Scattering Of SH-Wave By Semi-Cylindrical Hill With Hole Above Subsurface Cavity

This paper studies the ground motion of semi-cylindrical hills with homocentric hole above subsurface cavities while impacted by SH waves. Firstly, a model of single semi-cylindrical hill with homocentric hole above single subsurface cavity is established. The methods of complex function and moving coordinate system are used here. The model is divided into two parts, a standing wave function which satisfies the condition of stress free at the wedges is constructed in one part, a scattering wave function which satisfied the condition of stress free at the horizontal surface is constructed in another part. And then moving coordinate system is used to transform the solving problem into a "conjunction" problem. Finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of infinite algebraic equations. Furthermore, the problems that single hill with homocentric hole above multiple subsurface cavities as well as multiple hills with homocentric hole above multiple subsurface cavities are solved step by step. Numerical examples are provided to show the effects of SH waves on hills while material parameter, wave number, geometrical parameter is different. The variation of displacement amplitude and DSCF(Dynamics Stress Concentration Factor) caused by these parameters are discussed finally. Then conclusions are acquired as followed:1. The existence of subsurface cavities and homocentric hole in the hills can cause the decreasing of the model's stiffness. Furthermore, the larger the cavities or hole is, the greater the surface displacement as well as the DSCF is. Therefore, their existence should be taken into account while designing.2. When the depth of the subsurface cavity arrives to 350-400 times than the radius of the hill, the influence caused by subsurface cavity can be ignored.3. If more than one subsurface cavities exist, the greater the distances of subsurface cavities is, the smaller their inter-influence is. When the displacement arrives to 400 times than the radius of the hill, their inter-influence on displacement and DSCF will disappear.4. When the model is consisted of several hills with homocentric hole and several subsurface cavities at the same time, the influence of hills will disappear if their distance is 100 larger than their radius. In this condition, subsurface cavities' inter- influence will disappear if their distance is about 50 times than the hill's radius.