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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. 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 to World Tunnel Congress 2008 - Underground Facilities for Better Environment and Safety - India 194 excavation; 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 time- consuming 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.
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 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. 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, overlapped to the measured values and fit curves. It is observed a good congruence between the curves. Sheorey equation 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.
In case the real in situ stress state it is not defined properly and rough analyses in hydrostatic conditions are carried out, the obtained results diverge from the real ones as a function of the value of the horizontal to vertical stress ratio k. The analyses carried out, for circular tunnel, enable to draw some general conclusions useful to weigh the reliability of the design of an underground structure.
(1) Convergence of an unlined tunnel
- (1a) for k < 1.5 the hydrostatic conditions provide valid results; we observe values of convergence that differ from real values at the most of 20?30 %; it is possible to correct the hydrostatic convergence values by mean of "corrective factors" (CFconvergence);
- (1b) for horizontal to vertical stress ratio k 1.5 the results obtained with hydrostatic solution differ in a substantial way from those obtained from the not hydrostatic solutions; it is not possible to define corrective factors; the results can be useful only to make qualitative studies.
(2) Shape and extension of the failure zone of an unlined tunnel
- (2a) up to k=1.5 it is possible to use for the definition of the shape and of the extension of failure zone the results of the hydrostatic conditions formulation adopting the corrective coefficients.
- (2b) for k > 1.5 the failure zone shape becomes strongly irregular and it is not possible to define a corrective coefficient.
(3) Eccentricity of support actions - the influence on action eccentricity of not hydrostatic state of stress is higher when the lining thickness increases; - for all analysed cases (0.5< k <2.0), even if the eccentricity increases for higher k, the cross- section remains completely in compression stress; - for k ? 1 we observe an increasing in lining stresses that became more and more significant for higher thickness and for value of k more different from k=1. All the cited influences, of the k value on structural and geomechanical behaviour of a tunnel, are evaluated for a circular cross section. It is evident that, the effects of a not hydrostatic state of stress will be greater for a not circular cross section; in that case an erroneous evaluation of the in situ state of stress can easily lead to an inadequate design. This will be subject of further studies.