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Model for the mechanics of jointed rock
... 14 This rock model consists of an assembly of Voronoi blocks interconnected by Goodman's joint elements. 15 The CVBM aims to represent the non-linear fracture process of hard rocks. For this purpose, the modeling concept was developed based on the following conventional laboratory tests: Brazilian test, unconfined compression test, and triaxial compression test. ...
... 38 Model's construction is performed by dividing the continuum medium into Voronoi blocks interconnected by Goodman's joint elements. 15 Internally, the blocks are discretized by a finite element mesh. Figure 1 shows the CVBM discretization process, the juxtaposed Voronoi blocks, and the FEM mesh inside each block. ...
... Goodman et al. 15 created an element that can represent the rocks' discontinuities in FEM analyses. This element is known as the Goodman's joint: a rectangular four-noded element with a finite length ( ) and a zero width ( ). Figure 1d presents a visual representation of this element. ...
In this paper, a numerical model is presented to represent the fracture process in hard rocks based on a pseudo-discontinuum method called the Continuum Voronoi Block Model (CVBM). To validate this tool, numerical models for one Brazilian test, one unconfined compression test, and multiple triaxial compression tests with different confining stress were calibrated to match laboratory test results for Creighton granite. The model proved robust and matched the following macro-properties: crack initiation (CI) stress, (CD) stress, peak strength, tensile strength, Young's Modulus, and Poisson's ratio. The calibrated model served as a basis for a sensitivity study to analyze how micro-properties influence the rock's macroscopic responses. From the sensitivity study, a calibration methodology was proposed, which shall facilitate the use of the CVBM in future works.
... All materials possess the property of elasticity and rock joints are no exception. The elastic deformations associated with rock joints was first described by Goodman et al. (1968) where joint stiffness was separated into two components, a normal stiffness (kn) and a shear stiffness (ks). Joint normal stiffness (kn) is defined as the normal stress increment required for a small closure of a joint or fracture at a level of effective stress and joint shear stiffness (ks) is the elastic deformation response in shear (Barton, 2007). ...
... Joint normal stiffness and joint shear stiffness are measured using displacement and stress data prior to yield and were first introduced by Goodman et al. (1968) as a response to the need to quantify the pre-yield elastic behaviour in finite element and finite difference numerical models that were beginning to use explicit structural elements. ...
... During this stage, shear displacement is held constant at zero. The original normal stiffness law was proposed by Goodman et al. (1968). This law was linear in nature and specifically created for use in numerical modelling. ...
The importance of discontinuity geomechanical properties is increasing as the use of numerical models with explicit or discrete rockmass structure becomes the state of practice. These numerical inputs are typically measured from laboratory testing and in the case of joint normal and shear stiffness this is measured from direct shear testing. This paper presents practical guidelines to correct direct shear testing data for machine influences with regards to normal and shear stiffness by accounting for system deformation and separating out the fracture deformation component. In this study, the joint normal stiffness of 23 rough granite, 10 smooth ground granite, and 6 rough limestone specimens are measured using a hyperbolic law. Joint shear stiffness is measured on 19 rough granite, 4 smooth ground granite, and 6 rough limestone specimens. This data set is used to compare the measured joint stiffnesses based on lithology and topology.
... The joint normal stiffness and joint shear stiffness parameters were first introduced by Goodman et al. (1968) as a response to the need to quantify the pre-yield elastic behaviour in finite element and finite difference numerical models that were beginning to use explicit structural elements. The Goodman finite element interface element is a four node and eight degrees of freedom element without thickness, the two interfaces are connected by countless tiny springs in the normal and tangential directions (Goodman et al. 1968). ...
... The joint normal stiffness and joint shear stiffness parameters were first introduced by Goodman et al. (1968) as a response to the need to quantify the pre-yield elastic behaviour in finite element and finite difference numerical models that were beginning to use explicit structural elements. The Goodman finite element interface element is a four node and eight degrees of freedom element without thickness, the two interfaces are connected by countless tiny springs in the normal and tangential directions (Goodman et al. 1968). At the introduction of these two terms, normal stiffness was defined at the normal stress per unit closure of the joint and the shear stiffness was the mean secant of the shear stress-shear displacement curve, up to peak shear strength (Barton 1972). ...
... Multiple closure laws for the determination of normal closure with respect to increasing normal stress in physical experiments are reported in the literature. The original normal closure law is a linear closure law defined as the normal stress per unit closure of the joint to be used as part of the Goodman joint element in finite element numerical modelling (Goodman et al. 1968). Goodman followed up the proposed linear closure law with Goodman (1974). ...
The importance of discontinuity geomechanical properties is increasing as the use of numerical models with explicit or discrete rock mass structure becomes the state of practice. Joint normal stiffness and joint shear stiffness are two parameters that characterize the deformation behaviour of discontinuities. This paper presents practical guidelines to correct direct shear testing data for machine influences with regard to normal and shear joint stiffness using a method originally employed by Goodman (Methods of geological engineering in discontinuous rocks. West Publishing Company, St. Paul, 1976) to correct the normal deformation of a direct shear test. This method of correcting the normal deformation has been extended to the shear deformation to account for machine influence during the shear loading stage. The normal stiffness of 23 rough fracture specimens and 10 smooth ground specimens were measured on discontinuities in granitic specimens from NQ and NQ3 sized core using a power law (Swan in Rock Mech Rock Eng 16:19–38, 1983), a hyperbolic law (Bandis et al. in Int J Rock Mech Min Sci Geomech Abstr 20:249–268, 1983), and two semi-logarithmic laws (Bandis et al. 1983; Evans et al. in Geotherm Resour Counc Davis Calif USA 16:449–456, 1992). Measurements from direct shear tests completed at varying maximum applied normal stress show a positive correlation between normal stiffness and normal stress. In addition, the shear stiffness was measured on 19 rough fracture specimens and 4 smooth ground specimens. The compilation of results from these measurements has a range of measured shear stiffness due to varying joint topology and roughness showed a positive correlation between shear stiffness and maximum applied normal stress. As the majority of the joints exhibited non-linear behaviour under normal loading conditions and linear behaviour under shear loading conditions, it is recommended that a stress-dependent normal stiffness model and a linear shear stiffness model be used for numerical modelling purposes.
... In addition, the imperfect interface with normal and tangential interface modulus, which can be used to simulate the conditions of the displacement and stress continuity between the adjacent layers, can be equivalently represented by the thin layer. Goodman et al. [35] proposed a simple and practical stiffness model to simulate an imperfect interface. They assumed that only the displacement had a discontinuity condition, and the stress at the interface was continuous. ...
... To represent the relative slip of the contact between the layers, interface parameters δ x and δ z , which are also known as the horizontal and vertical interface moduli, respectively, are introduced [35] . In this study, it is assumed that the horizontal interface modulus is similar in any direction of the horizontal plane, therefore it can be considered as a plane strain problem. ...
... In this study, it is assumed that the horizontal interface modulus is similar in any direction of the horizontal plane, therefore it can be considered as a plane strain problem. Moreover, the horizontal interface modulus has the following relationship with the displacement and stress at the interface [35] : ...
Although solving the dynamic response of layered media has always been a major concern in the engineering field, the problem of interlayer contact of layered media has seldom been addressed in the related studies. Thus, this paper proposes an algorithm to analyze the dynamic displacement and stress responses of two-dimensional layered media with imperfect interfaces between layers at an arbitrary point under time-harmonic loads. The Fourier transform was used to convert the dynamic equation of the generalized plane strain problem from the frequency-spatial domain to the frequency-wavenumber domain. In addition, combined with the introduction of dual variables, an integration algorithm with high precision was employed to solve the state equation. Based on the displacement response in the frequency-wavenumber domain, the dynamic displacement and stress responses at an arbitrary point were obtained using the inverse Fourier transform. This algorithm not only considers the transverse isotropic properties of layered media but also considers the contact problem at the interface between the adjacent layers of the layered media with different properties. In addition, the harmonic load can be applied to both the surface and inside of the medium. The accuracy of the proposed algorithm was verified by comparing the calculated data with the numerical results, and the influence of the imperfect interface parameters on the dynamic response of layered media was analyzed in detail. Finally, the mechanism of the impact of the imperfect interface between the layers on the dynamic displacement and stress responses of layered media was examined.
... The Continuum Voronoi Block Model was developed using the Rocsciense software RS2, a two-dimensional nu-69 merical program based on the FEM. In this model, the rock mass is represented as a set of particles (also called cells 70 or blocks) joined at their edges by Goodman joint elements (Goodman et al., 1968). The particles are established from 71 a Voronoi tessellation, and a finite element mesh internally discretizes each block. ...
... The discontinuities were modeled using Goodman joint elements (Goodman et al., 1968). The mechanical behavior 217 was characterized by shear and normal stiffness, and the Mohr-Coulomb failure criterion was adopted. ...
The Continuum Voronoi Block Model (CVBM), a pseudo-discontinuum modeling technique based on the Finite Element Method, was employed to investigate the impact of discontinuities on spalling phenomena around excavations in rocks under high-stress conditions. The CVBM’s ability to produce numerical results consistent with spalling was demonstrated through a case study of the Mine-by tunnel. The results show that the model can explicitly capture the formation of macro-fractures parallel to excavation walls, intact rock slabs, and V-shaped notches. The results of this case study support the application of CVBM for parametric analyses to investigate the role of discontinuities in spalling failure, integrating discrete fracture network (DFN) into the model. The influence of DFN parameters such as dip angle, spacing, persistence, position, and mechanical properties is also evaluated. It was found that discontinuities promote stress relief due to shear, thereby altering spalling damage around the excavation in highly stressed rock. This finding highlights the crucial role of discontinuities in influencing the behavior of excavations under such conditions.
... The characteristics of rock joint and fault interfaces often include roughness, contact area, joint length, and aperture distribution. Goodman et al. (1968) introduced joint stiffness as an effective parameter to capture the topological behavior of complex joint interfaces and provide quantitative values without detailed measurement and analysis of roughness, contact area, aperture distribution, and other parameters of the joint interface. It was found that the joint stiffness of a rock mass is directly related to the stress distribution, which can be used in the stability analysis of rock slopes and underground structures (Lang et al., 2016;Noorzad & Aminpoor, 2008). ...
