内源爆炸荷载作用下无限弹性土体中圆柱形衬砌隧道的瞬态响应解答

内源爆炸荷载产生的振动响应对地下衬砌隧洞的安全非常重要。采用Fourier变换和Laplace变换,推导出内源爆炸荷载作用下无限弹性空间中圆柱形衬砌孔洞的瞬态动力响应无量纲解答,利用Fourier和Laplace逆变换数值方法,计算分析内爆炸荷载产生的振动在衬砌和周围弹性介质中的分布和传播衰减规律。计算结果表明,爆源中心处衬砌内表面径向位移、切向应力和衬砌外表面土体径向位移、切向应力最大,向左右两侧迅速衰减,在6倍衬砌内径处衰减为0;衬砌内表面径向位移、切向应力和衬砌外表面土体径向位移、切向应力时程曲线峰值爆源中心处最大,离爆源中心越远,峰值越小,且在t~*=10时衰减为0。

Solution to transient response of a cylindrical lined tunnel in an infinite elastic medium under internal blast load

The vibration response resulting from internal explosion load is very important for the safety of the underground lined tunnels. The dimensionless dynamic transient solution to a cylindrical lined cavity under an internal blast load in an infinite elastic medium is derived by the Fourier transform and the Laplace transform. Utilizing the inverse Fourier transform and the inverse Laplace transform, the distribution and propagation attenuation laws of the vibration response generated by the internal explosion load in the lining and the surrounding elastic medium are calculated and analyzed. The results show that the radial displacement and the hoop stress on the internal lining surface and those of the soil on the interface between the lining and the soil reach the maximum at the explosion source center. The radial displacement and the hoop stress decrease rapidly with z* at both sides of the center, and eventually decay to zero at z*= 6. The peak value of the time history of the radial displacement and the hoop stress at the internal and outer lining surfaces are the maximum at the explosion source center. The further away from the explosion source center, the smaller the peak value. When t^*=10, the radial displacement and the hoop stress decay to zero.