Source of information: http://prime.mines.edu/papers/tutorial-wsc05.pdf
The knowledge of in situ stress has to be considered one of the key input parameter in tunnel
design. Several approaches have been developed to analyze the behaviour of a rock mass around a tunnel
excavation and to estimate the support pressure required to control the extent of the plastic zone and the
resulting tunnel convergence. The development of numerical analysis has provided engineers with an
extremely powerful analysis tool; it allows simulating complex in situ conditions and an accurate
representation of the soil-structure interactions. Analyses carried out by mean of numerical models reveal that
rock behaviour is influenced in a decisive way by the state of in situ stress, in particular the horizontal to
vertical stress ratio. Since stresses in rock masses are a fundamental concern in the design of underground
excavations, it is very important to measure the stress components and to acquire such information before the
design. The purpose of this paper is to investigate the influence of the state of in situ stress on tunnel design.
It illustrates and sums up the results of a great number of numerical analyses carried out varying the
horizontal to vertical stress ratio “k” and considering different geomechanical conditions.
Stresses in the subsurface are commonly divided
into primary and secondary; the primary stress, or in
situ stress, is the cumulative product of events in its
geological history, while the secondary rock stress
is man made by e.g. excavations. Therefore, rock or
soil, in natural state, is an uncommon engineering
material because it is preload, i.e. there is a preexisting
state of stress in the rock; these loading
forces are of unknown magnitude and orientation.
The tunnel designer is often inclined to ignore
specification and determination of the state of
stress.
It is generally considered that the behaviour of
an underground structure is above all influenced by
the relationship between the rock strength and the
weight of the overburden; fairly often the ratio of
the uniaxial compressive strength of the rock mass
to the weight of the overlying strata, i.e. where
is the unit weight of the overlying material and z
is the depth below surface, is the only parameter
considered in tunnel design. The state of stress is
usually represented with vertical stress component
valued equal to the horizontal component
(hydrostatic condition), identified with .
The same goes for the support pressure
required to control the convergences and the extent
of the plastic zone.This common approach ignores that in the
majority of stress states measured throughout the
world the horizontal component of the stress field
has greater magnitude than the vertical component
and that the stability of the underground structures
is often compromised by mechanisms, for instance
bending stress, that are influenced by the state of in
situ stress, in particular the horizontal to vertical
stress ratio, in a way much greater than the rock
strength parameters. The purpose of this paper is to
investigate, by means of numerical analyses
performed using the finite difference method and
the FLAC 2D code, the influence of the state of in
situ stress on tunnel design; in particular it analyzes
the influence of in situ state of stress on tunnel
convergences, on shape and extension of the failure
zone and on choice of the most appropriate support.
At the start, it is presented an overview of the
possible way to predict the magnitudes of the
principal stresses. Later on, we illustrate and sum up
the results of a great number of numerical analyses
carried out varying the horizontal to vertical stress
ratio “k” and considering different geomechanical
situations.
The tunnel engineer has always to consider that the
rock medium is subject to initial stress prior toexcavation; so the final, i.e. post excavation, state of
stress in any underground structure is the resultant
of the initial state of stress and of the stresses
induced by excavation. Since induced stresses are
directly related to the initial stresses, it is clear that
it is a necessary precursor to any design analysis.
Measuring the in situ stress is demanding and timeconsuming
but, since stresses in rock masses are a
fundamental concern, it is very important to
measure the pre-existing stress components and to
acquire such information before the design.
2.1 Stress condition
The in situ stress state is generally described by the orientations and the magnitudes of the three principal stresses assuming an approximation that they are one vertical component and two horizontal components. Following this assumption concerning orientations, it becomes possible to predict the magnitudes of these principal stresses through the use of elasticity theory. The in situ principal stresses are in general different and are connected to the geological history. Changes in the state of stress in a rock mass may be related to temperature changes and thermal stress, and chemical and physicochemical processes such as leaching, precipitation and re-crystallisation of constituent minerals. Mechanical processes such as fracture generation slip on fracture surfaces and viscoplastic flow throughout the medium can be expected to produce both complex and heterogeneous states of stress. The vertical stress is mostly based on the depth and density of rock; we might expect that the vertical component increases in magnitude as the depth below the ground surface increases due to the weight of the overburden; so this stress is estimated from this relationship.
In areas of uniform bedrock structure, for example, sedimentary basins, the vertical force at a known depth is dependent on the weight of overlying rock according to hydrostatic pressure. In areas of more complex geology, for example crystalline, hard rock, the vertical stress does not follow this rule with such accuracy.
Measurements made of the in situ stress, in various mining and civil engineering sites around the world, confirm that the estimate (1) of the vertical stress component is basically correct although there is a significant amount of cases where the predicted component is different to the measured component; there are cases at depth less than 500m where the measured value is about 4?5 times the predicted value. The horizontal stress is much more difficult to estimate. The main sources for horizontal forces are continental plate tectonics and vertical movements of less dense areas of bedrock. It is globally dominant near the surface. Usually, the ratio of the average horizontal stress to the vertical stress is denoted by the letter “k”.
The measurements made of the horizontal in situ stress allow determining two formulae as envelopes for all data (Hoek [3]).
Sheorey [6] defined an equation that can be used to estimate the value of k.
A plot of equation (4), overlapped to the measured values and fit curves (3) is given in figure 1 for a range of deformation moduli. It is observed a good congruence between the curves. Sheorey equation (4) is therefore considered to provide a reasonable basis for estimating the value of k. Hudson [4] gives a good explanation of the different reasons that cause high horizontal stress and underline it is caused by factors as erosion, tectonics, rock anisotropy, discontinuities; in case of horizontal stress component derived only from gravity we have 0 < k < 1. Observing the data, it is manifestly clear that it is the rule rather than the exception that the horizontal stress component is larger than thevertical stress component, in particular at depths typical of civil engineering. We can at last observe that, the previous equations and the existing measurements provide a good predictive estimation of the in situ stresses, particularly for the vertical component; however they are not reliable to give an adequate estimation in a specific location (Figure 1). The previous comments also point out that the in situ state of stress in a rock mass is not amenable to calculation by any known method and must be determined experimentally.
Figure 1. Vertical stress and ratio horizontal to vertical stress k (after Hoek 1998)