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This paper investigates potential differences between creep and consolidation in mechanised tunnelling through squeezing ground, placing focus on the practical question of using experiences gained from existing tunnels about the required thrust force as a reference for tunnels of different diameter or adjacent tunnels. The investigations focus on two aspects. First, the effect of the tunnel diameter on the risk of shield jamming is examined. The paper demonstrates that larger-diameter tunnels are more favourable in poor-quality ground, while the opposite holds in better-quality ground, as well as in the case of pronouncedly time-dependent ground behaviour due to consolidation or creep. Second, the effect of a tunnel on the required thrust force in a neighbouring tunnel built later is examined. The paper shows that this interaction effect is particularly important in water-bearing ground of low permeability, where the drainage action of the first tunnel induces pore pressure relief and ground consolidation in an extensive area, leading to a remarkable reduction of the thrust force in the second tunnel. Conversely, in the case of creep the interaction is negligible even under extremely squeezing conditions, due to the fundamentally different nature of the purely mechanical rheological processes from coupled hydromechanical processes. The presented investigations into the transferability of experiences are valuable for tunnelling practice, in cases of twin tunnels as well as in situations where a smaller-diameter tunnel is constructed prior to the main tunnel (e.g. a pilot tunnel for exploration, advance drainage or ground improvement), or also the opposite (e.g. upgrade of a road tunnel by later construction of a safety tunnel with a smaller diameter). Highlights: The rate of ground deformations is independent of diameter in the case of creep, but extremely increases with decreasing diameter in the case of consolidation. The risk of shield jamming is lower in larger-diameter tunnels crossing poor-quality ground without pronounced time-dependent behaviour. The risk of shield jamming is lower in smaller-diameter tunnels crossing ground of higher quality or exhibiting pronounced time-dependent behaviour. The effect of adjacent tunnel on shield jamming risk is generally minor in the case of creep, even for extreme squeezing conditions and large overcuts. The effect of adjacent tunnel on shield jamming risk is remarkable in the case of consolidation, leading to a substantial reduction of the thrust force. [ABSTRACT FROM AUTHOR]

Reliable shear strength determination of large in situ discontinuities is still a challenge faced by the rock mechanics field. This is principally due to the limited availability of surface roughness and morphology information of in situ discontinuities and the unresolved management of the 'scale effect' phenomenon. Recently, a stochastic approach for predicting the shear strength of large-scale discontinuities was established, encompassing random field theory, a semi-analytical shear strength model, and a stochastic analysis framework. A key aspect of the new approach is the application at field scale, thereby minimising or bypassing the scale effect. The approach has been validated at laboratory scale and an initial large-scale deterministic-based validation showed promising results. However, to date, no large-scale experimental-based validation has been undertaken. This paper presents the first rigorous application of the employed semi-analytical shear strength model and the stochastic approach on a 2 m-by-2 m discontinuity surface, with comparison of prediction to experimental shear strength data. The shear strength model was found to generally produce peak and residual predictions within a ± 10% relative error range, with good agreement between predicted and observed damage areas. It was observed that, applying the stochastic approach to seed traces with gradient statistics equivalent to that of the surface, produced predictions that closely resemble the experimental results. Whereas, predicting shear strength from different seed traces results in more variability of predictions, with many falling within ± 20% of the experimental data. The predictions of residual shear strength tended to be more accurate than peak shear strength. Highlights: The stochastic approach for discontinuity shear strength was applied to a 2 m per 2 m rock surface replica made of mortar. A sensitivity analysis conducted on the analytical shear strength model highlights the parameter influencing the most the shear strength prediction. The predictions of peak and residual strengths fall within 20% of the experimental data. The accuracy of prediction depends on the trace used to define the input statistics. [ABSTRACT FROM AUTHOR]

