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
P. Xu

Inclusive Dates: 01/15/99 - 01/15/2000

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 is 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 dynamic response of tunnels and fractures. 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. Note that cavity and fracture responses have been studied extensively but separately in the literature. No quality models existed prior to SwRI work to predict the dynamic response of a tunnel in a fractured host medium to an applied seismic wave.

Approach - This research project is aimed at developing a novel version of the boundary integral 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.

Unlike other approaches such as finite difference method (FDM) and finite element method (FEM), BIEM discretizes the boundary of the tunnel cross-section only. 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 a wide class of idealized geometries and for a large number of detectors, 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 unbounded host rock in the absence of the tunnel and 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 BIEM 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 intact and fractured excavations of various shapes in an otherwise uniform unbounded medium impinged by plane seismic waves were developed. Computer codes based on these principles were implemented, debugged, and tested. Benchmark analytical solutions were used to verify the accuracy of the BIEM program. Numerical results were obtained for typical excavation shapes such as circles, slots, loafs, and domes.  In addition, the research team implemented comprehensive tools to compute and display displacement and stress fields at a network of points around a fractured excavation. Preliminary numerical results were obtained for tunnels intercepted by a slip. These results involve various values of slip stiffness, fracture orientation, frequency, and incident angle. It was found that, in general, a fracture represented by such a slip model re-distributes the stress and increases its level along the surface of the cavity. For certain combinations of the above parameters, the amplification and complication of the hoop stress are very significant.

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