Triaxial Compression of Sand Reinforced with Fibers

Results from drained triaxial compression tests on specimens of fiber-reinforced sand are reported. It is evident that the addition of a small amount of synthetic fibers increases the failure stress of the composite. This effect, however, is associated with a drop in initial stiffness and an increase in strain to failure. Steel fibers did not reduce initial stiffness of the composite. The increase in failure stress can be as much as 70% at a fiber concentration of 2% (by volume) and an aspect ratio of 85. The reinforcement benefit increases with an increase in fiber concentration and aspect ratio, but it also depends on the relative size of the grains and fiber length. A larger reinforcement effect in terms of the peak shear stress was found in fine sand, compared to coarse sand, when the fiber concentration was small (0.5%). This trend was reversed for a larger fiber concentration (1.5%). A model for prediction of the failure stress in triaxial compression was developed. The failure envelope has two segments: a linear part associated with fiber slip, and a nonlinear one related to yielding of the fiber material. The analysis indicates that yielding of fibers occurs well beyond the stress range encountered in practice. The concept of a macroscopic internal friction angle was introduced to describe the failure criterion of a fiber-reinforced sand. This concept is a straightforward way to include fiber reinforcement in stability analyses of earth structures.     

Behavior of Concrete in Water Subjected to Dynamic Triaxial Compression

To understand the behavior of concrete material in ambient water, a series of triaxial compressive tests of concrete cylindrical specimens (? 100×200?mm) was conducted on a large scale triaxial machine. The acting pattern of water, confining pressure, loading strain rate, and moisture content were chosen as test parameters. The water acting patterns on concrete were directly divided into mechanical loading and real water loading according to whether the specimens were directly exposed to water or not. The confining pressure ranged from 0–8 MPa and the strain rate included 10?5/s, 10?3/s, and 10?2/s. By testing dry and saturated specimens, the effect of moisture on concrete strength was also examined. The test results indicated that the compressive strengths of both dry and saturated concrete increase obviously with the confining pressure under mechanical confining pressure. However, the effect on the strengthened dry concrete specimens is more significant. The strength of dry concrete under real water loading decreased remarkably, even less than its uniaxial strength, whereas the compressive strength of the saturated concrete specimen under real water loading is close to its uniaxial compressive strength. The strength of concrete increases with strain rate, and this phenomenon becomes more apparent under water loading.     

Strain Localization in Sand: Plane Strain versus Triaxial Compression

A comprehensive experimental investigation was conducted to investigate the effects of loading condition and confining pressure on strength properties and localization phenomena in sands. A uniform subrounded to rounded natural silica sand known as F-75 Ottawa sand was used in the investigation. The results of a series on conventional triaxial compression (CTC) experiments tested under very low-confining pressures (0.05–1.30) kPa tested in a microgravity environment abroad the NASA Space Shuttle are presented in addition to the results of similar specimens tested in terrestrial laboratory to investigate the effect of confining pressure on the constitutive behavior of sands. The behavior of the CTC experiments is compared with the results of plane strain experiments. Computed tomography and other digital imaging techniques were used to study the development and evolution of shear bands.     

Plasticity Model for Concrete under Triaxial Compression

Using the experimental background of 130 triaxial tests conducted on cylindrical specimens, a plasticity-based constitutive model of concrete behavior is developed. Parameters of the reference experimental database include the water:cement ratio (i.e., f′c), degree of saturation at testing, and load path used in the tests. In the model, damage is quantified by the volumetric expansion that builds up progressively in the material as it approaches failure and is caused by propagation of microcracks. This behavioral index is calibrated with reference to the available tests and subsequently used as the primary state variable in the model, determining for any stress state the degree of stiffness and strength degradation and the ductility in the response. Because failure is modeled as a damage-driven continuous process rather than a distinct event, the characteristic failure envelope is expanding (hardening) or contracting (softening) as a function of a scalar measure of plastic deformation. A nonassociated plastic flow rule calibrated against the experiments is used to describe the direction of plastic deformation. The model was tested against published triaxial test series and empirical confinement models. It was also used in the context of a finite-element formulation to study the mechanical behavior of reinforced-concrete circular columns. This particular test problem was selected because it is a real-life example of the experimental conditions used to derive the model.     

