Showing papers on "Discontinuity (geotechnical engineering) published in 2010"

Crack nucleation in a peridynamic solid

Abstract: A condition for the emergence of a discontinuity in an elastic peridynamic body is pro- posed, resulting in a material stability condition for crack nucleation. The condition is derived by deter- mining whether a small discontinuity in displace- ment, superposed on a possibly large deformation, grows over time. Stability is shown to be determined by the sign of the eigenvalues of a tensor field that dependsonlyonthelinearizedmaterialproperties.This condition for nucleation of a discontinuity in dis- placement can be interpreted in terms of the dynamic stability of plane waves with very short wavelength. A numerical example illustrates that cracks in a peri- dynamic body form spontaneously as the body is loaded.

Hydraulic Fracture Propagation in a Naturally Fractured Reservoir

Abstract: This paper (SPE 128715) was accepted for presentation at the SPE Oil and Gas India Conference and Exhibition, Mumbai, India, 20–22 January 2010, and revised for publication. Original manuscript received 17 February 2010. Revised manuscript received 20 July 2010. Paper peer approved 17 August 2010. Summary We present the results of numerical modeling that quantify the physical mechanisms of mechanical activation of a natural fault because of contact with a pressurized hydraulic fracture (HF). We focus on three stages of interactions: HF approaching, contact, and subsequent infiltration of the fault. Fracture interaction at the contact is shown to depend on four dimensionless parameters: net pressure in the HF, in-situ differential stress, relative angle between the natural fault and the HF, and friction angle of the natural fault. A numerical model based on the displacement discontinuity method (DDM) allowing for fracture closure and Mohr-Coulomb friction was used to calculate the displacements and stresses along the natural fracture as a result of the interaction with the pressurized HF. The analysis of the total stress state along the fault during the HF coalescence stage makes it possible to define a criterion for reinitiation of a secondary tensile crack from the natural fault. We show that the most probable location for tensile-crack initiation is the end of the open zone of the fault where the highest tension peak is generated by the HF contact. In our numerical analysis, we study the magnitude of maximum tensile stress and its position along the fault for a wide range of key dimensionless parameters. Given real reservoir properties, these measurements can be used to detect the possible fracturing scenarios in naturally fractured reservoirs. Using simplified uncoupled modeling of fluid penetration into the fault after the contact with the HF, we demonstrate that either an increase or a decrease of the tensile stress at the opposite side of the fault can be realized depending on the ratio of increments of net pressure and the fluid front as it penetrates the natural fault.

A numerical model of dyke propagation in layered elastic media

Abstract: SUMMARY We develop a mathematical model describing dyke propagation in proximity of an elastic discontinuity of the embedding medium. The dyke is modelled as a fluid-filled crack in plane strain configuration employing the boundary element method. The pressure gradient along the crack is assumed proportional to the difference between the densities of the host rock and the fluid. Mass conservation is imposed during propagation and fluid compressibility is taken into account. The path followed by the crack is found by maximizing the total energy release, given by the sum of the elastic and gravitational contributions. The mathematical simulations provide a sort of ‘refraction phenomenon’, that is a sudden change in the direction of propagation when the crack crosses the boundary separating different rigidities: if the dyke enters a softer medium, its path deviates towards the vertical, if the dyke enters a harder medium its path deviates away from the vertical and may even become arrested as a horizontal sill along the interface, if the rigidity contrast is large. Gravitational energy plays a major role during propagation; in particular, in proximity of layer boundaries, this role is enhanced by the shift of the centre of mass due to changes of dyke shape. Mathematical results were validated by laboratory experiments performed injecting tilted air-filled cracks through gelatin layers with different rigidities.

The Shear Behavior of Bedding Planes of Weakness Between Two Different Rock Types with High Strength Difference

