Cohesive-frictional Material Research Articles

An improved two phases-two points SPH model for submerged landslide

This research proposes an improved two phases-two points SPH model designed to simulate interactions between water and soil, particularly suitable for scenarios such as submerged landslides. This model treats water as a weakly compressible Newtonian fluid and soil as a cohesive-frictional material following an elastoplastic constitutive law, utilizing two layers of SPH particles to separately represent these two phases. An adaptive drag force formula is proposed that automatically switches between linear and nonlinear seepage modes based on the motion state of the porewater. Additionally, to improve the precision and stability of the model, a modified solid boundary condition and a method for calculating soil volume fraction are proposed, along with an SPH discretization formula that incorporates the effects of the volume fraction in a more effective way. The reliability of the improved two phases-two points SPH model is initially verified through two cases: a dry granular landslide and a submerged soil mass subjected to gravitational loading. Then, the effectiveness of the proposed improvement methods is further tested and validated through three submerged landslide cases with different grain diameters, demonstrating the applicability of the current model in simulating submerged landslides and its superiority in accuracy and stability compared to previous models.

Comparison of physical and physicochemical methods for 3D printing application with the focus on the unconfined uniaxial compression test

For a commercial success of 3D concrete printing, standardisation is necessary to enable industrial production. To select methods for standardisation from the material side, detailed knowledge of suitable methods and of material behaviour is required in advance. Therefore, this study aims to compare different methods for investigating stiff printable mortars during the transition regime of a non-Newtonian fluid to a cohesive frictional material by physical and physicochemical methods focusing on the unconfined uniaxial compression test. The study shows that all methods exhibit comparable progressions, although the results are affected differently by self-heating, material composition and progressive hydration.

Evaluation of the unconfined uniaxial compression test to study the evolution of apparent printable mortar properties during the early age transition regime

The aim of this study is the evaluation of the unconfined uniaxial compression test (UUCT) to study the evolution of the apparent material properties of the printable mortar during the early age transition regime between the non-Newtonian fluid and the cohesive frictional material. For this application it is important to establish validated and reliable test procedures. The main focus lies on the determination of the apparent static Young's modulus, which defines limitations for stability failure of 3D printed structures. The results of UUCT beyond the apparent elastic range help to better distinguish between ductile and brittle behavior. A numerical simulation of the UUCT by the Mohr-Coulomb material model with apparent material properties determined by UUCT and direct shear test is able to reproduce the behavior at different ages, including material stiffness and deformation patterns, which is considered as an additional validation of the test procedure.

Homogenization based kinematic limit analysis for finding the stability of an embankment over soft clay reinforced with granular columns

The present study examines the stability of an embankment of cohesive-frictional material placed over a purely cohesive stratum which is reinforced by means of uniformly spaced vertical granular cylindrical columns. By using the kinematic yield homogenization concept, the macroscopic yield strength envelope associated with the reinforced clay layer has been obtained numerically for different volumetric fractions of the granular column to the composite unit cell by using the semidefinite programming (SDP) technique. An upper bound approximation of the macroscopic yield criterion, using the least square method, is expressed as a summation of a number of convex ellipsoidal envelopes so that the solution for computing the stability factors for the embankment on granular column (in the presence of surcharge pressure) can be obtained later with the usage of the second order cone programming (SOCP) while performing the upper bound finite elements limit analysis. The methodology avoids the usage of any stress variable and the complete procedure has been clearly described and the associated code has been written in MATLAB. The study will be not only useful for designing embankments constructed over soft clay reinforced with granular columns but also for solving different geomechanics stability problems by using the homogenization based kinematic limit analysis approach.

Indentation hardness of the cohesive-frictional materials

An analytical model is proposed to correlate the indentation hardness with the cohesion and friction angle of a cohesive-frictional material. The model is based on the slip-line analysis of a conical (self-similar) indenter that is forced to penetrate an elastic-perfectly plastic solid of the Mohr-Coulomb type. Using Berkovich indenter as an example, we have validated the proposed model based on the numerical analyses of 50 different materials. It shows that the model predicts an accurate hardness-to-cohesion ratio for a material if its friction angle is less than or equal to 45° When the friction angle of the material is larger than 45°, the model overestimates the hardness-to-cohesion ratio. Finally, we have discussed the major reasons that cause the overestimation of the hardness-to-cohesion ratio for larger friction angles.

