的椭球形空洞的稳定性，利用叠加原理得到了线弹性各向同性无限大体中在远场三轴应力作用下椭球形空洞壁上出现极值的关键点应力精确解，为此又采用Matlab程序求解当s(短、长半轴之比)趋近于1时的极限而退化成球形空洞的应力精确解。最后利用摩尔-库仑准则判定椭球洞在三轴应力作用下的稳定性。分析结果表明，在远场应力状态相同的条件下，椭球洞相对于对应的椭圆孔不易失稳，指出土洞的三维椭球洞模型要比对应的二维椭圆孔模型和球形空洞更符合实际。

Stability analysis of an ellipsoidal cavity in foundation

To analyze the stability of an ellipsoidal cavity in soil foundation, the exact stress solutions for the extremum key points on the surface of ellipsoidal cavity in linear elasticity and isotropy infinite body under far field triaxial stresses are obtained based on principle of superposition. The limit of exact stress solution for an ellipsoidal cavity is degenerated to the counterpart solution for a spherical cavity when the shape ratio s is equal to 1 by Matlab program. Then Mohr-Coulumn criterion is used to estimate the stability of ellipsoidal cavity under triaxial compressive stresses. The results indicate that the ellipsoidal cavity is less easy to lose stability than the corresponding elliptical hole under the same far field stress condition. It is concluded that three dimensional ellipsoidal cavity model is more practical than either the corresponding two dimensional elliptical hole model or the spherical cavity model.