Abstract: In this article, the shear behavior of discontinuities caused by bedding planes of weakness between two different rock types with high strength difference is investigated. The effect of roughness and compressive strength of joint wall in such discontinuities are studied. The designed profiles consist of two regular and three irregular artificial joints molded by three types of plaster mortars with different uniaxial compressive strengths. Firstly, it is demonstrated that the shear behavior of discontinuities with different joint wall compressive strengths (JCS) is different from rock joints with identical wall compressive strengths by showing that Barton’s empirical criterion is not appropriate for the former discontinuities. After that, some correlation equations are proposed between the joint roughness coefficient (JRC) parameter and some surface statistical/fractal parameters, and the normal stress range of Barton’s strength criterion is also modified to be used for such discontinuities. Then, a new empirical criterion is proposed for these discontinuities in such a way that a rational function is used instead of JRC log10(JCS/σ n) as i 0(σ c/σ n)a/[b + (σ c/σ n) a ] by satisfying the peak dilation angle boundary conditions under zero and very high normal stress (physical infinite normal stress causing zero peak dilation angle). The proposed criterion has three surface parameters: i 0, a, and b. The reason for separation of i 0 from JRC is indicated and the method of its calculation is mentioned based on the literature. The two remaining coefficients (a and b) are discussed in detail and it is shown that a shows a power-law relationship with b, introducing the coefficient c through b = c a . Then, it is expressed that a is directly related to discontinuity surface topography. Finally, it is shown that the coefficient c has higher values in irregular profiles in comparison with regular profiles and is dominated by intensity of peak dilation angle reduction (majorly related to the surface irregularity and minorly related to roughness). The coefficient c is to be determined by performing regression analysis on experimental data.

Controls on Block Toppling Using a Three-Dimensional Distinct Element Approach

Abstract: Analysis methods for block toppling are most commonly undertaken in two dimensions. This paper investigates the influence of discontinuity orientations on three-dimensional block toppling mechanisms using a three-dimensional distinct element code. The three-dimensional models allow one to kinematically appraise if toppling conditions derived for two-dimensional geometries can be extended into three dimensions. Two conceptual model geometries were considered in order to represent a road cut or open-pit bench. The first geometry examined a slope with fixed vertical lateral boundaries, while the second geometry assumed an unrestrained lateral slope as a model boundary condition. This “along-strike slope profile” of the models was found to play an important role in the failure mechanism and displacement direction. The dip direction and dip angle of the toppling, basal and lateral release discontinuities were varied one at the time using angular ranges of up to 30° from an assumed mutual orthogonal relationship. This made it possible for the influence and importance of each discontinuity set to be independently evaluated. The results are presented in a stereographic format with preliminary zones outlining discontinuity aspect combinations that potentially result in block toppling failures.

Deformation, fracture, and fragmentation in brittle geologic solids

Abstract: A model is developed for mechanical behavior and failure of brittle solids of geologic origin. Mechanisms considered include elastic stretch and rotation, thermal expansion, and deformation associated with micro-cracks. Decohesion on preferred cleavage planes in the solid, and subsequent effects of crack opening and sliding, are modeled. Explicit volume averaging over an element of material containing displacement discontinuities, in conjunction with the generalized divergence theorem, leads to an additive decomposition of the deformation gradient into contributions from thermoelasticity in the intact material and displacement jumps across micro-cracks. This additive decomposition is converted into a multiplicative decomposition, and the inelastic velocity gradient is then derived in terms of rates of crack extension, opening, and sliding on discrete planes in the microstructure. Elastic nonlinearity at high pressures, elastic moduli degradation from micro-cracking, dilatancy, pressure- and strain rate-sensitive yield, and energy dissipation from crack growth and sliding are formally addressed. Densities of micro-cracks are treated as internal state variables affecting the free energy of the solid. The mean fragment size of particles of failed material arises from geometric arguments in terms of the evolving average crack radius and crack density, with smaller fragments favored at higher loading rates. The model is applied to study granite, a hard polycrystalline rock, under various loading regimes. Dynamic stress–strain behavior and mean fragment sizes of failed material are realistically modeled. Possible inelastic anisotropy can be described naturally via prescription of cleavage planes of varying strengths.

High-resolution transition zone structures of the Gorda Slab beneath the western United States: Implication for deep water subduction