... The change in the wave transmission during the whole shear process was observed. Based on the displacement discontinuity theory model (Goodman et al., 1968), the measured transmission coefficient was used to calculate the joint stiffness. This allowed the evolution law of rock joint stiffness during uniaxial compression and shear to be determined. ...
Slip behavior of planar discontinuities in rock masses is the basis of rock slope failure and fault movement. Local failure at different locations of the slip interface occurs before global slip failure, and a precursor signal [acoustic rock joint behavior (elastic stiffness, transmitted wave amplitude, etc.)] is generated. Therefore, detecting the precursor signal before shear stress reaches its peak can be used to predict the instability of rock slopes and fault slip in the macroscopic range. The composition of rocks, distribution of stress, roughness of joints and fault interfaces, and non-uniform distribution of the actual contact area are the primary factors that control the friction strength and slip behavior of joints. The combined influence of these factors enhances the complexity of monitoring local precursor signals. The distribution of rock joint stiffness has previously been obtained based on the elastic wave measurement method to determine the parameter characterization of rock joint contact behavior. Here, the evolution law of joint stiffness during uniaxial compression and shear was studied through laboratory tests and used to analyze the local contact state of rock joints and faults through the change of joint stiffness. A continuous and nondestructive monitoring method is proposed.
... (Rocscience 2019). This model uses Voronoi cells interconnected by Goodman joint elements (Goodman et al. 1968) to represent the rock mass. ...
... The particles are established from a Voronoi mosaic, and a finite element mesh internally discretizes each block. Goodman joint elements (Goodman et al. 1968) are inserted at the edges of the particles, which allow the simulation of blocks interaction. ...
In this work, a new numerical approach based on the Finite Element Method and an implicit continuum formulation, called Continuum Voronoi Block Model-CVBM, is proposed to represent the fracturing process in hard rocks and also the rupture of underground works with high field stresses. In this model, developed with the RS2 program, the rock mass was simulated by a set of blocks, formed by a Voronoi mosaic, joined at their interfaces by joint elements. Different case studies were represented on a laboratory and field scale. The model proved to be robust on the laboratory scale and described the rock's relevant macro-properties in conventional tests: crack initiation stress, crack damage stress, and peak strength. On a field scale, the model represented the mass deterioration process explicitly, captured the rupture geometry, and the excavations' displacements. Such results show the CVBM's potential for modelling the behavior of underground works with high field stress.
... CVBM is a pseudo-discontinuum modeling technique implemented in the RS2 software (Rocscience, 2019). This model uses Voronoi cells interconnected by Goodman joint elements (Goodman et al., 1968) to represent the rock matrix. Rógenes et al. (2022) showed that CVBM could represent the different non-linear stages involved in the fracturing processes of hard rocks at a laboratory scale (crack initiation stress, crack damage stress, and peak strength). ...
... The Continuum Voronoi Block Model was developed using the Rocsciense software RS2, a two-dimensional numerical program based on the FEM. In this model, the rock mass is represented as a set of particles (also called cells or blocks) joined at their edges by Goodman joint elements (Goodman et al., 1968). The particles are established from a Voronoi tessellation, and a finite element mesh internally discretizes each block. ...
In this study, the pseudo-discontinuum modeling technique, called continuum Voronoi block
model (CVBM), was applied to represent the behavior of hard-rock pillars from underground
mines subjected to high field stresses. The CVBM’s ability to produce numerical results consistent
with the observed behavior of pillars is demonstrated through the numerical analysis of
a hypothetical case and a back analysis of the Creighton mine pillar. The results show that
the model can capture convergence displacements and explicitly show the formation of macrofractures
parallel to excavationwalls, intact rock slabs, andV-shaped notches. These components
are characteristics of brittle failure induced by highly stressed ground conditions. The studies
presented in this work confirm the CVBM as a convenient tool for the numerical modeling of
intact rock pillars excavated in deep underground mines.
... (Rocscience, 2019). This model uses Voronoi cells interconnected by Goodman joint elements (Goodman et al., 1968) to represent the rock mass. ...
... The particles are established from a Voronoi mosaic, and a finite element mesh internally discretizes each block. Goodman joint elements (Goodman et al., 1968) are inserted at the edges of the particles, which allow the simulation of blocks interaction. ...
Deep underground works commonly present a brittle failure process, known as spalling, together with high convergence displacements, called bulking. In the present work, a pseudo-discontinuum modeling technique called Continuum Voronoi block model - CVBM was applied to represent the spalling and bulking phenomena in excavations with high stresses. The ability of CVBM to produce numerical results compatible with the behavior observed in the field is demonstrated through the numerical simulation of a rock pillar. The
model captured the failed region shape caused by spalling, explicitly presented the rock mass deterioration process, and represented the displacements caused by bulking. These results confirm the applicability of CVBM in the simulation of brittle failure in deep underground excavations.
... Zero-thickness interface elements were originally introduced in the late 1960s and early 1970s, motivated by the need to model discontinuities in rock masses. Based on the proposal by Goodman et al. (1968) and the subsequent improvements in later works (e.g. Ghaboussi et al., 1973;Desai et al., 1984;Gens et al., 1988), the formulation of interface elements has been widely implemented in Finite Element codes and has been applied to many practical problems. ...
... To this end, the constitutive model is used in the case of a zero-thickness interface element which connects the six vertex nodes of two triangular faces in 3D. For the finite element formulation of zero-thickness interface elements, the reader is referred to earlier works (Goodman et al., 1968;Rots, 1988;Gens et al., 1988;Plesha, 1987;Gens et al., 1995). ...
In the framework of the Finite Element Method, zero-thickness interface elements have been widely used to model fracturing processes in quasi-brittle materials in a broad variety of problems. In particular, interface elements equipped with elastoplastic constitutive laws that account for the softening of the material strength parameters due to the fracturing mechanical work has been proved to accurately reproduce observed fracture propagation behaviour in concrete. Along this line, this paper presents the extension of an existing constitutive law of this kind to include the effect of chemical degradation of the material in the formation of fractures. The law is defined in terms of the normal and shear stresses on the average plane of the crack and the corresponding normal and shear relative displacements. A hyperbolic cracking (plastification) surface in the stress state determines the crack initiation. The softening of the cracking surface is governed by two history variables: an internal variable that accounts for the dissipated fracturing (plastic) work, and an external variable to be provided by a chemical degradation model that accounts for the effect of chemical degradation on the strength parameters. After a detailed discussion of the formulation, the main characteristics of the proposed law are illustrated with a number of academic examples for different combinations of mechanical loading and chemical degradation sequences. The model is finally validated against experimental results from the literature consisting of three-point bending tests performed on mortar samples previously exposed to an aggressive solution for different time periods.
... In order to minimize the interpolation error associated with the mesh discretization of the model, the mesh is refined inside the pile structure, and within a zone of 3D below the tip and beside the shaft, respectively; see Figure 3. To address possible occurrence of relative displacements and plastic slip parallel to the soil-structure contacts, standard zero-thickness interface elements are considered at soil-structure contacts [58,59]. The interface elements are extended beyond the physical pile boundary in order to reduce the effect of singular plasticity points developing close to the pile edge [11,60]. ...
... The raft of the simplified model is supported by nine jet-grout columns, which are symmetrically arranged on the foundation axis; see Figure 14b. SSI between soil and raft boundaries are addressed by means of zero-thickness interface elements [58,59] (not shown). The base model boundary condition is defined as fully fixed, whereas the vertical boundaries are set to allow vertical movement of soil layers (i.e., roller supports). ...
The numerical analysis of many geotechnical problems involves a high number of structural elements, leading to extensive modelling and computational effort. Due to its exceptional ability to circumvent these obstacles, the embedded beam element (EB), though originally intended for the modelling of micropiles, has become increasingly popular in computational geotechnics. Recent research effort has paved the way to the embedded beam element with interaction surface (EB-I), an extension of the EB. The EB-I renders soil–structure interaction along an interaction surface rather than the centreline, making it theoretically applicable to any engineering application where beam-type elements interact with solid elements. At present, in-depth knowledge about relative merits, compared to the EB, is still in demand. Subsequently, numerical analysis are carried out using both embedded beam formulations to model deep foundation elements. The credibility of predicted results is assessed based on a comprehensive comparison with the well-established standard FE approach. In all cases considered, the EB-I proves clearly superior in terms of mesh sensitivity, mobilization of skin-resistance, and predicted soil displacements. Special care must be taken when using embedded beam formulations for the modelling of composite structures.
... This model can be extended to the small scale by associating a set of discontinuities to a set of microcracks. In the following, a classical procedure is illustrated to obtain the equivalent elasticity matrix for a volume containing one or more sets of cracks [10]. The contribution of microcracks to rock compliance M can be evaluated on the basis of deformability, orientation and frequency of each set. ...
... The behaviour of a single set of cracks in elastic conditions is described by means of the stiffness constants K n , K s associated respectively to the relative displacement in the normal and tangential direction [10]. To determine the contribution of the cracks to the global deformation of the elementary volume, the relative displacements are divided by the mean spacing d . ...
Stress-strain response of foliated rocks shows that mechanical behaviour and degree of anisotropy are influenced by the spatial arrangement of phyllosilicates. But the anisotropy of these rocks is essentially due to the characteristics and distribution of cracks aligned with mica beds. At the laboratory scale, the elastic symmetry can be represented by the transverse isotropy, with the lowest elastic modulus perpendicular to the plane of aligned microcracks. These issues are discussed with reference to experimental data obtained for two gneisses of the same geological formation. The gneisses show a quite similar strength behaviour, but very different deformabilities. The measures of dynamic and static deformabilities under loading prove the influence of the progressive closure of open cracks on the compliance tensors of both gneisses. The relationship between the elastic parameters and the characteristics of the crack distributions is discussed in the framework of non-interacting crack models. Assuming the presence of two different sets of cracks, crack densities have been estimated. The different deformabilities of the two gneisses can be ascribed to their different microcrack distributions. The degree of anisotropy due to cracks reduces as stresses increase, differently for the two gneisses.
... Early continuum methods, e.g., the finite element method (FEM), finite difference method (FDM), and boundary element method (BEM), model the macroscopic behavior of fractured media by implementing the corresponding macroscopic constitutive models (Swoboda et al., 1998;Zhao, 2015, e.g.,). Then, Lei et al. (2017) combine continuum approaches with DFN to model fractured rocks with only a few or plenty of fractures associated with only a small amount of displacement/rotation by introducing interface or joint elements (Goodman et al., 1968;Lei et al., 2017). However, modeling the high-density and complex DFNs remains difficult, resulting from the intrinsic limit of continuum-based methods (Goodman et al., 1968;Lei et al., 2017). ...