Due to the challenge of measuring rock bridges in the field and the negligence of progressive damage and changes in stresses within a rock mass when defining rock bridges, it is questionable to evaluate mechanical properties of rock bridges using only geometric parameters. A demonstration is the scale effects of rock bridges, because the same geometric parameter may refer to different sizes and numbers of rock bridges, leading to erroneous equivalent rock mass responses. In this context, in-plane rock bridges in rock slope engineering were equivalent to rock bridges subjected to direct shear by conducting numerical simulations employing the Universal Distinct Element Code (UDEC) and described by constant geometric parameters, i.e., joint persistence, while the sizes and numbers of rock bridges were variant. In this way, the scale effects of rock bridges were investigated from the perspective of load–displacement curves, stress and displacement fields, crack propagations and AE characterizations. The results revealed that the mechanical properties of rock bridges deteriorated with decreasing scales. More specifically, the shear resistance and the area and value of stress concentration decreased with decreasing scale. Furthermore, an uneven distribution of displacement fields in an arc manner moving and degrading away from the load was observed, indicating the sequential failure of multiple rock bridges. It was also found that the propagation of tensile wing cracks was insensitive to scale, while the asperity of macro shear fracture mainly formed by secondary cracks decreased with decreasing scale. In addition, increasing the dispersion of rock bridges would overlap the failure precursors identified by intense AE activities. Based on the abovementioned results, the scale effects of rock bridges were characterized using existing rock bridge potential (RBP) index and degree of persistence (DoP) index. Interestingly, a scale threshold to possibly identify a rock bridge was found. Highlights: The mechanical properties of rock bridges deteriorated with decreasing scales. The scale effects of rock bridges were appropriately characterized using existing indices. A possible scale threshold to identify a rock bridge was found. [ABSTRACT FROM AUTHOR]

Rock joint surface roughness is usually characterized by heterogeneity, but the determination of a required number of samples for achieving a reasonable heterogeneity assessment remains a challenge. In this paper, a novel method, the global search method, was proposed to investigate the heterogeneity of rock joint roughness. In this method, the roughness heterogeneity was characterized based on a statistical analysis of the roughness of all samples extracted from different locations of a given rock joint. Analyses of the effective sample number were conducted, which showed that sampling bias was caused by an inadequate number of samples. To overcome this drawback, a large natural slate joint sample (1000 mm × 1000 mm in size) was digitized in a laboratory using a high-accuracy laser scanner. The roughness heterogeneities of both two-dimensional (2D) profiles and three-dimensional (3D) surface topographies were systematically investigated. The results show that the expected value obtained from conventional methods failed to accurately represent the overall roughness. The relative errors between the population parameter and the expected value varied not only from sample to sample but also with the scale. The roughness heterogeneity characteristics of joint samples of various sizes can be obtained using the global search method. This new method could facilitate the determination of the most representative samples and their positions. Highlights: We propose the global search method to investigate the heterogeneity of roughness. Analyses of the effective sample number are conducted to prove the sampling bias. We investigate roughness heterogeneity by 2D profiles and 3D surface topographies. The method is applied to determining the most representative samples. [ABSTRACT FROM AUTHOR]

Representative elementary volume (REV) is a significant parameter in analyzing the size effect and the continuous media theory of natural jointed rock masses. Generalized RVEs, which include the REV of jointed rock masses (RREV) and the REV of mechanical parameters of jointed rock masses (PREV), were introduced and investigated based on the anisotropy of natural jointed rock masses. A two-dimensional model was developed based on the available geology, material heterogeneity and Monte Carlo simulation of joint network. The size effect and anisotropy of the elastic modulus and the uniaxial compressive strength (UCS) of jointed rock masses were investigated, and then, the PREV was determined. Numerical results showed that the PREVs for both the elastic modulus and UCS exhibited strong anisotropy. The RREV dimension was determined as 14 × 14 m based on the PREV of different rotational directions. The equivalent mechanical parameters of the elastic modulus and UCS were determined for different rotational directions. It is suggested that the anisotropy of the PREV should be considered when the RREV and corresponding equivalent mechanical parameters are assessed. [ABSTRACT FROM AUTHOR]

A fundamental study on the tensile failure of rock is conducted using the three-dimensional lattice spring model. The model covers three aspects: (1) the relationship between the mesoscopic tensile/shear failure and the corresponding macroscopic tensile failure; (2) the effects of the size, shape, and location of the initial defect on the macroscopic tensile failure; and (3) the effects of the porosity, heterogeneity, crystal structure, mesoscopic constitutive model, and model scale on its macroscopic tensile responses. Through investigation, this study reveals that the mesoscopic strength heterogeneity affects the macroscopic pre-peak response of rock, and the initial defect could control its macroscopic post-peak response. The post-peak characteristics of the mesoscopic constitutive model influence both the macroscopic pre-peak and post-peak responses, which are scale independent and scale dependent, respectively. Based on these investigations, a parameter-selection method for the mesoscopic constitutive model is established to fully utilize the macroscopic tensile experimental data. [ABSTRACT FROM AUTHOR]

