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Knowledge of the in situ stress state of rock mass is fundamental for engineering, geological and geophysical applications. In situ stress state determination requires in principle the evaluation of the three principal stresses and the related principal directions, but it is widely recognized in the literature that the maximum horizontal stress is the most difficult component to accurately estimate. In the context of borehole methods, this paper proposes a step-by-step analytical procedure to estimate some bounds to the maximum horizontal stress, starting from a geomechanical description of the rock and relying on information generally available in the engineering practice. The procedure is divided in substeps, each one requiring additional information about the mechanical properties of the rock and on the geometrical properties of the failed portion of rock: more information available implies a lower uncertainty on in situ stress estimate. Furthermore, since the proposed procedure is analytical, it allows a complete and very easy implementation in a spreadsheet. The aim of the work is thus to provide a rigourous but simple analytical tool that can be used in engineering practicte to estimate some bounds to the maximum horizontal in situ stress state. The approach is finally validated by means of both numerical simulations, performed with a sophisticated numerical tool, and experimental field data coming from the literature.

We present a simplified model of damaging porous material, obtained through consistent linearization from a recursive-faulting material model described in (Pandolfi et al. 2016). The brittle damage material model is characterized by special planar micro-structures, consisting of nested families of equi-spaced frictional-cohesive faults in an otherwise elastic matrix material. The linear kinematics model preserves the main microstructural features of the finite kinematics one but offers a far better computational performance. Unlike models commonly employed in geo-mechanical applications, the proposed model contains a small number of parameters, to wit, two elastic moduli, three frictional-cohesive parameters, and three hydraulic response parameters, all of which having clear physical meanings and amenable to direct experimental measurement through standard material tests. The model is validated by comparison to triaxial hydro-mechanical experimental data. Despite the paucity of material constants, the salient aspects of the observed behavior are well captured by the model, qualitatively and quantitatively. As an example of application of the model, we simulate the excavation of a borehole in a rocky embankment.

Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm and a fully implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed.

Knowledge of the in situ stress state in rock and soil deposits is very important in many problems in civil, mining and petroleum engineering and energy development, as well as in geology and geophysics. The prediction of the response of rock masses interacting with underground structures is highly influenced by the stress field. For example, as pointed out in [1], in civil and mining engineering, in situ stresses control the distribution and magnitude of the stresses around underground openings such as tunnels, mines, shaft or caverns. Stress concentrations in the excavation walls may be large enough to overstress the rock, mobilize the strength of the rock mass and induce failure. On the other hand, tensile stresses in excavation walls may open existing fractures or create new ones which could result in block stability problems. An exact prediction of in situ stress acting over a rock mass, together with its spatial variation, is a very complex topic; the current stress state is a mixed consequence of tectonic conditions and of mechanical effects due to local thermochemo-hydraulic conditions. Due to the complex nature of rocks and rock masses, the stress field is rarely homogeneous and also its time evolution can be significant within a geological formation. Stress state is a symmetric second-order tensor and so it is defined by six independent components, e.g. the three principal stresses and the three principal directions. Stresses in rocks cannot be measured directly and can only be inferred by disturbing the rock. Amadei and Stephansonn [2] presented a detailed summary of the available sources of information from which it is possible to obtain the in situ stress state, involving hydraulic methods (i.e. hydraulic and sleeve fracturing), relief methods, jacking methods, strain recovery methods, borehole failure methods as well as fault-slip data analysis and earthquake focal mechanisms. Zoback [4] proposed an overview of a possible strategy to characterize the stress field: the vertical stress can be determined from the equilibrium in the vertical direction, i.e. by integration of the density logs, while observations of the geometrical arrangement of drilling-induced tensile fractures are an effective way to check whether the vertical stress is a principal stress. The orientation of the other principal stresses can be determined from wellbore observations, recent geologic observations and earthquake focal mechanisms, as well as from stress recovery methods. The magnitude of the minimum principal stress can be estimated from the analysis of hydraulic fracturing and leak-off tests, while the pore pressure can be either measured directly or estimated with some caution from geophysical logs or seismic data. In this paper the vertical stress is assumed to be a principal stress, so that the remaining two directions are supposed to be horizontal. This assumption is reliable for non-active regions or regions already relaxed from the previous tectonical stress. As pointed out by Bell [3], the free surface of sedimentary basins is generally horizontal, so that the principal stress directions are, to a good approximation, horizontal and vertical. From a practical point of view, if the vertical direction is assumed to be a principal one, it is sufficient to know just a horizontal principal direction, since the remaining one is orthogonal to the plane on which the other two are lying. Throughout the paper, Sv will represent the principal vertical in situ stress, SH represents the maximum horizontal in situ stress and Sh represents the minimum horizontal in situ stress, whose magnitude can be evaluated through hydraulic fracturing or leak off tests (except for reverse faulting regimes). Assuming that Sv and Sh are known, the aim of the note is to present a methodology for the definition of some boundaries for

This work presents an insight into double-structure effects on the coupled chemo-hydro-mechanical behaviour of a compacted active clay. In the first part, selected pore size distribution curves are introduced, to highlight the influence of solute concentration on the evolution of the microstructure of compacted samples. An aggregated structure with dual-pore network is induced by compaction even at relatively high water contents. This structural arrangement is enhanced by salinisation, and has a notable influence on transient volume change behaviour – that is, the occurrence of different stages of swelling upon pore water dilution and higher volume change rates upon salinisation. A coupled chemo-hydro-mechanical model, taking into consideration double-structural features from a chemo-mechanical viewpoint, is described and then used to interpret these behavioural responses and present complementary information on local transient processes. The model is designed to identify an intra-aggregate and an inter-aggregate domain, and assigns different values of hydraulic pressure and osmotic suction to each domain. Distinct constitutive laws for both domains are formulated, and the flow of salt and water between the two domains is accounted for by a physically based mass exchange term. The model is used to simulate salt diffusion tests run in an oedometer at constant vertical stress. Parameters used in the formulation are calibrated based on separate experimental evidence, both through direct test results and through back-analyses of laboratory experiments.

Experimental data from different testing methodologies on different compacted clayey soils, with dominant bimodal pore size distribution, are presented and analysed, to provide a comprehensive picture of the evolution of the aggregated fabric along hydraulic and mechanical paths. Fabric changes are analysed both from the porous network viewpoint, by means of careful mercury intrusion porosimetry investigation, and from the soil skeleton viewpoint, by quantifying swelling and shrinkage of the aggregates in an environmental scanning electron microscopy study. The consequences of the aggregated fabric evolution on the water retention properties of compacted soils are analysed and discussed. A new model for water retention domain is proposed, which introduces a dependence of the intra-aggregate pore volume on water content. The model succeeds in tracking correctly the evolution of the hydraulic state of the different soils investigated along generalised hydromechanical paths. The proposed approach brings to light coupling between intra-aggregate and inter-aggregate pores in the retention properties of compacted clayey soils. Dependence of the air entry and the air occlusion values on swelling and shrinking of aggregates, besides void ratio, is introduced and discussed.