... Then, Lei et al. (2017) combine continuum approaches with DFN to model fractured rocks with only a few or plenty of fractures associated with only a small amount of displacement/rotation by introducing interface or joint elements (Goodman et al., 1968;Lei et al., 2017). However, modeling the high-density and complex DFNs remains difficult, resulting from the intrinsic limit of continuum-based methods (Goodman et al., 1968;Lei et al., 2017). For more complex DFNs, discrete-based approaches seem more suitable (Jing and Hudson, 2002), especially those with a wide range of mineral compositions and fabric anisotropies (Liu and Fu, 2020a,b;Liu et al., 2021). ...
Crack microgeometry vitally influences effective elastic characteristics and sonic responses. Researchers commonly employ seismic-wave-based exploration methods to assess and interpret fracture attributes. Numerical simulation, as a promising way for this issue, still faces some challenges. With the rapid development of computers and computational techniques, discrete-based numerical approaches with desirable properties have been increasingly developed but not yet extensively applied to seismic response modeling in complex fractured media. For this purpose, we use the modified lattice spring model (LSM) coupled with discrete fracture networks (DFN) to examine the validity of emulating elastic wave propagation and scattering in naturally fractured media. By comparing the dynamic elastic moduli with the theoretical and the static ones, we validate the implementation of the scheme with input parameter optimization. Numerical results are consistent with the tendency of theoretical predictions. It shows the potential for modeling the seismic responses in complex fractured media and quantitatively investigating the correlations and differences between static and dynamic elastic moduli.
... The research on soil-structure interfaces started in the 1970s. The most representative study was on a hyperbolic relationship model between the shear stress and relative displacement established conducted by Clough and Duncan in 1971 [12,8]. On this basis, many scholars have carried out in-depth experimental, theoretical, and numerical simulation studies on the constitutive relation of soil-structure interfaces. ...
... By substituting Eqs. (12) and (13) into Eq. (10), the following equation can be obtained: ...
To study the shear mechanical properties and deformation mechanism of the interface between cemented soil and warm frozen soil, the key parameters are provided for the design and evaluation of cemented soil structure in warm frozen soil ground. In this study, a series of negative temperature direct shear tests of the cast-in-place cemented soil-frozen soil interface were conducted under the influence of different factors. The binary medium model was used to investigate the mechanical stress and deformational mechanisms of the interface, and the damage rate and stress sharing rate functions were introduced. Assuming that the strength of each element of the interface obeyed the Weibull probability distribution, the constitutive equation of the warm frozen soil-cemented soil interface was established. The results showed that the stress-displacement curve of the interface was a strain-softening type, and the entire deformation process of the interface was divided into four stages: the linear elastic, elastic-plastic, softening, and residual stability stages. The constitutive model based on the binary medium theory revealed the micro stress–strain mechanism of the interface and better described the entire stress–displacement process of the interface and the strain softening phenomenon, which can provide a basis for the numerical simulation and theoretical calculation of the structure in the frozen soil ground.
... The subway station was assumed to be made of reinforced concrete that was assumed to be linearly elastic, with an elastic modulus of 3.6 × 10 7 kPa, a Poisson's ratio of 0.2, and a unit weight of 2.5 × 10 3 kN/m 3 . The interface between the sandy soil and the subway station was modeled by using Goodman contact elements (Goodman, Taylor, and Brekke 1968). ...
... This explicit approach to modelling the discontinuities inside rocks can also be classified into two approaches. The first approach to modelling the properties of discontinuities using specific elastic elements was first introduced by Goodman (1968). The stress and strain around this fictional elastic element, also called a 'joint element', is in a linear elastic relationship. ...
Shale anisotropy characteristics have great effects on the mechanical behaviour of the rock. Understanding shale anisotropic behaviour is one of the key interests to several geo-engineering fields, including tunnel, nuclear waste disposal and hydraulic fracturing. This research adopted the finite discrete element method (FDEM) to create anisotropic shale models in ABAQUS. The FDEM models were calibrated using the mechanical values obtained from published laboratory tests on Longmaxi shale. The results show that the anisotropic features of shale significantly affect the brittleness and fracturing mechanism at the micro-crack level. The total fracture number in shale under the Uniaxial Compressive Strength (UCS) test is not only related to the brittleness of shale. It is also strongly dependent on the structure of the shale, which is sensitive to shale anisotropy. Two new brittleness indices, BIf and BICD, have been proposed in this paper. The expression for BIf directly incorporates the number of fractures formed inside of the rock, which provides a more accurate frac-ability using this brittleness index. It can be used to calculate the frac-ability of rocks in projects where there are concerns about fractures after excavation. Meanwhile, BICD links brittleness to the CD/UCS ratio in shale for the first time. BICD is easy to obtain in comparison to other brittleness indices because it is based on the Uniaxial Compressive Strength test only. In addition, it has been shown there is a relationship between tensile strength and the crack damage strength in shale. Based on this, an empirical relationship has been proposed to predict the tensile strength based on the Uniaxial Compressive Strength test.
... And this paper studies the pavement interlayer contact as a non-completely continuous case, so it is necessary to consider how the interlayer contact conditions can be characterized by mathematical formulas. Goodman [15] model is clear in theory, clear in thought, and easy to apply in the derivation of formulas. So this paper adopts Goodman model to define the interlayer contact conditions. ...
For understanding the mechanical behavior of asphalt pavement in the long slope section, this study focuses on the dynamic response of asphalt pavement both considering the horizontal and vertical vehicle load. Firstly, a theoretical model of asphalt pavement was built considering the interface bonding conditions under vertical and horizontal vehicle loads. Then, the performance of the interface bonding between the asphalt layer and the base course layer was presented by a transformation matrix. At last, the analytical expression and numerical solution of the dynamic response in the pavement were obtained by Hankel-Laplace integral transformation. The results of the practical example show that horizontal vehicle load increases the stress on the pavement and affects the distribution of the stress. The bond strength between the asphalt surface layer and the base layer is an important factor affecting the dynamic response of the long longitudinal slope asphalt pavement.
... The energy dissipated by the bolted joint can be predicted using the Iwan model [1,2], Bouc-Wen model [3,4], Dahl model [5,6], Lu-Gre model [7], and Valanis model [8]. These analytical models can be incorporated into the FEM model using the whole joint approach [9], node-to-node elements [10], thin layer elements [11][12][13], and zero thickness elements [14,15]. The parameters of the analytical model incorporated into the FEM model can be obtained from the experimental hysteresis loop of a bolted structure. ...
... The mechanism of discontinuity propagation and coalescence determines the failure form and strength characteristics of rock mass. Therefore, scholars began to deepen the study on the failure mechanism of rock mass with multiple cracks from the middle of the 20th century (Goodman et al., 1968;Toshikazu, 1988;Li and Zhu, 1992). ...
To investigate the failure mode and strength characteristics of rock-like materials containing two non-coplanar closed discontinues, and the influence of crack attitude on the shear failure of rock mass, a series of direct shear tests are carried out on rock-like materials containing two pre-existing cracks of different attitudes, one of them is horizontal crack, and the other is inclined crack. The specimens containing pre-existing cracks of four inclinations (0°, 45°, 135°, and 180°) and three dip angles (30°, 60°, and 90°) are prepared, and the failure form and stress-displacement curve are recorded during the tests. The results show that the attitude of the crack has a significant effect on the failure form and strength characteristics. In positive shear, the shear stress increases slowly and the crack initiation of the crack occurs relatively late, and in negative shear, the shear stress increases rapidly and the crack initiation stage appears earlier. Under the normal stress of 1 MPa, the fracture surface fluctuates along the pre-existing cracks, and the difference in shear strength of each specimen is less than 1.0 MPa. Under the normal stress of 5 MPa, the fracture surface mostly distributes along the horizontal direction, and the difference in shear strength of each specimen is about 2.0 MPa. Under the same level of normal stress, the crack initiation and peak stress vary with the attitude of pre-existing crack, and the variation trend of peak stress is changed when the normal stress increased due to the difference in failure form. It is calculated that the ratio of crack initiation stress to peak stress ranges from 0.61 to 0.80.
... The parameters of the Dun-Chang E-B constitutive model for backfill soil are presented as Table 4. We employed the Goodman joint element [39] to model the contact effect. We chose the nonlinear bond-slip constitutive curve developed by Di [40] due to the absence of bond-slip testing curves between high-strength concrete and plain wires, which were taken from the test of ordinary concrete and crescent wires, as presented in Equation (3) ...
The precise analysis of the overall mechanical performance of prestressed concrete cylinder pipes (PCCPs) with broken wires is a complicated problem. In this article, powerful finite element numerical means are applied to solve this problem. Firstly, the advantages and shortcomings of the current prestress simulation methods in the finite element analysis (FEA) literature are discussed, and the initial stress method based on a novel single-spring joint element method to model the pre-stress of wires is proposed. Then, different distributions of broken zones, including random broken distributions, are developed for two typical PCCP pipes with different wire-wrapped layers. The established nonlinear FEA model considers actual service processes such as manufacturing, installation and operation to investigate the mechanical behavior of two typical PCCP pipes with different breakage distribution regions and breakage ratios, and in particular, the overall mechanical behavior of a pipe with random breakage is determined first. To verify the accuracy of the proposed pre-stress simulation method and the established nonlinear finite element model, the overall mechanical response of a pipe before wires broke is compared with the results obtained via the specifications. The computed results under the corresponding breakage assumptions are consistent with the conclusions in the existing literature, providing important guidance for pipeline management and operation.
... Although the limit equilibrium method is widely used in slope stability analysis, the jointed rock slope stability analysis is not satisfactory. In order to better analyze the stability of jointed rock slope, with the rapid development of computer technology, a variety of numerical analysis methods have gradually developed (Hammah et al., 2007), including FEM (Goodman et al., 1968), Finite Difference Method (FDM) (Fredlund & Krahn, 1977), Discrete Element Method (DEM) (Cundall & Strack, 1979), and Discontinuous Deformation Analysis (DDA) (Shi, 1992). Because numerical simulation can consider different mechanical and physical properties of rock mass and joint Jing (2003), it is broadly used in slope stability calculation (Feng et al., 2020). ...
