内源爆炸荷载作用下饱和土中圆形衬砌隧道的瞬态响应解答

Exact solutions for dynamic responses of a cylindrical lined tunnel in saturated soil to internal blast loads

内源爆炸荷载作用下隧道的动力响应,经常被简化为以爆源为中心的二维平面应变问题,其实际上是一个三维岩土工程问题。为评价隧道爆源及周围区域的爆炸破坏,采用Laplace和Fourier变换,提出一种在内源爆炸荷载作用下,饱和土体中圆形衬砌隧道的瞬态响应精确解答。基于Biot波动理论,将周围土体和衬砌结构分别看成饱和两相介质和弹性介质,推求了Laplace和Fourier变换域内爆炸荷载作用下衬砌和周围饱和土体的动力响应解析解。利用Laplace和Fourier反变换的数值方法,进行了爆炸荷载作用下衬砌和周围土体的动力响应数值分析。结果表明:与简化的二维平面应变模型相比,基于三维模型得到的切向应力、径向位移和孔隙水压力较小;隧道的动力响应随时间而迅速减小,并随着与爆源距离的增加,而在径向和轴向上呈指数衰减。

The dynamic response of tunnels under internal explosion in reality is a three-dimensional geotechnical problem, however, it is often simplified as a plane strain problem in 2D model which can only deal with the dynamic responses of tunnels at the source of explosion. To evaluate the damage of the explosion to the surrounding areas of the tunnel apart from the section at the source of explosion, a set of exact solutions for the three-dimensional dynamic responses of a cylindrical lined tunnel in saturated soil due to internal blast loads are derived by using the Fourier transform and Laplace transform. The surrounding soil is modelled as the saturated medium based on the Blot theory and the lining structure modeled as the elastic medium. By utilizing a reliable and efficient numerical method for the inverse Laplace transform and Fourier transform, the numerical solutions for the dynamic responses of the lining and surrounding soil are obtained. The 3D dynamic responses of the lined tunnel and the surrounding saturated soil medium due to internal blast loads are then presented and discussed. The results show that （a） compared to the simplified 2D plane strain model, the 3D model yields smaller predictions in the hoop stresses, radial displacements, and pore water pressures; （b） the dynamic responses of tunnels decrease sharply in an oscillating manner as the time elapses, while such responses attenuate exponentially with the increasing distance away from the explosion source center at both radial and axial directions of the tunnel.