TY - JOUR
T1 - Analytical Solutions for Long Tunnels Under Arbitrary Dynamic Loadings
AU - Yu, Haitao
AU - Cai, Chuang
AU - Zhang, Zhengwei
N1 - Publisher Copyright:
© 2018, Editorial Department of Journal of Tongji University. All right reserved.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - Assuming the long lined tunnel as an infinite homogeneous beam resting on a Pasternak foundation, the governing equation of the dynamic problem can be established based on Euler-Bernoulli beam theory. Integration transform and Residue theorem are applied to solve the differential equation, thus the analytical solutions of displacement, velocity, acceleration, bending moment, shear force for long lined tunnels subjected to arbitrary dynamic loads are obtained. The specified solutions for harmonic line loads, moving line loads and travelling loads are discussed and compared with the exiting solutions, and therefore, the validation of the presented generic form of solutions is verified. Taking travelling loads as an example, parametric analyses are performed to investigate the influence of the velocity and frequency of travelling loads and the shear modulus of foundation on the tunnel dynamic responses. The proposed solution is of value for seismic design of long line tunnel.
AB - Assuming the long lined tunnel as an infinite homogeneous beam resting on a Pasternak foundation, the governing equation of the dynamic problem can be established based on Euler-Bernoulli beam theory. Integration transform and Residue theorem are applied to solve the differential equation, thus the analytical solutions of displacement, velocity, acceleration, bending moment, shear force for long lined tunnels subjected to arbitrary dynamic loads are obtained. The specified solutions for harmonic line loads, moving line loads and travelling loads are discussed and compared with the exiting solutions, and therefore, the validation of the presented generic form of solutions is verified. Taking travelling loads as an example, parametric analyses are performed to investigate the influence of the velocity and frequency of travelling loads and the shear modulus of foundation on the tunnel dynamic responses. The proposed solution is of value for seismic design of long line tunnel.
KW - Analytical solution
KW - Dynamic loads
KW - Integration transform
KW - Long lined tunnel
KW - Longitudinal response
UR - http://www.scopus.com/inward/record.url?scp=85046775129&partnerID=8YFLogxK
U2 - 10.11908/j.issn.0253-374x.2018.01.001
DO - 10.11908/j.issn.0253-374x.2018.01.001
M3 - Article
AN - SCOPUS:85046775129
SN - 0253-374X
VL - 46
SP - 1
EP - 6
JO - Tongji Daxue Xuebao/Journal of Tongji University
JF - Tongji Daxue Xuebao/Journal of Tongji University
IS - 1
ER -