The Finite Element Method (FEM) has been applied to a variety of slope stability problems, including cracked rock masses. In the present study, the generated mesh is imported from FEM software, and the model is analyzed for determining the cracked rocks slope displacement. Furthermore, a computer program is developed for the stochastic analysis of the slope. In the next step, the effect of different configurations of cracks, such as crack length and orientation, on the maximum displacement of the slope is assessed. To the stochastic analysis of the slope, the elastic modulus and possion's ratio are considered uncertainties variables. The mean and standard deviation of the maximum slope displacement is obtained via Point Estimate Method (PEM). The results show that the length and orientation of the crack have a remarkable effect on the output. Comparing the probability density functions of the maximum displacement indicate that crack length is more effective than orientation in the maximum displacement of the slope.
... Currently, the acquisition of mechanical parameters of rock mass is carried out using three main methods: in situ field tests [12][13][14], laboratory tests [15,16], and numerical simulation [17,18]. Specifically, in situ testing is the most effective method of obtaining the mechanical parameters of rock mass on an engineering scale. ...
In the engineering of underground construction, the discontinuous structures in rock mass have important influences on the mechanical behaviors of the subsurface of rock mass. The acquisition of mechanical parameters is the basis of rock mass engineering design, construction, safety, and stability evaluation. However, the mechanical parameters and failure characteristics of the same rock mass under different mechanical conditions cannot be obtained due to the limitations of specimen preparation techniques. In recent years, with the continuous development of 3D printing (3DP) technology, it has been successfully applied to the repetitive preparation of rock mass samples. The combinations of 3DP and other techniques, such as 3D scanning and CT scanning, provided a new approach to study the mechanical behavior of complex structural rock masses. In this study, through a comprehensive review of the technical progress, equipment situation, application fields, and challenges of the use of 3DP technology, the following conclusions were obtained: (1) 3DP technology has advantages over traditional rock mass specimen preparation techniques, and the verification of test results using 3D printed samples shows that the 3DP has broad application prospects in geotechnical engineering. (2) The combination of 3DP and other advanced techniques can be used to achieve the accurate reconstruction of complex structural rock masses and to obtain the mechanical and failure characteristics of the same rock mass structure under different mechanical boundary conditions. (3) The development of 3DP materials with high strength, high brittleness, and low ductility has become the major bottleneck in the application of 3DP in geotechnical engineering. (4) 3D printers need to meet the high precision and large size requirements while also having high strength and long-term printing ability. The development of 3D printers that can print different types of materials is also an important aspect of the application of 3DP in geotechnical engineering.
1. Introduction
Rock mass is characterized by discontinuity, inhomogeneity, and anisotropy. It is composed of various weak structural joints within certain engineering scales [1–4]. The internal structures of rock mass are generally complex and contain defects such as pores, joints, and fissures that directly affect the strength, deformation, and seepage characteristics of the rock mass, which are closely related to the stability of rock engineering [5–8]. Therefore, the mechanical behavior and failure characteristics of complex structural rock masses have become the key factors of rock mass engineering design, construction, safety, and stability evaluation [9–11].
Currently, the acquisition of mechanical parameters of rock mass is carried out using three main methods: in situ field tests [12–14], laboratory tests [15, 16], and numerical simulation [17, 18]. Specifically, in situ testing is the most effective method of obtaining the mechanical parameters of rock mass on an engineering scale. However, the large size of rock mass specimens used in in situ testing causes many problems, such as a long test period, high costs, and influences on construction, leading to less data being obtained through in situ testing. Laboratory tests have been the most important means of obtaining the mechanical parameters of rocks because they can visualize the mechanical characteristics, such as the strength, deformation, and failure characteristics, of rock mass specimens under different mechanical boundary conditions. However, due to the limitations of the testing equipment in terms of the size of rock samples and the difficulty in preparing samples of complex structures, it is hard to obtain the mechanical parameters via laboratory tests. Moreover, since the experimental testing of rocks is generally destructive, it is impossible to accurately obtain the change rule of mechanical properties of the same rock mass. Numerical simulation has the advantages of low cost and repeatability, so it has become an effective supplement to in situ tests and laboratory tests on rock masses. However, the complex structures of rock mass are often simplified in the simulation process due to the limitations of calculation conditions, making the numerical model differ from the real structures of rock mass. In addition, the selection of material parameters and determination of constitutive relation in the simulation process would affect the calculation results [19–21].
As was discussed above, when laboratory tests are used to study the mechanical and failure properties of rock mass, the specimens need to be representative of their structural characteristics. Due to the complexity of natural rock mass structures, it is difficult to obtain rock mass specimens with identical structures and properties. So, it is impossible to obtain the mechanical properties of the same rock mass structure under different mechanical boundary conditions. Such problems can be solved by using similar material model tests. However, it is difficult to make specimens with natural joint surfaces, special internal structures, and chamber excavation models, although these structural characteristics have important influences on the strength, deformation, and failure characteristics of rock masses [22–25]. Therefore, the repetitive preparation of complex structural specimens is the key to carrying out laboratory tests.
As an additive manufacturing technology, the 3DP differs from traditional manufacturing techniques such as cutting and grinding because it uses a layer-by-layer accumulation method to achieve the precise reconfiguration of complex structures. In recent years, the 3DP has been widely used in many fields such as biomedicine, aerospace, automobile manufacturing, and electronic components [26–29]. With the development of 3DP technology, some studies have begun to explore the applications of 3DP in the field of rock mechanics. For example, the combination of technologies of 3DP, stress freezing technique, CT scanning, and X-ray scanning has enabled the quantitative characterization and visualization of complex structures inside deep rock masses [30–34]. Based on this technology, transparent natural sand conglomerate specimens have been produced to investigate the effects of complex structures on the stress field and plastic zone [35, 36]. Furthermore, some materials such as polylactic acid (PLA), gypsum, and photosensitive resin have also been used in the preparation of rock-like specimens. The feasibility of 3DP in rock mechanics tests was initially verified by comparing the mechanical and failure properties of rock specimens [37, 38]. After that, several regular rock masses were assessed using 3DP, and the influences of the structural characteristics on the overall mechanical properties were studied [39–41]. Recently, the 3DP technique has been applied to the structural reconstruction of irregular columnar jointed rock masses, and the feasibility and superiority of this method in the reconstruction of complex structural rock masses have been demonstrated by comparing the results of mechanical and laboratory tests [42–44].
Thus, it is clear that the 3DP has advantages over other techniques used in rock mechanics testing, such as the accurate and rapid specimen preparation of complex structural rock masses [45]. However, compared with the mechanical and failure characteristics of high strength and high brittleness in rock mechanics tests, the specimens prepared using 3DP usually have low strength and high plasticity, which limit the applications of 3DP in rock engineering. Therefore, on the basis of 3DP technology in complex structural rock mass reconstruction and mechanical testing, the applications and progress of the use of 3DP technology in the rock mass are reviewed from the aspects of materials, equipment, and test methods. In addition, the deficiencies of current 3DP technology in rock mass engineering are discussed to provide guidance for its engineering application.
2. The Technologies, Materials, and Equipment of 3DP
2.1. The Technologies of 3DP
The difference between 3DP technologies and traditional methods lies in the printing materials and accumulation methods. Table 1 describes the common 3DP technologies and their corresponding materials, which are mainly divided into three categories: (1) Extrusion 3DP technology includes fused deposition manufacturing (FDM), fused filament fabrication (FFF), directed ink writing (DIW), and continuous fibre fabrication (CFF) [46–49]. The principle of this method is that the material is melted at a high temperature and ejected from the nozzle; then, the material solidifies quickly after being ejected. (2) 3DP using photography includes stereolithography (SLA), digital light processing (DLP), and continuous liquid interface production (CLIP) [50, 51]. The principle of this method is that the liquid photosensitive resin is sprayed from the nozzle, and the liquid in the target area is irradiated with ultraviolet light, so that the liquid can be rapidly solidified. (3) The 3DP via layer powder bonding includes powder-based 3DP, electron beam melting (EBM), selective laser melting (SLM), selective heat sintering (SHS), selective laser sintering (SLS), and direct metal laser sintering (DMLS) [52–57]. The principle of SLS consists in spreading the first layer of powder, and then, the infrared laser is used to sinter the powder into the desired solid object. The powder bed is preheated a few degrees below the melting temperature of the polymer, and the laser locally provides only the thermal energy necessary to melt the polymer. In addition, the commonly used 3DP techniques also include laminated object manufacturing (LOM) [58], directed energy deposition (DED) [58, 59], and electron beam freeform fabrication (EBF³) [58].
Technical types
Technical names
Materials
Printer manufacturer
Sources
Melt extrusion
Fused deposition manufacturing (FDM)
Thermoplast, eutectic alloy, rubber
Stratasys
3D Systems
[46]
Fused filament fabrication (FFF)
Thermoplast, eutectic alloy, rubber, etc.
[47]
Directed ink writing (DIW)
Ceramics, alloy, metal ceramic, etc.
[48]
Continuous fibre fabrication (CFF)
Nylon, straps, glassfibre, etc.
[49]
Photopolymerization
Stereolithography (SLA)
Photosensitive resin
3D Systems
[51]
Digital light processing (DLP)
Photosensitive resin
Continuous liquid interface production (CLIP)
Photosensitive resin
Layer powder bonding
Powder-based 3DP
Almost any alloy, powdered polymer, gypsum
Z Corporation
3D Systems
Stratasys
[52]
Electron beam melting (EBM)
Almost any alloy (including titanium alloys)
[53]
Selective laser melting (SLM)
Titanium alloy, cobalt chromium alloy, stainless steel, aluminum
[54]
Selective heat sintering (SHS)
Thermoplastic powder
[55]
Selective laser sintering (SLS)
Hot plastic, metal powder, ceramic powder
[56]
Direct metal laser sintering (DMLS)
Almost any alloy
[57]
Lamination
Laminated object manufacturing (LOM)
Paper, sheet metal, plastic film
Helisys
[58]
Powder feeding
Directed energy deposition (DED)
Almost any alloy
Fraunhofer
[59]
Metal wire
Electron beam freeform fabrication (EBF³)
Almost any alloy
LARC
[58]
... Rock joint stiffness is a term used to describe these curves in both vertical and tangential directions. Goodman et al. (1968) used the terms joint shear stiffness ( ) and vertical stiffness ( ) to express the rate of change in vertical and shear stress versus relevant displacement, respectively. The and are the critical input mechanical parameters in discrete element numerical modeling. ...