Abstract: [1] The current data set from USArray provides an unprecedented opportunity to investigate mantle transition zone structures beneath the western United States. We have made transition zone images with the Common Converted Point (CCP) stacking method. More than 9600 high quality receiver functions were stacked with reference to two different three-dimensional tomography models and a one-dimensional velocity model. Where the Gorda plate passes through the transition zone, the 410 discontinuity has been elevated ∼25 km and the 660 discontinuity has been depressed ∼35 km. We interpret the transition zone topography in terms of mineral physics results in several different ways, noting in particular that recent measurements on the Clapeyron slope for the ringwoodite-to-perovskite phase transition under dry conditions give a phase boundary slope of ∼−1.3 to −0.4 MPa/K. The ∼35 km deflection of the 660 discontinuity observed in the receiver functions seems to be the evidence that the subducted slab can carry abundant water from the surface to the transition zone, and in the transition zone the water in the slab may be fully saturated (e.g. the water content is ∼2.0 wt%). Analyses of the velocity perturbations in the tomography models and the transition zone thickness indicate that the deep water is likely well confined within the subducted slab. We infer that the presence of water in the subducted Gorda slab might have contributed ∼15 km and the thermal anomaly in the slab might have contributed ∼20 km to the depression of the 660 discontinuity.

A Commentary on: “Diffusion of Carbon in Austenite with a Discontinuity in Composition”

Abstract: CONSIDER an allotropic transition between two phases in a pure substance. The phases are said to be in equilibrium when they have identical free energies. Pure ice and water coexist at precisely 273.15 K (0 C) and 1 atm of pressure. When this system consists of a mixture of common salt and H2O, the ice and water become solid and liquid solutions, respectively, but can still coexist in equilibrium, albeit under different circumstances. Yet, it has been known for many centuries that these impure phases have different chemical compositions, water being richer in salt than in ice. The astonishing fact is that there is no tendency for the salt to diffuse from the water into the ice to homogenize concentrations, no matter how long the mixture is observed. With solutions, it is not the free energy of the individual phases that must be equal for equilibrium to be achieved; rather the chemical potentials of the components (H2O and NaCl) must be uniform everywhere. This potential can be paraphrased as the mean free energy of a component in a solution of given composition. If all the potentials in the system are uniform, then there is no driving force for diffusion irrespective of spatial variations in concentration. When attempting to validate his laws of diffusion, the physiologist Fick used water and salt to conduct experiments. The diffusion flux, he proposed, depends on the concentration gradient. However, at some stage, it was realized that it should depend on the negative gradient of the chemical potential. A flux driven in this manner would lead to a reduction in free energy, which after all, is what is required for any process to occur spontaneously. I am not sure when this realization came about, but Darken refers to an 1888 article by Nernst on osmotic pressure. But the real motivation for Darken’s 1949 article was to demonstrate experimentally that ‘‘for a system of more than two components it is no longer necessarily true that a given element tends to diffuse towards a region of lower concentration.’’ The chemical potential gradient of that element may have a different sign to its concentration gradient. When dealing with a single phase, the chemical potential gradient has the same sign as an activity gradient so that the latter sometimes is used in describing diffusion. As pointed out by Darken, evidence for such diffusion could be found in a 1931 article by Hartley on ‘‘the distribution of a molecular solute [acetone] in a solvent [water] containing a gradient of concentration of a second solute [salt].’’ But he wanted to demonstrate this in the solid state; it should be borne in mind that the nature of diffusion in solids was, at the time, the subject of much debate. Proof for the vacancy mechanism for substitutional diffusion only just had been presented by Simgelkas and Kirkendall to an audience, which was not entirely receptive. The samples that Darken fabricated were similar to those in earlier work in which dissimilar steels were joined together to study diffusion. However, his goal was to realize the role of chemical potential gradients rather than to measure diffusion coefficients. Darken welded together two steels with similar carbon concentrations but different silicon concentrations. The choice of silicon as a substitutional solute seems to have been based on work by Smith, whose article on the activity of carbon in ternary steels predates that of Darken but is referred to by him as unpublished work. Smith demonstrated experimentally that silicon dramatically increases the activity of carbon in austenite, more so than manganese. The composition of the silicon-rich side of the weld was such that the whole of the diffusion couple would be austenitic at the heat-treatment temperature. It was understood that substitutional solutes would diffuse at a rate that is much less than the interstitial carbon so the carbon could be considered to migrate within an essentially fixed distribution of silicon. Darken succeeded in demonstrating the ‘‘uphill diffusion’’ of carbon and at the same time proved that although as a consequence of this diffusion, the carbon concentration changed discontinuously at the weld junction, the activity did not. He pointed out that Smoluchowski did not observe a similar partitioning of carbon in a diffusion couple containing a discontinuity of cobalt concentration, implying that the influence of cobalt on the activity of carbon is small in comparison with that of silicon. We now know that this is, in fact, the case. H.K.D.H. BHADESHIA, Professor, is with Materials Science and Metallurgy, University of Cambridge, Cambridge, UK. Contact e-mail: hkdb@cam.ac.uk *L.S. Darken, Trans. AIME, 1949, vol. 180, pp. 430–38. Article published online May 1, 2010

