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Dynamic Response of a Fractured Tunnel to Seismic Waves, 15-9116

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Principal Investigators
Jorge O. Parra
Chris L. Hackert
Amitava Ghosh

Inclusive Dates: 01/15/99 - 01/15/00

Background - The stability of underground tunnels, mine openings, and other excavations depends to a significant degree on the characteristics of fractures, faults, and prominent joints. In particular, the spatial distribution of fractures makes rock mass strength and stress distribution with associated deformability highly discontinuous. Furthermore, tunnel response to seismic events such as earthquakes, underground explosions, or rockbursts are influenced by fractures in the rock mass near the excavation, as these fractured zones are weaker than the intact rock. Thus, a thorough understanding of the dynamic response to seismic waves of fractures intersecting excavations is important for tunnel safety measures used to prevent rock fall in the excavation and to keep the excavation stable and usable.

Of particular interest is the combined response of tunnels and fractures. Cavity and fracture responses have been studied extensively but separately in the literature. No quality models exist to predict the dynamic response of a tunnel in a fractured host medium to an applied seismic wave. The free surface of the tunnel wall allows increased displacement in the rock and also can act as a waveguide for focusing seismic waves along the tunnel boundary. Recent studies by the Lawrence Berkeley National Laboratory have shown that fractures not only reflect seismic energy, but also serve as hosts for interface waves that can propagate for long distances with less attenuation than direct waves.

This research project is aimed at developing a novel version of the Boundary Iintegral Equation Method (BIEM) to simulate the dynamic response of fractured tunnels to seismic waves. The fracture will be modeled using a slip boundary condition that has been extensively analyzed, verified by experiments, and documented in the literature. Displacement and stresses along the fracture and tunnel wall will be related to the material properties of the rock, fractures stiffness, tunnel shape and fracture orientation, and frequency and incident angle of the seismic wave. Cases of no fracture, one fracture, and two parallel fractures will be examined. The modeling results will be validated by comparison with experimental data acquired during rock slippage. For the case of two fractures in particular, simultaneous slippage on both fracture faces could lead to rock fall.

Approach - In the BIEM, only the boundary of the tunnel cross section is discretized. The radiation condition at infinity is rigorously satisfied, avoiding the need for artificial boundary conditions. Frequency-dependent properties of the wave motion are modeled conveniently. Most importantly, for idealized geometries, the BIEM is much more efficient than other approaches. In the BIEM, the unknown displacement components on the boundary are coupled in boundary integral equations. The coefficients of the unknown quantities are the stress tensors associated with the Green's functions of the host rock in the absence of the tunnel, which is an unbounded medium with one or two fractures. The displacements along the free surface of the tunnel boundary are then solved by the linear equations resulting from discretization of the integral equation. Finally, displacement and stresses at any given field point can be determined through direct evaluation of the boundary integral using the previously obtained boundary displacements. The accuracy of the method will be tested by comparing results with multicomponent seismic data obtained in and around the Yucca Mountain tunnel and in an SwRI-simulated tunnel experiment. Damaging slippage of fractures under the calculated stresses and displacements will be determined using Coulomb failure models.

Accomplishments - The theory and software used to calculate the dynamic responses (both displacement and stress) of excavations of various shapes was developed for a plane of seismic waves in a uniform unbounded medium. Benchmark analytical solutions were used to test the BIEM program. Numerical results were obtained for typical excavation shapes such as circles, slots, and domes. In addition, the research team implemented a computational tool for the calculation of displacement and stress fields around a fractured excavation. In this case, the Green's functions and associated stresses were obtained for a fractured instead of a uniform medium and were expressed in terms of wave number integrals. The kernels of the integrals were obtained by the global matrix method, and the quadrature of the integral was carried out by the modified Clenshaw-Curtis integration technique. Computer codes based on these principles were implemented, debugged, and tested. Preliminary numerical results involving various values of interface stiffness, frequency, and incident angle were obtained. It was found that, in general, a fracture represented by a slip model increases the stress level along the surface of the cavity. For certain combinations of the above parameters, the amplification and complication of the hoop stress are significant. Preliminary numerical results were obtained for tunnels intercepted by a slip. The illustration shows stress concentrations around a tunnel intercepted by the slip in the presence of a plane impinging from the top of the tunnel.

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A 0.25-kHz P-wave is vertically impinging a dome cavity with a horizontally crossing fracture.

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