The deformational behavior of jointed rock masses is greatly influenced by the geometrical and mechanical characteristics of joints. Shear (ks) and normal (kn) stiffness of joints not only are vital input factors in the dis-continuum numerical analysis but also use to calculate elastic constants of an equivalent continuous material in the finite element numerical modeling. In this study, based on eighty-nine laboratory direct shear tests under constant normal loading (CNL) conditions the dependency of k_s and kn on normal stress (σn) is evaluated by the regression models. All natural and saw-cut discontinuity specimens belong to the meta-sandstone and limestone rock types. The range of the normal stress and ratio of normal stress to joint compressive strength was from 0.34 to 7.5 MPa and 0.01 to 0.24, respectively. The data analysis led to the inevitable outcome; the ks and kn versus σ_n increased by the power-law and exponential-law relationship, respectively. The shear stiffness not only in a natural joint, in which joint roughness coefficient (JRC) has a direct effect on the stiffness but also in a saw-cut specimens shows a power-law relationship with normal stress. Besides, the normal to shear stiffness ratio (kn⁄ks ) against the σn exhibit a non-linear trend line; the meta-sandstone bedding and joint show the power and the exponential trend line, respectively; the stiffness ratio (kn⁄ks ) at lower normal stress (0.5 MPa) were from 1.5 to 5.6, but by increasing the σn up to 7.5 MPa the stiffness ratio raised to 14.4. Considering the effect of normal stress on joint stiffness while choosing the reliable input factors for numerical analysis can avoid conservative analysis.
... The discontinuum elements are simple Goodman joint elements (Goodman et al 1968), with parameters based on Day et al. (2017), to represent inherent weakness associated with the argillaceous component of the Cobourg-Lindsay. The constitutive model has a linear normal stiffness (which (Eberhardt and Diederichs (2017) Content courtesy of Springer Nature, terms of use apply. ...
Ultra-long-term storage of spent nuclear fuel and other waste products is most likely to be accomplished through the construction and safe closure of deep geological repositories (DGRs). Around the world, numerous countries are planning, designing and in some cases, building such repositories in sound rock between 400 and 1000 m below surface. In Ontario, Canada, both crystalline (granite, gneiss, etc.) and sedimentary (limestone) are being considered as host formations. A critical element of the host rock (the geo-barrier) is the susceptibility to excavation-induced damage and the long-term evolution of this fracture damage over the lifetime of the repository. The excavation damage zone, EDZ, can form a pathway for the migration of radionuclides from the repository, bypassing seals and internal barrier structures. The Cobourg Limestone is a candidate formation for DGR construction in Ontario, Canada. The long-term performance of this barrier rock may be controlled in part by internal structures including pseudo-bedding in the form of varying clay mineral content and an argillaceous/calcite nodular structure. Typically, geotechnical assessment, analysis and design are based on standard rock properties obtained from laboratory testing on 50–75 mm diameter samples and the occurrence (if any) of jointing. Neglected are the impacts of the internal texture within the limestone. The potential impacts of these structures on EDZ evolution are numerically explored in this paper to provide a schematic illustration of their potential importance for ultra-long-term behaviour. It is evident from this scoping study that the physical (and geological) nature of the bedding structures as well as the internal intra-bed fabric plays as significant a role in behaviour as does the nominal as-measured bulk properties.
... To solve the problem of adequate simulation of the hierarchical-block environment, the authors have studied and analyzed available approaches to modeling the rock mass homogeneity disturbances, including the Goodman contact element [1], and developed its 3D modification. The SigmaGT modeling of the deposit's stress-strain state and its individual blocks implies the use of a regular structured finite element mesh, which allows the model layers to be automatically correlated with the mining plans. ...
The paper proposes a variant of the algorithm for 3D numerical simulation of the rock mass stress-strain state in the vicinity of structural heterogeneities by the finite element method. Modeling of the stress-strain state is used, among other things, when analyzing the fractures in the rock mass, which can occur as a breakage or a shear along the weakening planes. The rock massif has a block structure, where the boundaries of various-scale blocks are structural disturbances of different orders. The surface planes of structural heterogeneities usually have complex geometry and spatial orientation, so the most adequate results can be obtained by 3D modeling of the disturbed rock mass. Besides, it is important to take into account the type of the stress-strain state, which can be not only gravitational, but also gravitational-tectonic, including horizontal loading of the rock mass. Accounting these features allows obtaining the most adequate geomechanical model of the studied object. For this purpose, the authors have studied and analyzed the existing approaches to modeling heterogeneities in the rock mass, including using the Goodman contact element, and developed its 3D modification. A mining engineer needs to have a handy tool that allows creating and editing a geomechanical model, taking into account mining plans and related sections. The model navigation, edition of its individual blocks to specify geology and creation of local sub-models make it necessary to use structured meshes of finite elements. Modification of the model with the introduction of contact elements entails the creation of an unstructured mesh, which complicates further manipulations with it. To solve this problem, a special zero element was developed, which allows saving a structured mesh format when implementing a contact element. This zero element, like the contact element, has zero thickness, and its nodes have averaged strength characteristics of adjacent blocks of the undisturbed rock mass. The result of these studies is a tool that allows creating 3D models of the rock mass stress-strain state, taking into account its structural heterogeneities and preserving the regular structure of the finite element mesh.
... The interface element was initially developed to work in conjunction with two-and three-dimensional elements that represent a thin layer of material or the contact between two distinct materials, such as the case of soil-structure interaction. The first study on interface elements was by Goodman et al. (1968). In that study, the interface element was used to simulate the slip and separation between two bodies in contact. ...
Abstract A two-dimensional interface finite element capable of associating flat shell elements positioned one above the other was developed. The implemented interface element can physically simulate the contact between the flat shell elements and connect the reference planes of the shell elements above and below it. The formulation presented allows consideration of nonlinear behavior for the deformable connection as well as for the concrete and steel materials that make up the shell structure. One of the practical applications analyzed in this research is the numerical simulation of composite floors formed by a reinforced concrete slab connected to steel beams through a deformable connection. In this case, the concrete slab and the steel beams are discretized by flat shell elements and the deformable connection is discretized by two-dimensional interface elements. Experimental and numerical results from literature were used to validate the implemented elements. In the two examples analyzed, the results obtained for the displacements were close, with the difference, in the first case, being associated with uncertainties during the experimental test and in the second, the difference in theories used in the formulation of the implemented elements.
... It explains the post-peak softening behavior of quasi-brittle materials having a fracture zone which is also suitable for HMA. This type of interface uses cohesive elements of zero thickness or negligible thickness which are similar to the zero thickness interface element formulated by Goodman et al. [34]. The cohesive elements are placed between the continuum elements for capturing the behavior of the interface. ...
Reflective cracks are the major distress in Hot-Mix Asphalt (HMA) Overlays. Among the several mitigation methods adopted to reduce the reflective cracking, the application of geosynthetic layer between the old pavement and the new overlay is widely adopted due to the ease of application. The application of geosynthetics as interlayers reduces the tensile stress in the old pavement, thereby restricting the crack development. Though the interlayers are effective in delaying the progress of reflective cracking, they lead to a reduction in bond strength. The interlayer may also cause delamination, which affects the overall stability of the pavement. Hence the present study focuses on the analysis of the failure mechanism of the interface. The interface behavior with three different types of overlay fabrics made of glass (synthetic), jute and coir fibers was studied using finite element program ABAQUS at three different temperatures of 10, 20 and 30 °C. The interface zone between geosynthetic and asphalt layers was numerically simulated using the Cohesive Zone Model (CZM). The failure mechanism was expressed in terms of Scalar Stiffness Degradation Factor along with the principal strains developed in the geosynthetic layer. Further, the stresses developed at the surface of old pavement were examined to study the initiation and development of reflective cracks. It is concluded that among the natural geosynthetics, the coir geotextile interlaid sample is better compared to jute geotextile as it showed delayed degradation and developed lower stresses at the surface of old pavement.
... It is usually described with an empirical closure law (hyperbolic, semi-logarithmic or statistical distribution) combining normal stress and normal closure using laboratory experiments (e.g. step-pressure tests or purely mechanical tests) [133,28,347,112,58,345,260]. A hysteresis effect is typically observed in the uni-axial strain component measured across the fracture by comparing the aperture state before and after opening and closing cycle. ...
Hydraulic fracturing is a common technique used in a variety of fields like civil and mining engineering, oil & gas and geothermal industry. It can be used to enhance the permeability of low permeable rocks, to increase the connectivity of natural fractures, to modify the rock mass strength, or to measure the Earth’s stress field. In the context of deep geothermal energy exploitation, a heat exchanger needs to be created at depth with characteristics favorable for heat extraction i.e. sufficient permeability and heat exchanger area. The creation of the heat exchanger for geothermal heat extraction remains a critical element with high associated risks including poor reservoir performance and induced seismicity. Hence the need for a better understanding of the coupled seismic-hydromechanical processes during stimulation operations. The execution of experiments on the intermediate-scale has the advantage of a better control on the processes associated with induced seismicity and reservoir performance compared to full-scale and allow to use comprehensive real time monitoring of pore pressure, rock mass deformation and seismicity. This scale is closer to the full-scale stimulation than laboratory scale, where seismo-hydromechanical interactions are generally focused on single fractures. The decameter-scale In-situ Stimulation and Circulation (ISC) project took place between 2015 and 2018 at the Grimsel Test Site (GTS), Switzerland. The GTS is located in the Central Swiss Alps, beneath the mountains of the Grimsel Pass. Overall, the moderately crystalline fractured rock mass shows a pervasive foliation and was intersected by six major sub-vertical shear zones. For each of the two assumed stimulation endmembers, hydraulic shearing and hydraulic fracturing, six experiments were conducted. Prior to the experiments, the test volume was characterized in great detail with respect to geology, geophysics, hydrogeology and in-situ stress field. This doctoral thesis aims at better understanding tensile fracture growth. It includes study of fracture toughness and fracture process zone on laboratory scale and the investigation of the seismo-hydromechanical coupled processes during in-situ hydraulic fracturing experiments.
