为了研究移动的隧道轴向激励作用下饱和土体的动力响应，建立了隧道-饱和土体的动力分析模型；利用波函数展开法、镜像原理等，推导了频域内隧道轴向激励作用下饱和土体动力响应的解析解，并给出了饱和土体临界速度的经验公式；通过快速傅里叶逆变换得到了时-空域内饱和土体的动力响应。结果表明：轴向激励作用下，饱和土体临界速度只与土体的剪切模量和密度有关，且数值接近土体剪切波速的1.1倍；速度小于临界速度时，各响应数值随着剪切模量以及孔隙率的增大而减小，轴向位移随着隧道埋深的增大有小幅度减小，当隧道埋深超过半径的10倍时，轴向位移趋于稳定；速度大于临界速度时，各响应数值随着剪切模量以及孔隙率的增大而增大；角度对径向位移、轴向位移影响很小，对环向位移的影响较大。
Abstract
In order to study dynamic responses of saturated porous soil under a moving tunnel axial excitation, a dynamic analysis model for a tunnel-saturated soil system was established.The analytical solutions to the system’s dynamic responses in frequency domain were derived with the wave function expansion method, the mirror principle, and Graf addition formula.The empirical formula for the critical velocity of saturated soil was also deduced.The time-space domain solutions to saturated soil’s dynamic responses were obtained with the fast Fourier inverse transform.The results showed that the critical velocity of saturated soil under axial excitation is only related to soil’s shear modulus and density, and its value is close to 1.1 times of soil’s shear wave velocity;when velocity is less than the critical velocity, response values decrease with increase in soil’s shear modulus and porosity, and axial displacement slightly decreases with increase in tunnel buried depth, but when tunnel buried depth is more than 10 times of tunnel radius, axial displacement tends to be stable;when velocity is larger than the critical velocity, response values increase with increase in soil’s shear modulus and porosity; angle affects soil’s radial displacement and axial one slightly, while it affects soil’s circumferential displacement greatly.
关键词
轴向激励 /
饱和土体 /
临界速度 /
波函数展开法
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Key words
axial excitation /
saturated soil /
critical velocity /
wave function expansion method
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