Automated rock mass characterisation using 3-D terrestrial laser scanning

Abstract: The research investigates the possibility of using point cloud data from 3-D terrestrial laser scanning as a basis to characterise discontinuities in exposed rock massed in an automated way. Examples of discontinuities in rock are bedding planes, joints, fractures and schistocity. The characterisation of discontinuities is of importance, since they determine to a large extend the geotechnical behaviour of the entire rock mass. The conventional way of characterising discontinuities is by manual geological survey using geological compass and measuring tape. A logical alternative to the conventional methods for surveying rock faces is the use of 3-D terrestrial laser scanning. A 3-D terrestrial laser scanning survey yield a 3-D point cloud but this data does not yet provide the information on the character of the discontinuities that can be seen in the rock exposure. In this research two different approaches are followed: the first approach uses surface reconstruction through interpolation of the point cloud and the second approach makes use of direct segmentation of the original point cloud. The main conclusion of this research is that it is possible to automate the derivation of discontinuity orientation and spacing information with both methods. Point cloud segmentation is however, the most preferred approach, since it does not require prior surface reconstruction, is therefore faster, and is not strongly influenced by vegetation and other noise in the data. Point cloud segmentation uses the original point cloud, so there is no data loss, which is unavoidable with a surface reconstruction approach.

Mantle transition zone topography and structure beneath the central Tien Shan orogenic belt

Abstract: [1] In this study we calculated receiver functions (RFs) from teleseismic P waveforms recorded by stations of four seismic networks to determine the topography of the mantle transition zone (MTZ) beneath the central Tien Shan. We converted the RFs from the time domain to the depth domain and selected the depths of 410 and 660 km discontinuities after stacking the RFs in narrow raypath bins. To better determine the MTZ topography, we applied an updated RF method to invert the depth differences between the 410 and 660 km discontinuities in each RF for lateral depth variations of the two discontinuities. Using this approach, we detected several anomalies in the 410 and 660 km discontinuity depths beneath the central Tien Shan region. Extensive synthetic tests were carried out to confirm the main features of the result. Beneath the south and east of Lake Issyk-Kul, the 410 km discontinuity becomes shallower while the 660 km discontinuity becomes deeper, leading to a thicker MTZ with a lower temperature, possibly caused by pieces of thickened lithosphere dropping down to at least the bottom of the MTZ. Beneath the northwest of Lake Issyk-Kul, the 410 km discontinuity becomes deeper while the 660 km discontinuity becomes shallower, resulting in a thinner MTZ with a higher temperature, which may reflect a small-scale hot upwelling from the lower mantle.

Modeling of a jointed rock mass under triaxial conditions

Abstract: One of the most important aspects of designing a structure on or in a rock mass is based on the strength response of a jointed rock mass. Understanding this important aspect, the present study was undertaken to understand the strength response of a jointed rock mass with the help of a finite difference package FLAC3D. In the present work, an attempt has been made to understand the effect of discontinuity angle on the failure mode and strength of the rock mass. For this purpose, stress and displacement in the model were studied and various stress–strain histories were recorded at constant strain loading rate. Rock discontinuity plays a critical and vital role to understand physico-mechanical characteristics of a rock mass. It has wider application in the rock excavation engineering, e.g., caverns, tunnels, slope stability, dams, etc. Simulated rock results are compared with the analytically calculated results of the jointed rock mass and found in good agreement.

The effect of viscoelasticity on a rising gas bubble

Abstract: This paper investigates the role of viscoelasticity on the dynamics of rising gas bubbles. The dynamics of bubbles rising in a viscoelastic liquid are characterised by three phenomena: the trailing edge cusp, negative wake, and the rise velocity jump discontinuity. There is much debate in the literature over the cause of the jump discontinuity, which is observed once the bubble exceeds a certain critical volume. In this paper, the employment of some choice modelling assumptions allows insights into the mechanisms of the jump discontinuity which cannot be ascertained experimentally. The ambient fluid is assumed incompressible and the flow irrotational, with viscoelastic effects included through the stress balance on the bubble surface. The governing equations are solved using the boundary element method. Some Newtonian predictions are discussed before investigating the role of viscoelasticity. The model predicts the trademark cusp at the trailing end of a rising bubble to a high resolution. However, the irrotational assumption precludes the prediction of the negative wake. The corresponding absence of the jump discontinuity supports the hypothesis that the negative wake is primarily responsible for the jump discontinuity, as mooted in previous studies.