Shakedown analysis of cavities in cohesive-frictional materials and its application to underground energy storage caverns

In this paper, a shakedown analysis is conducted for both cylindrical and spherical cavities in cohesive-frictional materials subjected to cyclic internal pressures. Based on Melan’s lower-bound shakedown theorem, theoretical shakedown conditions for a two-layered cavity system are developed using the stress and strain solutions obtained from cavity expansion and contraction analyses. The shakedown limits are investigated in relation to the dimensions of the two-layered cavity system and the elastic/plastic material parameters. Numerical validation is conducted through a comparison of the stress path of the critical element and the failure lines of the materials. In addition, closed-form solutions for special cases, namely, the analytical shakedown conditions of cavities in an unbound cohesive-frictional material and in a bound material with different boundary conditions, are explicitly expressed. Finally, the shakedown solutions are applied to solve the thickness design problem of underground compressed air energy storage in lined and unlined caverns.

A cohesive-frictional force field (CFFF) for colloidal calcium-silicate-hydrates

Calcium-silicate-hydrate (C-S-H) gel is a cohesive-frictional material that exhibits strength asymmetry in compression and tension and normal-stress dependency of the maximum shear strength. Experiments suggest the basic structural component of C-S-H is a colloidal particle with an internal layered structure. These colloids form heterogeneous assemblies with a complex pore network at the mesoscale. We propose a cohesive-frictional force field (CFFF) to describe the interactions in colloidal C-S-H materials that incorporates the strength anisotropy fundamental to the C-S-H molecular structure that has been omitted from recent mesoscale models. We parameterize the CFFF from reactive force field simulations of an internal interface that controls mechanical performance, describing the behavior of thousands of atoms through a single effective pair interaction. We apply the CFFF to study the mesoscale elastic and Mohr–Coulomb strength properties of C-S-H with varying polydispersity and packing density. Our results show that the consideration of cohesive-frictional interactions lead to an increase in stiffness, shear strength, and normal-stress dependency, while also changing the nature of local deformation processes. The CFFF and our coarse-graining approach provide an essential connection between nanoscale molecular interactions and macroscale continuum behavior for hydrated cementitious materials.

Evolution of strength and failure of SCC during early hydration

The early strength evolution of self-consolidating concrete (SCC) is studied by a set of non-standard mechanical tests for compressive, tensile, shear and bending failure. The results are applicable in an industrial environment for process control, e.g. of slip casting with adaptive molds in robotic fabrication. A procedure for collapsing data to a master evolution curve is presented that allows to distinguish two regimes in the evolution. In the first, the material is capable of undergoing large localized plastic deformation, as expected from thixotropic yield stress fluids. This is followed by a transition to cohesive frictional material behavior dominated by crack growth. The typical differences in tensile and compressive strength of hardened concrete are observed to originate at the transition. Finally, the evolution of a limit surface in principal stress space is constructed and discussed.

An adaptive selective ES-FEM for plastic collapse analysis

Abstract We present a selective edge-based smoothed finite element method (sES-FEM) of kinematic theorem for predicting the plastic limit loads in structures. The basic idea in this method is to use two levels of mesh repartitioning for the finite element limit analysis. The master level begins with an adaptive primal-mesh strategy guided by a dissipation-based indicator. The slave level consists of further subdividing each triangle into three sub-triangles and creating a dual mesh through a careful selection of a pair of two sub-triangles shared by the corresponding common element edge. By applying a strain smoothing projection operator to the strain rates on the dual mesh, the flow rule constraint is enforced over the edge-based strain smoothing domains, and likewise everywhere in the problem domain. This numerical procedure is performed for a cohesive-frictional material. This numerical procedure is also performed necessarily to avoid the volumetric locking problem for a purely cohesive material. The optimization formulation of limit analysis is next presented by the form of a second-order cone programming (SOCP) for the purpose of exploiting the efficiency of interior–point solvers. The present method uses linear triangular elements and handles a low number of optimization variables. This leads to a convenient way to design and solve the large-scale optimization problems effectively. Several numerical examples are given to demonstrate the simplicity and effectiveness of the proposed method.

Experimental validation of a nonlinear μFE model based on cohesive-frictional plasticity for trabecular bone.