The tested intact Grimsel Granodiorite samples indicate that the resistance against material failure is significantly higher across the foliation plane than along it. The results from Digital Image Correlation (DIC) confirm the development of a semi-elliptical fracture process zone (FPZ) with an average length to width ratio of about two for both principal directions. This agrees well with the available results in the literature. The experimental results of the length of the FPZ give supporting evidence to the fact that a nonlinear cohesion stress distribution provides an accurate cohesive model that agrees well with the experimental results. Additionally, the conformity of the ratio of the FPZ length in two principal directions with the theoretical predictions gives supporting evidence to the proportionality of the FPZ length with respect to the square of fracture toughness to tensile strength.
At the decametric scale during the in-situ experiment, the hydromechanical coupled responses of the rock mass and its fractures were captured by a comprehensive monitoring system installed along the tunnels and within dedicated boreholes. At the borehole scale, these processes involved newly created tensile fractures intersecting the injection interval while at the cross-hole scale, the natural network of fractures dominated the propagation process. The six HF experiments can be divided into two groups based on their injection location (i.e., south or north to a brittle ductile shear zone), their similarity of injection pressures and their response to deformation and pressure propagation. The experiments executed north of the shear zone, show smaller injection pressures and larger backflow during bleedoff phases. In addition, we observe re-orientation of the seismic cloud as the fracture propagated away from the wellbore. The re-orientation during propagation is interpreted to be related to a strong stress heterogeneity and the intersection of natural fractures striking different from the propagating hydraulic fracture. This leads in the details to complex geometry departing from theoretical mode I fracture geometries. The seismic activity was limited to about 10 m radial distance from the injection point. In contrast, strain and pressure signals reach further into the rock mass indicating that the process zone around the injection point is larger than the zone illuminated by seismic signals. Furthermore, strain signals indicate not just single fracture openings but also the propagation of multiple fractures.
Various methods to estimate the fracture opening and fracture contact pressure were applied and compared from single injection borehole observations with the strain gauge in distance from the injection point. The results show, that the fracture opening pressure was also observed at the strain gauge, associated with a strong increase of fracture transmissivity. The combination of injection pressure and strain observation allows to define an aperture-stress relationship with a general trend toward decreasing normal fracture stiffness during fracture opening. The fracture contact pressure can be estimated, but hydromechanical superposition of pump shut-in and corresponding pressure loss and interaction of the connected surrounding fractures make this task very challenging and error-prone. The pore pressure data set differentiate two distinct responses based on lag time and amplitudes. This allow to distinguish a near- and far-field response. The near-field response is due to pressure
diffusion and the far-field response is due to stress perturbation. The far-field pore pressure response is consistent for all experiments, indicating the dominant failure mechanism. This change in the far-field are very sensitive and can be used as a complementary method to seismic monitoring during hydraulic stimulations. The exceptional hydromechanical dataset allow to test numerical stimulations and can help to improve injection strategies, the monitoring design and the numerical modelling.
... Rocks in deep underground generally contain dozens of preexisting conjugate flaws induced by geological tectonic movement and engineering activities [2,17,25]. In addition to static pre-compression due to tectonic stress, underground rock masses containing preexisting conjugate flaws are also likely subjected to dynamic disturbance from blasting vibration, excavation, or drilling [40], as shown in Fig. 1, where conjugate flaws (Fig. 1d) are generally formed with two intersecting flaws or more groups of intersecting flaws suffering the same geotechnical conditions [1,27]. ...
Conjugate flaws widely exist in rock masses and play a significant role in their deformation and strength properties. Understanding the mechanical behaviors of rock masses containing conjugate flaws is conducive to rock engineering stability assessment and the related supporting design. This study experimentally investigates the mechanical properties of conjugate-flawed sandstone specimens under coupled static–dynamic compression, thereby providing insight into how conjugate fractures interact to produce tracing tensional joints. Results indicate that the coupled compressive strength and the dynamic elastic modulus of conjugate-flawed rock specimens show remarkable loading rate dependence. For a fixed strain rate, the specimen with a static pre-stress equal to 60% of its uniaxial compressive strength has the highest coupled strength. Besides, both higher static pre-stress and strain rate can induce smaller mean fragment size and greater fractal dimension of the specimen, corresponding to a more uniform distribution of the broken fragments with smaller sizes. When the static pre-stress is lower than 80%UCS, the flawed specimen under a higher strain rate is characterized by higher absorbed energy. However, when the pre-stress equals 80%UCS, the value of the energy absorbed by the specimen in the dynamic loading process is negative due to the release of the preexisting considerable elastic strain energy input from the static pre-loading. As for the failure modes, cracks always penetrate the preexisting ipsilateral flaw tips to form anti-wing cracks. Under dynamic loading, the conjugate-flawed specimen generally shows tensile failure at a low strain rate, while the shear failure dominates at a high strain rate. In addition, based on progressive failure processes of the conjugate-flawed rock specimens, the evolution of tracing tensional joints in the field is discussed.
... Zur Simulation des Kontaktproblems im Rahmen der FEM werden in dieser Arbeit ZT-Elemente verwendet, welche ursprünglich aus dem Fachbereich der Geomechanik stammen. So fanden sie erstmalig Erwähnung in Goodman et al. (1968) und wurden ausführlich in Hohberg (1995) B. Beer (1985), Swoboda und Lei (1994), Buczkowski und Kleiber (1997) Parallel hierzu wurden zur Simulation von Rissausbreitung sogenannte Kohäsivzonenelemente entwickelt, siehe z. B. Xu und Needleman (1994), Ortiz und Pandolfi (1999), Zhang (2007), M. Alfano et al. (2008), Utzinger et al. (2008), Dias-da-Costa et al. (2012), Ottosen et al. (2016) und Khisamitov und Meschke (2018), die in ihrer Formulierung sehr große Ähnlichkeiten mit den ZT-Elementen besitzen. ...
Elektrische Maschinen und Motoren sind in unserem heutigen Leben allgegenwärtig und Bestandteil vieler Gebrauchsgüter sowie zentrales Betriebsmittel für die Produktion in Industrie und Gewerbe. Jeder elektrische Motor beinhaltet einen Rotor und einen Stator, deren Eisenkern zur Bündelung des magnetischen Flusses jeweils kein Vollmaterial darstellt, sondern eine geschichtete Struktur aufweist. Diese sogenannten Blechpakete, welche aus einzelnen weichmagnetischen, gegeneinander isolierten und paketierten Elektroblechen bestehen, werden eingesetzt, um Wirbelstromverluste zu minimieren und die Effizienz der gesamten Maschine zu erhöhen. Durch den geschichteten Aufbau des Blechpakets ist die strukturmechanische Materialmodellierung, die Simulation und die damit verbundenen Vorhersagen für diese Komponenten und für die gesamte elektrische Maschine deutlich erschwert, sodass sich diese Arbeit mit der Identifikation eines Materialmodells geschichteter Blechpakete beschäftigt. Im Zuge dessen wird die Interaktion der Einzelbleche auf mikroskopischer Ebene miteinbezogen, da im Rahmen einer Homogenisierung die große Relevanz der akkuraten Erfassung der Mikrostruktur für die makroskopischen Eigenschaften des gesamten Blechpakets aufgezeigt wird. Anhand des angewendeten Fügeverfahrens wird hierbei zwischen zwei Arten von Blechpaketen unterschieden, die jeweils eine unterschiedliche Modellierung der Mikrostruktur bedingen. Dies umfasst zum einen vollflächig verklebte Blechpakete, bei denen hier exemplarisch das Backlackverfahren betrachtet wird. Zum anderen wird sich mit Blechpaketen befasst, die nur punktuell, beispielsweise durch Klammern oder Schweißnähten, fixiert sind und deren Blechinteraktion von einem rauen Oberflächenkontakt charakterisiert wird. Für beide Klassen von Blechpaketen werden (linearisierte) äquivalente transversal isotrope Materialparameter unter Berücksichtigung der vorliegenden Mikrostruktur identifiziert und im Rahmen einer Sensitivitätsanalyse der Einfluss der mikroskopischen Eingabeparameter auf die makroskopischen Ergebnisse untersucht. Hierbei wird für vollflächig verklebte Blechpakete die große Relevanz der Schichtdicke des dünnen Backlacks für die makroskopischen Materialparameter offengelegt, sodass eine experimentelle Charakterisierung dieser Beschichtung mithilfe zweier Verfahren erfolgt, der Laserscanning-Mikroskopie und der Nanoindentierung. Die auf diese Weise bestimmten Größen können durch einen Abgleich einer experimentellen und numerischen Modalanalyse einer Teststruktur vollumfänglich bestätigt werden. Bei Blechpaketen mit rauem Oberflächenkontakt hingegen ist keine Zwischen- bzw. Klebeschicht präsent, sodass die verwendeten, phänomenologischen konstitutiven Kontaktgesetze zur Beschreibung der Blechinteraktion sorgfältig ausgewählt werden müssen. Dabei wird mithilfe einer analytischen und numerischen Homogenisierung ein (nichtlineares) makroskopisches Materialmodell identifiziert, das bei einer Simulation des Paketiervorgangs mithilfe der Methode der finiten Elemente eingesetzt wird. Mit diesen Ergebnissen wird aufgezeigt, wie äquivalente Materialparameter durch eine Linearisierung um einen Punkt, um den das Blechpaket betrieben wird und verbaut ist, identifiziert werden können. Wichtige Einflussgrößen diesbezüglich sind das konstitutive Kontaktgesetz, der maximal aufgebrachte Paketierdruck und die Anzahl der Fixierungen.
... To some extent, it can simulate the growth of sample cracks and the way of crack evolution in real working conditions, which can provide guidance and basis for theory and practice. The introduction of Goodman joint element [1] greatly promoted the application of the finite element method in the simulation of crack growth. However, continuous numerical methods are based on the assumption of continuity, so they are not effective in simulating large deformations such as crack propagation, and they cannot reflect the initiation and nucleation of micro-cracks during crack propagation. ...