A shear-displacement criterion for soil-infilled rock discontinuities

Abstract: An infilled rock joint is likely to be the weakest plane in a rock mass. The most pronounced effect of the presence of infill material is the reduction in friction of the discontinuity boundaries (i.e. rock to rock contact of the joint walls). The thicker the infill, the smaller the shear strength of the rock joint. Once the infill reaches a critical thickness, the joint walls (rock) play no significant role in the overall shear strength. Several models have been proposed to predict the peak shear strength of infilled joints under both constant normal load and constant normal stiffness boundary conditions, taking into account the ratio of infill thickness (t) to the height of the joint wall asperity (a), that is the t/a ratio. Models based on the constant normal stiffness condition provide a much more accurate representation of the infilled joint behaviour in the field, but only a limited number of studies have focused on the more realistic constant normal stiffness stress–strain behaviour. This paper pre...

The Planar Shape of Rock Joints

Abstract: Knowing the planar shape of discontinuities is important when characterizing discontinuities in a rock mass. However, the real discontinuity shape is rarely known, since the rock mass is usually inaccessible in three dimensions. Information on discontinuity shape is limited and often open to more than one interpretation. This paper discusses the planar shape of rock joints, the most common discontinuities in rock. First, a brief literature review about the shape of joints is presented, including some information on joint-surface morphology, inferences from observed trace lengths on different sampling planes, information based on experimental studies, and joint shapes assumed by different researchers. This review shows that joints not affected by adjacent geological structures such as bedding boundaries or pre-existing fractures tend to be elliptical (or approximately circular but rarely). Joints affected by or intersecting such geological structures tend to be rectangular. Then, using the general stereological relationship between trace length distributions and joint size distributions developed by Zhang et al. (Geotechnique 52(6):419–433, 2002) for elliptical joints, the effect of sampling plane orientation on trace lengths is investigated. This study explains why the average trace lengths of non-equidimensional (elliptical or similar polygonal) joints on two sampling planes can be about equal and thus the conclusion that rock joints are equidimensional (circular) drawn from the fact that the average trace lengths on two sampling planes are approximately equal can be wrong. Finally, methods for characterizing the shape and size of joints (elliptical or rectangular) from trace length data are recommended, and the appropriateness of using elliptical joint shapes to represent polygonal, especially rectangular, joints is discussed.

Micromechanical Modelling of Stress Waves in Rock and Rock Fractures

Abstract: The goal of this paper is to simulate the interaction of stress waves and rock fractures in a particle micromechanical model. Stress waves travelling in fractured rock masses are slowed down and attenuated by natural heterogeneities, voids, microcracks and, above all, by faults and fractures. Considerable laboratory and theoretical investigation have uncovered the major aspects of this phenomenon, but models that cover the core mechanisms of the wave propagation in rock masses are necessary to investigate aspects of wave–fracture interaction, which are not completely clear, and in the future simulate full-scale real problems. The micromechanical model is based on the particle discrete element model that reproduces rock through a densely packed non-structured assembly of 2D disks with point contacts. The model of a hard rock core is developed and an irregular rock joint is generated at mid-height. A new contact constitutive model is applied to the particles in the joint walls. Numerical static joint compression tests are performed and a typical hyperbolic stress–displacement curve is obtained. Conditions for good quality wave transmission through non-jointed unorganized particulate media are determined, hybrid static–dynamic boundary conditions are established and plane waves are emitted into the compressed joint. The transmitted and reflected waves are extracted and analysed. Joint dynamic stiffness calculated according to the hypotheses of the Displacement Discontinuity Theory shows to increase with the static joint compression until the joint is completely closed. Still in its early stages of application, this rock micromechanical model enables the joint behaviour under static and dynamic loading to be analysed in detail. Its advantages are the reproduction of the real mechanics of contact creation, evolution and destruction and the possibility of visualizing in detail the joint geometry changes, which is hard to accomplish in the laboratory.

