Dynamic Response of a Fractured Tunnel
to Seismic Waves, 159116
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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. Frequencydependent
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 SwRIsimulated 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 ClenshawCurtis 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.
A 0.25kHz Pwave is vertically impinging a dome cavity
with a horizontally crossing fracture.
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