When a flat steel with double cracks fails, the stress fields between different cracks will interact. The area between the cracks, that is, the steel bridge area, will be penetrated. This paper embeds the strain strength criterion into the discrete element numerical simulation method, and uses the block discrete element software UDEC to simulate the crack propagation and penetration in the steel bridge region of the prefabricated double-crack flat steel sample. Numerical simulation results show that there are four basic penetration modes in the double-crack steel sample during compression: (1) Discontinuous mode, which is characterized by no penetration between cracks, and the two pre-crack tip wing cracks independently expand; (2) Shear penetration mode, which is characterized by shear cracks penetrating the steel bridge. The principal stress field and shear stress field are concentrated in the steel bridge area, but the shear stress plays a leading role in penetration; (3) Tensile penetration mode, its characteristics: In order to penetrate the steel bridge with tensile cracks, the principal stress field is highly concentrated accumulated and nucleated in the area of the steel bridge, and the steel bridge penetration is instantaneous; The process occurs after the peak intensity.
... Baecher (Baecher et al., 1977), Veneziano (Dershowitz, 1985), and Voronoi (Dershowitz, 1985;Dershowitz & Einstein, 1988). In RS2, the Voronoi joint network can be employed to subdivide a homogeneous finite element model into non-overlapping convex polygons (i.e., Voronoi cells) to generate a GBM simulating the microstructure of crystalline rocks, In the Voronoi tessellated model (or GBM), the contact between two grains representing the grain boundary is an open-ended joint element (also called finite element interface; Ghabaussi et al., 1973;Goodman et al., 1968). The joint element is a one-dimensional fournoded quadrilateral element with a negligible thickness (Riahi et al., 2010). ...
Pillars are commonly used in underground mines to maintain the stability and integrity of the openings. An optimum design of mine pillars dictates that the pillars should be as small as possible and meet the load-bearing requirements. Therefore, a proper estimation of the rock mass strength is of paramount importance for a reliable design of mine pillars. It is known that the Hoek-Brown failure criterion, with its strength parameters obtained based on the Geological Strength Index, tends to underestimate the confined strength of well interlocked jointed hard rock masses. Therefore, pillar designs based on this approach could lead to oversized pillars due to underestimated strength of the pillar core. The central objective of this research is to better understand the strength and failure mechanisms of highly interlocked jointed pillars. For this purpose, a grain-based model is developed using the continuum numerical program RS2 to reproduce the laboratory behavior of intact and heat-treated Wombeyan marble. The heat-treated Wombeyan marble is considered to serve as an analogue for a highly interlocked jointed rock mass. An iterative calibration procedure is utilized to match the macro-properties of RS2-GBM to those of marble. It is found that the calibrated RS2-GBM captures some of the most important characteristics of brittle rocks, including the non-linear strength envelope and the change in the failure mode with increasing confinement. Next, the calibrated RS2-GBM of granulated marble is upscaled to simulate jointed pillars of various width-to-height ratios. The results of numerical simulations inferred that the slope of the pillar stability curve obtained from this approach is comparatively steeper than those of existing continuum and discontinuum models of jointed pillars. This is attributed to the high degree of block interlock leading to higher rock mass strength at the pillar core. It is demonstrated that this modeling approach provides more realistic results in terms of pillar failure processes compared to other continuum models, in which the rock mass is simulated as a homogeneous medium. The advantage of the continuum over the discontinuum GBM is its shorter computation time. Therefore, the proposed modeling approach can be used as a practical tool for stability analysis and design of mine pillars in jointed rock masses.
... The author pointed out that the interface element performed well, but numerical difficulties could arise when adjacent elements were assigned with very high different strength properties. For advanced application in the field of jointed rock masses, a specialized interface element has been developed over the past forty years (e.g., Ghaboussi et al., 1973;Goodman et al., 1968;Zienkiewicz et al., 1970). This has been extended and successfully applied to soil-structure interaction problems by many researchers (Clough and Duncan, 1971;Coutinho et al., 2003;Gaul and Mayer, 2008;Lü et al., 2013;Lü and Low, 2011;Segura and Carol, 2004;Sia and Dixon, 2007;Stutz et al., 2014). ...
This paper extends the use of the skew boundary condition in two-and three-dimensional (3D) finite element analysis for both structural and geotechnical applications when the need of the freedom directions at the interface nodes is different from the global Cartesian directions. For instance, jack-up structures have three conical-shaped footings, whose freedom directions at the interface nodes are not suitable for Cartesian directions. In addition, there is no axisymmetric movement of the soil as the load is applied to the jack-up's hull. Thus, a more reliable solution of jack-up-soil interaction should be analyzed in a full 3D version. This paper develops a simple 3D interface model for soil-structure interaction that uses skew boundary conditions and incorporates the visco-plastic strain method into the finite element program. The work was validated by computing bearing capacity factors of conical footings with different scenarios, such as plane strain, axisymmetric and 3D analysis. The results of the present analysis are in good agreement with the existing solutions. The fields of the displacement vector and failure patterns at the collapse state are demonstrated and discussed for each apex angle, and the influence of the conical angle on the bearing capacity factor (N c) is also examined.
... In geomechanics, the above contact constraints are generally modelled within the numerical 287 framework of interface element-based methods, such as Goodman element (Goodman et al., 1968) 288 and Desai thin-layer element (Desai et al., 1984). As aforementioned, these methods are insuf-289 ficient in large opening or sliding problems and generally require a globally conforming mesh. ...
Extrusion damage in the concrete face was widely observed in high concrete-faced rockfill dams in the last two decades. However, the accurate estimation of the concrete stress remains a great challenge. In this paper, a thermo-mechanical coupling method is presented to numerically evaluate the solar radiation effect on the concrete stress within the dual mortar finite element framework. The heat conduction is modelled as a transient time-dependent equation and hence the heat flow can be determined by meteorological data. The thermo-mechanical coupling is conducted in a weak way such that the linear system can be split into two subsystems friendly to the linear solver. The present method based on using nonconforming meshes is validated by the comparisons with node-to-segment method, conforming mesh and analytical solution. The application to a concrete-faced rockfill dam indicates that the phase lag and amplitude damping effects are apparent in the thermal analysis, confirming the importance of using transient heat conduction theory. The observed slab-slab separations emphasis the importance of using dual mortar contact method. The thermal stress is found to be larger than 10 MPa and therefore needs to be considered in the design and safety assessment.
Layered shale is a kind of rock with obvious anisotropy, which is significantly influenced by the inclination angle of the rock. In this study, the influence of bedding dip on the strength characteristics, failure mode, and internal fracture evolution of layered shale was investigated through laboratory triaxial compression tests and three-dimensional discrete element numerical simulations. Results show that the numerical model of layered shale constructed using the bonded block model can simulate the layered shale in terms of U-shaped strength variation and failure modes very well. Based on the distribution of cracks and failure characteristics of layered rocks, the failure modes of layered rocks are classified as follows: Shear failure across the bedding plane, slip failure along bedding planes, combined tensile splitting and shear failure. The development of microcracks damage in the slip failure model is controlled by interlayer joints, while in other failure modes, it is jointly controlled by the rock matrix and interlayer joints. The relationship between microscopic joint parameters and the variations of Young’s modulus and peak strength has been proposed.
This introductory chapter on the mathematical theory of finite element methods (FEMs) discusses its h‐version for elliptic boundary value problems in the displacement formulation. Topics addressed range from a priori to a posteriori error estimates and also include weak forms of elliptic PDEs, Galerkin schemes, finite element spaces, and adaptive local mesh refinement. Nonconformities and variational crimes as well as algorithmic aspects conclude the chapter.
A R T I C L E I N F O Keywords: Concrete face rockfill dams Stochastic dynamic response Seismic fragility Earthquake and parameter uncertainties GPDEM A B S T R A C T The multiple uncertainties of soil properties and ground motions significantly affect the seismic response of high concrete face rockfill dams (CFRDs). Three types of randomness (the material parameter randomness, stochastic seismic excitation, and their coupling) are generated by stochastic ground motion model and generalized F-discrepancy (GF-discrepancy) method. The generalized probability density evolution method (GPDEM) is used to analyze the influence of randomness on the stochastic dynamic response and system reliability of high CFRDs. The limit state of CFRD is defined according to the crest subsidence and the stress of face-slab, and a performance-based reliability evaluation framework is established. The results show that the randomness of ground motions dominates stochastic dynamic response of the CFRD and the dynamic reliability at different safety thresholds can be obtained by the above methods. Moreover, the proposed seismic safety evaluation framework provides a significant guidance for designing and analyzing practical engineering projects.
In numerous applications of environmental fluid mechanics, problems of retroactive interaction between the fluid medium and the discrete solid medium are encountered. This requires the implementation of appropriate numerical coupling techniques and of discrete element methods to take into account the discrete nature of the solid units of the studied medium. This is the case, for example, when studying the problems concerning the stability of rockfill dikes or even the flight of highspeed train ballasts, where the solid medium consists of discrete blocks. In this thesis, the Discontinuous Deformation Analysis (DDA) method is adopted to study discontinuous and discrete problems. In the first part of the thesis, twodimensional Discontinuous Deformation Analysis (2-D DDA) is initially used to study the ballast flight caused by dropping snow / ice blocks on high-speed railways and to analyze the dynamic behavior of ballast particles during their collision with a snow / ice block. The numerical results show that the velocity, shape and incident angle of the snow / ice block play an important role in the ballast flight. Specifically, the number and the maximum displacement of ballast particles increase with the speed of the train while the incident angle greatly affects the direction of motion of the ballast particles. The shape of the ice block affects the amount and the extent of the ballast flight. Afterward, the coupling between 2D-DDA and the Computational Fluid Dynamics (CFD) equations (2D-DDA / CFD) is carried out to study the stability of a breakwater under violent wave impacts by using a triple-coupled Fluid-Porous-Solid model. Here, the fluid model is described by the Volume-Averaged Reynolds-Averaged Navier-Stokes equations in which the nonlinear Forchheimer equations for the porous medium are added to the inertia terms. The 2D-DDA method is used to analyze the movement and the stability of the caisson and armor units by taking into account the shapes of the armor units, as well as the contact between blocks. In the second part of the thesis, the 3D version of the DDA method is developed by programming in the C ++ language. Particular attention is given to the detection of contacts between blocks, considered as rigid solids. Thus, the techniques of the Common Plane and of the soft contact method are used to avoid the processes of penetration between solid blocks. The 3D-DDA method is verified and validated first of all by academic test cases. Then, the 3D-DDA model is tested by a fluidstructure interaction procedure which concerns the stability of a hydraulic gravity dam with pre-existing cracks. The stability and damage of the structure are examined as the water level rises and as a function of the cohesion between the blocks.
