##### Abstract

The impact of earthquakes, due to ground shaking, which affects the whole tunnel length from ovaling

of the tunnel cross section, is investigated in this thesis. The influence of rock mass quality Q and the

tunnel dimension is also studied. Finally, an approach to determine the new seismic support system using

existing Q-system design chart and expected peak ground acceleration at the tunnel site is presented.

The earthquake loading is modeled through quasi-static seismic loading in Phase2, a finite element

modeling program by Rocscience, Inc. for design of underground structures and slopes. The quasi-static

assumption is valid in rocks, as due to their higher velocity, the wavelength of shear waves is > 20D,

where D is tunnel diameter. At this scale, the dynamic interaction between the tunnel and the passing

seismic waves is minimal and thus validates the quasi-static assumption. The seismic coefficient, a

unitless vector dependent on the peak ground acceleration (PGA), serves as a representative parameter

for the expected critical earthquake.

Four rock mass classes with Q = 1 - 40, to represent "very poor" to "very good" rock masses are

modeled by varying the deformation modulus and Mohr-Coulomb parameters, determined from empirical

relations. The increase in support pressure (represented by axial force) is investigated as function of

rock mass quality Q and tunnel dimension.

A model comprising of a 10 m diameter tunnel at 60 m depth surrounded by rock masses with Q

ranging from 1 - 40 is used to investigate the influence of rock mass quality Q. While the seismic loading

is unchanged, the magnitude of the axial force on the lining and the net increase due to seismic loading,

referred to as seismic axial force, increases as the rock mass quality decreases.

To check the influence of tunnel diameter, the diameter of a circular tunnel at 60 m depth and under

fixed seismic loading is increased from 5 m to 20 m at 5 m interval. The magnitude of the axial force and

the seismic axial force increases with tunnel diameter for rock mass with Q = 1 ("very poor" rock mass).

Conversely, the increase in magnitude of axial force and seismic axial force on the lining is relatively

insignificant for rock mass with Q = 40 ("very good" rock mass).

Inferred from the above findings, an approach to determine the seismic support pressure by using the

concept of Qseismic, first introduced by Barton (1984), is presented. During earthquakes, the required

support pressure is expected to increase due to additional seismic load. However, this increase in support

pressure can be visualized as a decrease in rock mass quality Q around the tunnel and thus a new Q for

seismic condition, called Qseismic = kQstatic, can be employed. The constant k mainly depends on

the seismic coefficient used to represent the PGA or intensity of the expected critical earthquake, and

rock mass quality. The relationship

k = e Kh

was determined for a 10 m diameter tunnel at 60 m depth for different rock masses. Kh is the horizontal

seismic coefficient and the constant depends on the rock mass quality, i.e. 4.3 for Q = 1, 3.1 for Q =

4 - 40, and 2.5 for elastic models. As Kh is increased from 0.05 to 0.70, k decreases from 0.81 to 0.06

for very poor rock masses with Q = 1.

The new seismic support system can be obtained using Qseismic from the existing Q-system tunnel

design chart. As a general trend, the increases in support pressure correspond to decrease in bolt

spacing and increase in the thickness of the fiber-reinforced shotcrete (Sfr). Unfortunately, the increase

in thickness, which decreases the flexibility ratio, adversely affects the performance of the liner during

earthquakes and therefore other measures to increase the support pressure are recommended. Nonetheless,

this approach results in a refined rule-of-thumb that incorporates rock mass quality Q and seismic

coefficient (= PGA) into the seismic design of tunnel support using Q-system.