Extended Finite Element Method for the Analysis of Discontinuities in Rock Masses

Abstract: The strength and deformability of rock mass primarily depend on the condition of joints and their spacing and partially on the engineering properties of rock matrix. Till today, numerical analysis of discontinuities e.g. joint, fault, shear plane and others is conducted placing an interface element in between two adjacent rock matrix elements. However, the applicability of interface elements is limited in rock mechanics problems having multiple discontinuities due to its inherent numerical difficulties often leading to non-convergent solution. Recent developments in extended finite element method (XFEM) having strong discontinuity imbedded within a regular element provide an opportunity to analyze discrete discontinuities in rock masses without any numerical difficulties. This concept is based on partition of unity principle and can be used for cohesive rock joints. This paper summarizes the mathematical frameworks for the implementation of strong discontinuities in 3 and 6 nodded triangular elements and also provides numerical examples of the application of XFEM in one and two dimensional problems with single and multiple discontinuities.

A cohesive zone model which is energetically equivalent to a gradient-enhanced coupled damage-plasticity model

Abstract: Modeling the fracture of a material can take two different approaches. A first solution consists in using models which preserve a continuous description of the material throughout the fracture process. These models are often regularized in order to deal with the softening part of the material’s behavior properly. Another solution consists in introducing discontinuity surfaces into the structure along with the possibility of taking into account cohesive forces between the two sides of the discontinuity. Many works have been devoted to the establishment of a relation between these two families of models. The present work is based on the equivalent crack concept, which states that a localized damage zone can be replaced by a crack as long as the energy dissipated by the structure is preserved when switching models. In a first paper, we introduced a method of construction of a cohesive law based on an elastic-damageable reference model. For a given test case, the cohesive model was built incrementally from the known solution given by the continuous reference model. There was no prerequisite assumption on the form of the cohesive law. In that work, the presence of plastic strains in the structure had not been taken into account, which limited the range of applicability of the method to elastic-damageable models. The objective of this paper is to eliminate this limitation by extending the method to the more general class of elastic–plastic damageable models.

Development of a New Experimental Apparatus for the Study of the Mechanical Behaviour of a Rock Discontinuity Under Monotonic and Cyclic Loads

Abstract: The shear behaviour of rock discontinuities in seismic condition is still not fully understood although earthquakes can be an important triggering cause of instability phenomena of rock blocks. For this purpose, a special apparatus was designed and developed at the University of Parma (Italy), which is to be placed inside the MTS press available in the Laboratory of Materials Testing. The press allows the application of monotonic and cyclic loads, in load or in deformation control. Quantitative evaluation of the rock-joint damage is realized by a photogrammetric survey of the discontinuity before and after the tests. The surface comparison enables the identification of the damaged areas. Finally, theoretical and experimental results are interpreted in the light of the damage model developed by Belem et al. (Rock Mech Rock Eng 33(4):217–242, 2001) for a quantitative evaluation of joint roughness and resistance.

A broad 660 km discontinuity beneath northeast China revealed by dense regional seismic networks in China

Abstract: [1] We examined the P wave velocity structure around the 660 km discontinuity at the tip of the subducting Pacific slab beneath northeastern China by forward modeling waveform triplication data. A total of 742 broadband seismograms were recorded by dense regional seismic networks in China from a deep earthquake that occurred near the border of east Russia and northeast China, providing an unprecedented density of ray coverage near the front edge of the subducting Pacific slab. Multiple P waves were observed on single seismograms in the distance range of ∼14°–29°. The P wave triplication shows the following two features: (1) the direct arrival traveling above the 660 km discontinuity (AB branch) extends as far as ∼29°, approximately 6° further than the prediction from velocity model of International Association of Seismology and the Physics of the earth's interior (iasp91); (2) the refracted wave propagating through the lower mantle (CD branch) appears at a distance a few degrees greater than that of the iasp91 synthetics. Forward waveform modeling suggests that they are best explained by a high-velocity transition zone underlain by a ∼50–70 km thick 660 km discontinuity. The broadened discontinuity is likely caused by multiple phase transitions associated with the dissolutions of olivine and garnet components.