Quantitative predictions of natural and induced phenomena in fractured rock is one of the great challenges in the Earth and Energy Sciences with far‐reaching economic and environmental impacts. Fractures occupy a very small volume of a subsurface formation but often dominate fluid flow, solute transport and mechanical deformation behavior. They play a central role in CO2 sequestration, nuclear waste disposal, hydrogen storage, geothermal energy production, nuclear nonproliferation, and hydrocarbon extraction. These applications require predictions of fracture‐dependent quantities of interest such as CO2 leakage rate, hydrocarbon production, radionuclide plume migration, and seismicity; to be useful, these predictions must account for uncertainty inherent in subsurface systems. Here, we review recent advances in fractured rock research covering field‐ and laboratory‐scale experimentation, numerical simulations, and uncertainty quantification. We discuss how these have greatly improved the fundamental understanding of fractures and one's ability to predict flow and transport in fractured systems. Dedicated field sites provide quantitative measurements of fracture flow that can be used to identify dominant coupled processes and to validate models. Laboratory‐scale experiments fill critical knowledge gaps by providing direct observations and measurements of fracture geometry and flow under controlled conditions that cannot be obtained in the field. Physics‐based simulation of flow and transport provide a bridge in understanding between controlled simple laboratory experiments and the massively complex field‐scale fracture systems. Finally, we review the use of machine learning‐based emulators to rapidly investigate different fracture property scenarios and accelerate physics‐based models by orders of magnitude to enable uncertainty quantification and near real‐time analysis.
The interface bonding condition between asphalt pavement layers is always imperfect because of the differing material properties of different layers and the limitation of construction techniques. Therefore, designing asphalt pavement by considering the interface to be completely continuous is not precise. The viscoelastic character of the asphalt layer contributes significantly to the performance of asphalt pavement. To explore the influence of the imperfect interface on the viscoelastic dynamic response of asphalt pavement, the Hankel–Laplace transformation was applied to convert the partial differential equations to ordinary differential equations and a transfer matrix was introduced to describe the behavior of the imperfect interface. Based on the boundary condition and integral inverse transformation technique, an analytical solution for the displacement, stress, and strain of the pavement can be obtained. By considering the variation in the interface condition and the viscoelastic characteristics of the asphalt layer, the dynamic response of the pavement was calculated based on a practical example. The results show that the interface condition between the asphalt layer and the base course has a marked influence on the viscoelastic dynamic response of the pavement and that enhancing the strength of this interface can reduce the deflection of the pavement. The series elastic component in the modified Burgers model is another significant factor that affects the calculation results of the pavement dynamic response.
This chapter presents how the multiphysical soil–structure interactions can be modeled using the finite element method. Hydro-mechanical couplings have become particularly important in many applications, as the loading rate and soil permeability are such that the soil behavior is not completely drained or undrained. The chapter provides a basic formulation of hydromechanically coupled finite elements of the interface. It also provides the governing equations and finite element formulations. The chapter highlights the importance of considering hydromechanically coupled interfaces in the soil–structure interaction. An example of suction caisson modeling is provided to illustrate the inherently partially drained (between drained and undrained) behavior of this foundation in the offshore environment and how interface elements are used to simulate this behavior. The fast development of offshore foundation technologies and the increasing complexity of simulations are likely to generalize the use of coupled interface elements.
Carbonate reservoirsbeing the main carriers of oil with a great deal of natural gas found in the past five years.Carbonate Reservoirs contribute to more than half of the World's Conventional Petroleum Reserves. The characteristics of carbonates make the Hydrocarbon exploration and production a complex.Rock Heterogeneityvaries at all scales and properties (porosity, permeability and flow mechanisms).The application of innovative techniques for the new plays in carbonate rocks epitomizes frontier exploration. The permeability is controlled by fractures and faults in most of the low-matrix-porosity hydrocarbon reservoirs that are productive. Geological risk can be reduced by understanding the reservoir basic fractures and faults which in turn reduces the well costs and increasing the hydrocarbon recovery. Investigation for the long-standing recognition of naturally fractured carbonate reservoirs is needed to evaluate the new fracture and fault analysis is important for the prediction techniques and understanding of the concepts of carbonate reservoirs with low matrix porosity. Fractures and diagenesis are particularly essential in carbonate reservoirs for the related challenges of geomechanics and mechanical stratigraphy will become increasingly important. With the application of new techniques and concepts to investigate carbonate reservoir rocks continues to build through the successful production of hydrocarbon oil & gas in ultra-deep carbonate reservoir targets and diagenetically and geomechanically complex resource plays in carbonate rocks.
De nombreux secteurs d’activités impliquent une occupation de l’espace souterrain. Le creusement dans un massif rocheux présente différents modes de ruine qu’il faut savoir identifier pour utiliser les outils de conception adaptés. Parmi eux, l’instabilité de blocs est un problème courant dans les massifs rocheux fracturés. Les approches numériques de blocs multiples permettent de considérer le massif dans son ensemble mais leur utilisation peut s’avérer lourde et requiert beaucoup de données d’entrée parfois indisponibles. L’approche Isobloc est basée sur le concept de bloc isolé et, comparée aux autres méthodes du même type, elle est plus rigoureuse dans la résolution du problème de mécanique du bloc. Dans cette thèse, cette méthode a été étudiée afin de pouvoir l’intégrer dans la démarche de conception en milieu rocheux fracturé. Une première partie s’intéresse spécifiquement à la loi de comportement normal des joints, et à la définition d’indicateurs afin de quantifier la sécurité de l’état d’équilibre du bloc. Une autre partie présente les réflexions et manières de modéliser une solution de soutènement avec Isobloc. Trois types sont proposées suivant le degré de connaissance du soutènement. Enfin une application de la méthode Isobloc dans la démarche d’étude de stabilité de blocs a été proposé à partir de données d’un site d’étude réel.
In this work, a new numerical approach based on the Finite Element Method and an implicit continuum formulation, called Continuum Voronoi Block Model-CVBM, is proposed to represent the fracturing process in hard rocks and also the rupture of underground works with high field stresses. In this model, developed with the RS2 program, the rock mass was simulated by a set of blocks, formed by a Voronoi mosaic, joined at their interfaces by joint elements. Different case studies were represented on a laboratory (Lac du Bonnet pink granite and Creighton granite) and field scale (Mine-By tunnel and Creighton pillar). The model proved to be robust on the laboratory scale and described the rock's relevant macro-properties in conventional tests: crack initiation stress, crack damage stress, simple and triaxial compression strength, tensile strength, Young's modulus and Poisson's ratio. The calibrated laboratory model served as the basis for a sensitivity study that analyzed how micro-properties influence macroscopic responses, thus generating a calibration methodology for Brazilian and UCS tests. On a field scale, the model represented the mass deterioration process explicitly, captured the rupture geometry, and the excavations' convergence displacements. The real case studies supported the use of CVBM for parametric studies that sought to assess the influence of discontinuity families on deep underground works' behaviour. It was found that the presence of discontinuities tends to promote stress relief due to shear. Consequently, discontinuities in the mass with high in situ stresses tend to favour excavation stability. Such results show the CVBM's potential for modelling the behaviour of underground works with high field stress.
Eccentric load effect of prestressing in composite beam leads to nonlinear coupling oof deflection-slip. For the prestressed composite beam, considering axial force and eccentric moment of the prestressing equivalent load, variational equilibrium equations are imposed by the virtual work theorem which involves the interfacial slip condition. With relevant boundary conditions of different structural form, the closed-form solution can be derived. The model and closed-form solution are then validated by means of finite element analysis.
La surveillance des structures de génie civil constitue un enjeu majeur et fait encore l’objet de nombreuses recherches. En particulier, les problématiques de coût, de durabilité des capteurs et de fiabilité des mesures restent des aspects fondamentaux à prendre en compte pour toute nouvelle solution d’instrumentation. Les capteurs à fibre optique (FO) rencontrent un intérêt croissant pour l’acquisition de mesures réparties de déformation/température dans les ouvrages en béton armé et pour le monitoring de structures en général, en raison des avantages offerts en termes de précision, de déport de la mesure sur de longues distances et d’une faible intrusivité par rapport aux capteurs traditionnels. Dans ces applications, des câbles à FO sont généralement collés en parement ou noyés à l’intérieur de la structure en béton. Selon la configuration, ils sont alors exposés aux conditions climatiques ou soumis à l’environnement alcalin de la matrice cimentaire, et leurs caractéristiques physiques/mécaniques peuvent alors évoluer dans le temps sous l’effet des vieillissements. La durabilité des capteurs et la fiabilité des mesures sur le long terme restent encore mal connues dans ces environnements de service complexes, et sont également peu documentées par les fabricants ou dans la littérature. Le travail mené dans cette thèse vise donc à mieux appréhender ces problématiques à travers une vaste étude expérimentale de durabilité en laboratoire, complétée par une étude de terrain sur des corps d’épreuves massifs instrumentés par capteurs à FO.Le premier volet de la thèse propose un programme expérimental complet portant sur des éprouvettes de béton instrumentées par deux câbles à FO du commerce, qui sont exposées à des vieillissements accélérés représentatifs des applications considérées et à un vieillissement naturel sur site extérieur. Des caractérisations mécaniques, physico-chimiques et géométriques de ces échantillons sont alors réalisées à différentes échéances de temps au cours des vieillissements et permettent d’évaluer la durabilité de ces deux câbles à FO pour les deux configurations d’instrumentation possibles (câbles noyés / collés en parement). L’évolution du transfert d’effort du béton vers le cœur de la FO est ensuite évaluée numériquement en intégrant les résultats expérimentaux dans un modèle aux éléments finis simplifié. En parallèle de cette étude de laboratoire, plusieurs blocs de béton du projet ODOBA de l’IRSN, destinés à subir des cycles de vieillissement accéléré pour déclencher les pathologies de gonflement du béton, ont été instrumentés au moyen de câbles à FO noyés et collés en parement. Ce second volet de la thèse vise à démontrer l’aptitude de cette technologie pour la détection et le suivi à long terme des pathologies de gonflement potentiellement rencontrées sur les enceintes de centrales nucléaires (réaction sulfatique interne : RSI, réaction alcali-granulat : RAG et couplage RAG/RSI). Les résultats obtenus contribueront à établir des critères objectifs permettant de choisir l’instrumentation des structures de centrales nucléaires ainsi que des méthodes facilitant l’interprétation des mesures sur le long terme
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