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Extension of discontinuous deformation analysis and application in cohesive-frictional slope analysis

This paper extends the discontinuous deformation analysis (DDA) by using an additional evaluation of edge-to-edge contact, with the aim that it can be used to accurately model the failure behaviour of joints dominated by both cohesion and interface friction angle. The original DDA can deal well with the effects of interface friction angle. However, when cohesion exists, DDA results often show an inscrutable behaviour, i.e. a slope may be unstable even if the cohesion is much greater than the theoretical value required for its critical stability. After many detailed investigations and validations, joint contact treatment was found to be the key reason why the original DDA cannot simulate the cohesive material accurately, in which every edge-to-edge contact is treated as two vertex-to-edge contacts that may have different contact states associated with different cohesion treatments. In order to solve this problem, an additional contact type determination process for an edge-to-edge contact was added into the original computer code to avoid the unreasonable situation when two contact states exist in one joint. Several examples were performed to illustrate the accuracy of the modified code and a real landslide case was analysed by using the improved DDA to estimate the shear strength on the interface. Our results show that the improved DDA can simulate the failure of cohesive-frictional material accurately.

Solving Axisymmetric Stability Problems by Using Upper Bound Finite Elements, Limit Analysis, and Linear Optimization

A numerical formulation has been proposed for solving an axisymmetric stability problem in geomechanics with upper bound limit analysis, finite elements, and linear optimization. The Drucker-Prager yield criterion is linearized by simulating a sphere with a circumscribed truncated icosahedron. The analysis considers only the velocities and plastic multiplier rates, not the stresses, as the basic unknowns. The formulation is simple to implement, and it has been employed for finding the collapse loads of a circular footing placed over the surface of a cohesive-frictional material. The formulation can be used to solve any general axisymmetric geomechanics stability problem.

Bearing Capacity Factors for Eccentrically Loaded Strip Footings Using Variational Analysis

Bearing capacity factors for eccentrically loaded strip smooth footings on homogenous cohesive frictional material are deduced by the variational limit equilibrium method and by assuming general shear failure along continuous curved slip surface. From the calculated results, the effective width rule suggested by Meyerhof for bearing capacity factors due to cohesion of soil is justified, and the superposition principle of bearing capacity for eccentrically loaded strip smooth footings is derived together with the bearing capacity factors for cohesion and unit weight of soil. The two factors are represented by soil strength parameters and eccentricity of load. The bearing capacity factor related to unit weight for cohesionless soil is less than that for cohesive frictional soil. The reason for this discrepancy lies in the existence of the soil cohesion, for the shape of the critical rupture surface of footing soil depends on both soil strength parameters rather than on friction angle alone in the previous limit equilibrium solutions. The contact between footing and soil is decided by both the load and the mechanical properties of soil. Under conditions of higher eccentricity and less strength properties of soil, part of the footing will separate from the underlying soil.

Finite elements for cohesive-frictional material

New finite elements comprising parts (rods and spiral springs) with independent behaviors, which can be determined from the corresponding independent experiments – shear, deviatoric loading, hydrostatic loading – are suggested for isotropic material in 2D and 3D cases and applied for solving some problems for cohesive-frictional material. The material is assumed to be non-linear with the stress–strain relationship of hyperbolic type and failure conditions determined by Mohr–Coulomb law. The difficulty of the problems consists in the fact that the limit stresses themselves depend on unknown stress distribution, so a stress–strain equation cannot be written in the explicit form before solving the problem. This difficulty is avoided by iterations: a suitable initial stress distribution (e. g. from the corresponding elastic problem) is supposed and, knowing the material properties, the new stress distribution (appearing as a result of slow gradual load application) can be found which is taken as the initial for the next iteration, and so on. The following two problems are considered: failure of a horizontal layer under action of a uniform pressure applied to a rectangular area on the layer surface and the problem of slope stability.

Approximate model for blunt objects indenting cohesive-frictional materials

SUMMARY An approximate two-dimensional model for indentation of blunt objects into various types of rigid-perfectly plastic cohesive-frictional material is derived. Particular emphasis is placed on considering indentation as a process involving evolution of the boundary of material displaced by the indenter. Force–penetration relationships are obtained by an incremental approach utilizing key kinematic and static information from indentation of a flat punch. Albeit approximate, the proposed model applies to arbitrary indenter geometry and weightless or ponderable cohesive-frictional materials exhibiting associated or non-associated plastic flow. Two specific indenter geometries, the cylinder and blunt wedge, are explored in detail. Favorable agreement is found between the analytic results and those obtained using the finite element method (FEM). For both the wedge and cylinder, it is further shown that accurate analytic expressions relating indentation force explicitly to penetration can be derived. In the case of the wedge and weightless material, predictions of indentation force obtained from the derived expressions are very close to those computed from implicit equations available in the literature. Copyright © 2011 John Wiley & Sons, Ltd.

