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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。
In order to analyze the stability of the ellipsoidal cavity in the foundation, the exact solution to the stress at the critical point of the ellipsoidal cavity wall under the action of the far-field triaxial stress is obtained by the principle of superposition. Also using the Matlab program to solve the s (short, long semi-axial ratio) approaching the limit of 1 and degenerated into spherical cavity stress accurate solution. Finally, the stability of ellipsoid cavity under triaxial stress is judged by Moore - Coulomb criterion. The results show that the ellipsoid cavity is not prone to instability with respect to the corresponding elliptical hole under the same stress conditions in the far field. It is pointed out that the three-dimensional ellipsoid cavity model is more suitable than the corresponding two-dimensional elliptical hole model and spherical cavity actual.