Natural discontinuities are known to play a key role in the stability of rock masses. However, it is a non-trivial task to estimate the shear strength of large discontinuities. Because of the inherent complexity to access to the full surface of the large in situ discontinuities, researchers or engineers tend to work on small-scale specimens. As a consequence, the results are often plagued by the well-known scale effect. A new approach is here proposed to predict shear strength of discontinuities. This approach has the potential to avoid the scale effect. The rationale of the approach is as follows: a major parameter that governs the shear strength of a discontinuity within a rock mass is roughness, which can be accounted for by surveying the discontinuity surface. However, this is typically not possible for discontinuities contained within the rock mass where only traces are visible. For natural surfaces, it can be assumed that traces are, to some extent, representative of the surface. It is here proposed to use the available 2D information (from a visible trace, referred to as a seed trace) and a random field model to create a large number of synthetic surfaces (3D data sets). The shear strength of each synthetic surface can then be estimated using a semi-analytical model. By using a large number of synthetic surfaces and a Monte Carlo strategy, a meaningful shear strength distribution can be obtained. This paper presents the validation of the semi-analytical mechanistic model required to support the new approach for prediction of discontinuity shear strength. The model can predict both peak and residual shear strength. The second part of the paper lays the foundation of a random field model to support the creation of synthetic surfaces having statistical properties in line with those of the data of the seed trace. The paper concludes that it is possible to obtain a reasonable estimate of peak and residual shear strength of the discontinuities tested from the information from a single trace, without having access to the whole surface. [ABSTRACT FROM AUTHOR]

The shear strength of the concrete-rock interface is a key factor to justify the stability of a hydraulic structure foundation. The Mohr-Coulomb failure criterion is usually used as shear strength and evaluated by extrapolating shear tests results carried out in a laboratory on small-sized samples. This paper presents an experimental study on the concrete-rock interface shear behavior. The effect of rock surface morphology on shear behavior was studied by performing laboratory direct shear tests on prepared square samples with a previously characterized rock surface. The scale effect and the test conditions were also studied by comparing the results to those obtained by performing usual laboratory shear tests on cored samples at lower scale. The tested interfaces were composed of the same concrete and granite and have a natural rock surface. The results displayed that the peak shear strength is strongly dependent on the concrete-rock bonding, the rock surface morphology and the applied normal load. A new surface morphology description tool was developed in order to characterize the main waviness. Moreover, the concrete-rock shear behavior at medium scale was reproduced by a 2D finite elements model to study the stress distribution along the sheared interface. Under low normal load, the concrete-rock adhesion is thus progressively mobilized according to the waviness on the rock surface and the local shear failure mechanisms depend on the type of this main waviness. Consequently the shear strength of a concrete-rock interface must be analyzed with respect to the various morphology aspects on its rock surface. [ABSTRACT FROM AUTHOR]

Estimation of representative elementary volume (REV) is significant to analyze fractured rock mass in the framework of continuum mechanics. Engineers can therefore simplify the analysis by using an equivalent rock block with an average property, and the influence of fractures can be neglected in finite element modelling. The indicators to determine the REV size based on the joint geometrical parameters include the volumetric fracture intensity ( P ) and the fracture tensor, but this type of calculation generally provides a lower bound evaluation. A novel conceptual framework of damage coefficient is introduced in this paper to consider the mechanical properties of fractures, such as joint aperture and roughness. A parametric study has been performed to establish the correlation between the proposed dimensionless damage coefficient and the traditional derived P value. The effectiveness of the developed method is demonstrated by a case study, where a larger mechanical REV size is indeed calculated based on the damage coefficient. [ABSTRACT FROM AUTHOR]