Incremental linear-elastic response of rocks containing multiple rough fractures: Similarities and differences with traction-free cracks

Abstract: Fractures in the subsurface serve as conduits for fluids and gas, connecting remote hydrocarbon reservoir sections to production wells. Seismic and sonic data are popular sources for information on fracture properties. The most commonly used model to extract fracture information from such data is based on the paradigm of the displacement discontinuity interface, without a direct link to relevant characteristics such as the surface roughness properties of a fracture. Indeed, fractures can be modeled as displacement discontinuity surfaces, and in this sense they resemble traction-free cracks. In literature, cracks and fractures are not always properly distinguished, perhaps because the terms are often perceived as synonyms. However, microstructural parameters that control magnitudes of the discontinuities — and thus the effective stiffnesses — are entirely different: statistics of contacts for fractures versus crack density for traction-free cracks. We explore the effective elasticity of rocks containing multiple fractures using a model of a fracture as two rough surfaces with isolated contacts. This is done in the context of the incremental, linear elastic response to small stress changes, typical in wave-propagation problems. Fractures are dry or may have diverse orientations, and contacts may or may not be Hertzian. A link exists between contact characteristics and effective stiffness of single and multiple fractures. Our work examines and accounts for the strong effect of interactions between individual contacts by means of a double sum over mutual positions as well as outlines the differences and similarities between theories for cracks and fractures.

On the Automatic Generation of Strut and Tie Patterns under Multiple Load Cases with Application to the Aseismic Design of Concrete Structures

Abstract: Strut-and-tie modelling (STM) is a well-known technique for the design of the discontinuity regions in reinforced concrete structures, that is mainly based on the research of suitable load paths to transfer external forces to constraints. A simple energetic approach resorting to the minimum compliance optimization is herein implemented to derive truss-like models for the preliminary design of discontinuity regions under multiple load conditions. Peculiar attention is paid to the effect of the horizontal forces, as the ones induced by the seismic action, which act upon corbels and beam-column connections along with gravity loads. Numerical investigations in the bidimensional framework point out the remarkable crossing of stress-fluxes that must be handled in the bulk of the joints and calls for ad hoc shear reinforcement in the critical zone at the top of the columns. The methodology is also applied within the three-dimensional framework, addressing the design of box-shaped structures under multiple load c...

Two-layer earth model corrections to the MLTWA estimates of intrinsic- and scattering-attenuation obtained in a uniform half-space

Abstract: SUMMARY Following the numerical scheme of Yoshimoto we synthesized seismogram envelopes in the multiple scattering framework. We supposed the earth model constituted by a inhomogeneous crust overlying a transparent mantle. In this model velocity is assumed depth-dependent through a continuous function of the depth, v = v(h); Moho discontinuity is approximated by a sharp increase of the velocity around the crust–mantle boundary; inhomogeneity in the crust is parametrized through a depth-dependent scattering coefficient (the inverse of mean free path) g = g0 f (h), with f (h) function of depth, and g0 the scattering coefficient at zero depth; intrinsic attenuation is parametrized in terms of the intrinsic attenuation coefficient, ηi , that is assumed independent of depth. Generating a suite of energy envelopes as a function of lapse time and distance, for reasonable values of B0 , the seismic albedo and Le −1 , the extinction length inverse (which are functions of g0 and ηi ), we span a wide range including most of the measurements done through the world. Then, we apply the ordinary MLTWA technique to these synthetic envelopes. In this application, we assume a constant g and a constant velocity, v = which equals the average of v(h) calculated in the depth range characteristic of the volume encompassed by the scattered waves. In this way, we obtain the estimates of B0, and Le −1 , for a constant half-space. The relationship between the estimates of B0 and Le −1 , obtained assuming half-space, and the correspondent values used in the simulation, results to be well approximated by a second-order polynomial. Then, evaluating the best fit polynomial coefficients, we obtain a correspondence map between attenuation parameters retrieved for a uniform model with those characteristic of a more realistic structure. This map is useful to reinterpret all the couples B0 and Le −1 already calculated through the world in geological structures similar to the one adopted in our simulation. Results show that scattering and intrinsic-attenuation coefficients estimated using MLTWA in the assumption of a uniform half-space are always overestimated.

Discontinuities and distributed innovation:the case of biotechnology in food processing

Abstract: This paper examines the organization of distributed innovation shaped by the major discontinuity in the life sciences and their associated technologies that has unfolded over the past three decades...