Lower bound limit analysis of masonry bridges including arch–fill interaction

Collapse tests on full and model scale masonry bridges have shown the structural role of fill and spandrels, which has to be taken into account to obtain realistic evaluations of the load carrying capacity of existing bridges. A plane model of multi-span masonry bridge is proposed in which the vault–fill interaction effects are considered, whose lower bounds on collapse load are obtained by a finite element application of the lower bound theorem of limit analysis. Arches and piers are modelled as beams made up of no tension, ductile in compression material and the fill as a cohesive-frictional material with a tension cut-off. The fill domain is discretized by triangular elements connected by interface elements in order to increase the ratio of the unknowns to the conditions of static admissibility; arches and piers are discretized by two-node straight beam elements. By linearisation of the conditions of plastic admissibility, a Linear Programming problem is formulated and lower bounds on the collapse load are obtained. The procedure is successfully applied to two example bridge models, where a comparison with the results obtained from the kinematic approach is made. The first example is a simulation of a collapse test on a single span bridge; the second concerns a multi-span bridge and highlights the capability of the procedure to describe complex interactions between the arch–pier structural system and the fill at collapse.

Shakedown of a cohesive-frictional half-space subjected to rolling and sliding contact

The problem of rolling and sliding contact of a cylinder on the surface of a half-space of cohesive-frictional material is considered. Three shakedown multipliers, of which two are upper bounds and one is exact are computed using a simple numerical procedure. This latter solution differs significantly from previously published analytical solutions which, for realistic material parameters, typically overestimate the shakedown load by a factor of 1.5–2.5.

Two-dimensional finite element upper bound limit analysis of masonry bridges

A two-dimensional model for the evaluation of the load carrying capacity of masonry bridges is proposed that takes into account the strengthening effects due to arch–fill interaction observed in experimental tests. Upper bounds on the collapse load and the corresponding mechanism are obtained by means of a finite element application of the Kinematic Theorem of Limit Analysis. Arches and piers are modelled as beams made up of non-tensile resistant (NTR) and ductile in compression masonry, while the fill is represented as a cohesive-frictional material with tension cut-off. Kinematically admissible mechanisms are obtained by discretizing the fill domain with triangular elements and including velocity discontinuities in order to increase the degrees of freedom of the model and thus reduce locking; arches and piers are discretized by two-node straight beam elements. A piecewise linearization of the limit domains allows the upper bound on the collapse load and the corresponding mechanism to be obtained as a solution of a Linear Programming problem. The capabilities and the validity limits of the proposed numerical model are shown in two examples. The collapse test on a real single span bridge is simulated and discussed in the first example; a multi-span bridge is analysed in the second, where complex interactions between arches, piers and fill are obtained.

Stabilité frontale d'un tunnel

ABSTRACT Within the framework of the kinematic approach of yield design theory, a new 3D failure mechanism, in the shape of a rhinoceros horn and based on logarithmic-spirals, is presented for the stability analysis of the tunnel face in cohesive-frictional material. The model leads to a kinematic bound, on the unsafe side, of the critical face pressure which appears better (thus safer) than existing solutions. The case of shallow tunnels is examined. The critical face pressure estimates are very close to 3D numerical results, obtained by finite difference displacement method, and the optimized critical mechanism compares remarkably well with experimental and numerical observations.

Cavity expansion in cemented materials: structure degradation effects

A numerical solution of a cylindrical cavity expansion problem is presented herein, which is formulated within the framework of non-associated plasticity. The work extends the solution proposed by Mántaras & Schnaid in a companion paper in which a drained analysis has been developed based on postulates embedded on Rowe's stress dilatancy theory. This new formulation aims at demonstrating the significance of structure degradation during shear for a bonded cohesive-frictional material. The proposed solution makes it possible to derive the continuous variations of strains, stresses and volume changes produced around an expanding cavity. The significance of the method is demonstrated by a parametric study designed to highlight the influence of strength reduction during shear on cavity expansion analysis.