This paper presents a joint constitutive model that represents the shear behaviour of a large-scale opened rock joint. Evaluation of the degree of opening is made by considering the ratio between the joint wall aperture and the joint amplitude. Scale dependence of the surface roughness is investigated by approximating a natural joint profile to a fractal curve patterned in self-affinity. Developed scaling laws show the slopes of critical waviness and critical unevenness tend to flatten with increased sampling length. Geometrical examination of four 400-mm joint profiles agrees well with the suggested formulations involving multi-order asperities and fractal descriptors. Additionally, a fractal-based formulation is proposed to estimate the peak shear displacements of rock joints at varying scales, which shows a good correlation with experimental data taken from the literature. Parameters involved in the constitutive law can be acquired by inspecting roughness features of sampled rock joints. Thus, the model can be implemented in numerical software for the stability analysis of the rock mass with opened joints. [ABSTRACT FROM AUTHOR]

The paper presents the results of test campaigns on small-scale strength properties (particularly, micro-hardness) performed on two homogeneous materials: calcite, a very common and widespread mineral that is characterized by its relatively low Mohs hardness and its high reactivity with even weak acids; and glass, an amorphous solid characterized by the absence of the long-range order which defines crystalline materials. After a synthetic description of the principles underlying two of the three classical comminution laws, known as Kick's law and Rittinger's law, experimental results are discussed. The results of the tests performed show that both scale effect and size effect contribute to the non-constancy of mechanical properties at small scale for crystalline materials. On the other hand, for amorphous materials, a theoretical law considering size effects gives considerably different results from empirical measurements. Considerations and an extended discussion address these findings. [ABSTRACT FROM AUTHOR]

This study presents an improved model for calculating mechanical deformation of individual fractures subject to shearing and compression processes. Considering that the fracture-surface roughness can be characterized by fractals, a relationship between asperity angle and size of a fracture with fractal surfaces is derived. In addition, plastic work is employed to account for the effects of fracture-asperity degradation during the shearing process. Based on these developments, a scale-dependent relationship between shear stress and displacement is proposed, and also a formulation to calculate fracture aperture during shearing and compression processes is developed, by relating normal displacement to shear displacement for fractal surfaces. The usefulness of this model is demonstrated by agreements between calculated results and observations from laboratory experiments under different test conditions. [ABSTRACT FROM AUTHOR]

The effect of specimen size on the measured unconfined compressive strength and other mechanical properties has been studied by numerous researchers in the past, although much of this work has been based on specimens of non-standard dimensions and shapes, and over a limited size range. A review of the published literature was completed concentrating on the presentation of research pertaining to right cylindrical specimens with height:diameter ratios of 2:1. Additionally, new data has been presented considering high strength (70 MPa) cement mortar specimens of various diameters ranging from 63 to 300 mm which were tested to failure. Currently, several models exist in the published literature that seek to predict the strength-size relationship in rock or cementitious materials. Modelling the reviewed datasets, statistical analysis was used to help establish which of these models best represents the empirical evidence. The findings presented here suggest that over the range of specimen sizes explored, the MFSL (Carpinteri et al. in Mater Struct 28:311-317, ) model most closely predicts the strength-size relationship in rock and cementitious materials, and that a majority of the empirical evidence supports an asymptotic value in strength at large specimen diameters. Furthermore, the MFSL relationship is not only able to model monotonically decreasing strength-size relationships but is also equally applicable to monotonically increasing relationships, which although shown to be rare do for example exist in rocks with fractal distributions of hard particles. [ABSTRACT FROM AUTHOR]

Understanding the scale effect on the mechanical behavior of a single rock joint is still very important in rock engineering. Rock joints can be classified into three different categories depending on their scale: the “micro scale” which is the scale of the asperities; the “meso scale” is the scale of the specimens tested in laboratory; and the “macro scale” which is the scale of the rock mass. The purpose of this paper is to propose an effective way to model rock joints at both the meso and macro scale . An original constitutive mechanical model, in which parameters are deduced from experimental results, has been developed. This model is then extended to simulate the discontinuities occurring at a larger size. At the macro scale, the constitutive modeling was carried out for both small and large relative displacements. Large displacements lead to substantial changes in dilation. For both cases, the peak shear stress vanishes for joints longer than 2 m. [ABSTRACT FROM AUTHOR]