Creep-Effect on Mechanical Behavior of Concrete Confined by FRP under Axial Compression

Despite many successes in concrete creep studies, its effect on the mechanical behavior of concrete members is far from a thorough case-specific understanding. For the members that have been subjected to a long-term load, the classical stress-strain models describing the short-term behavior of either confined or unconfined concrete are unsuitable. In order to investigate this creep-effect, an experiment on eight concrete cylindrical columns confined by fiber-reinforced polymer (FRP) is carried out. Based on the theory of plasticity for concrete, a constitutive model that takes into account the effect of creep on mechanical behavior of concrete confined by FRP is presented. In the model, the creep law inspired in the microprestress-solidification theory is generalized to triaxial stress condition for the calculation of the creep of the concrete columns confined by FRP. The predictions of the model agree well with the experimental results. The present study indicates that the creep increases the elastic modulus, slightly decreases the compressive strength, and degrades the deformation capability of the concrete confined by FRP.     

Shear Strength Behavior of Fiber-Reinforced Sand Considering Triaxial Tests under Distinct Stress Paths

The results of drained triaxial tests on fiber reinforced and nonreinforced sand (Osorio sand) specimens are presented in this work, considering effective stresses varying from 20 to 680?kPa and a variety of stress paths. The tests on nonreinforced samples yielded effective strength envelopes that were approximately linear and defined by a friction angle of 32.5° for the Osorio sand, with a cohesion intercept of zero. The failure envelope for sand when reinforced with fibers was distinctly nonlinear, with a well-defined kink point, so that it could be approximated by a bilinear envelope. The failure envelope of the fiber-reinforced sand was found to be independent of the stress path followed by the triaxial tests. The strength parameters for the lower-pressure part of the failure envelope, where failure is governed by both fiber stretching and slippage, were, respectively, a cohesion intercept of about 15?kPa and friction angle of 48.6?deg. The higher-pressure part of the failure envelope, governed by tensile yielding or stretching of the fibers, had a cohesion intercept of 124?kPa, and friction angle of 34.6?deg. No fiber breakage was measured and only fiber extension was observed. It is, therefore, believed that the fibers did not break because they are highly extensible, with a fiber strain at failure of 80%, and the necessary strain to cause fiber breakage was not reached under triaxial conditions at these stress and strain levels.     

Mode II Fracture Localization in Concrete Loaded in Compression

As an alternative to a series-coupling model for localization of deformations under uniaxial and confined compression, an approach based on Mode II crack growth is proposed. Such a model appears to be in closer agreement to experimental observations than the presently used series-coupling model, and has the advantage that both material and structural aspects of softening are incorporated directly. Similarities to tensile fracture exist that would make the approach universal.     

Elastic Anisotropic Viscoplastic Modeling of the Strain-Rate-Dependent Stress–Strain Behavior of K0-Consolidated Natural Marine Clays in Triaxial Shear Tests

This paper presents a new three-dimensional (3D) anisotropic elastic viscoplastic (EVP) model for the time-dependent stress–strain behavior of K0-consolidated marine clays. A nonlinear creep function with a limit for the creep volumetric strain under an isotropic or odometer K0-consolidated stressing condition and a nonsymmetrical elliptical loading locus are incorporated in the 3D anisotropic EVP model. An α-line defines the inclination of the nonsymmetrical elliptical loading locus in the p′-q plane and is commonly used for natural soils. All model parameters are determined from the results of one set of consolidated undrained compression tests and an isotropic consolidation/creep test. With the parameters determined, the 3D anisotropic EVP model is used to simulate the behavior of K0-consolidation tests and the strain-rate-dependent stress–strain behaviors of the K0-consolidated triaxial compression and extension tests on natural Hong Kong marine deposit clay specimens. These triaxial K0-consolidated specimens were sheared at step-changed axial strain rates from +2?to?+0.2, +20, ?2 (unloading) and +2%/h (reloading) for compression tests; or from ?2?to??0.2, ?20, +2 (unloading), and ?2%/h (reloading) for extension tests, all in an undrained condition. The simulation results of all these tests are compared with the test results. The validation and limitations of the model are then evaluated and discussed.     

Nonlinear Creep Damage Model for Concrete under Uniaxial Compression

An isotropic model for creep damage of concrete under uniaxial compression is proposed, where the combined effect of nonlinear viscous strain evolution and crack nucleation and propagation at high stress levels is considered. Strain splitting assumption is used for creep and damage contributions. Creep is modeled by a modified version of solidification theory. As usual in the modeling of damage of concrete, a damage index based on positive strains is introduced. As particular cases, the proposed model reduces to linear viscoelasticity for long time low stress levels whereas, for very high stresses, tertiary creep causing failure at a finite time can be described. The effect of strength variation with time is also included. The model is numerically implemented to perform time integration of nonlinear equations by means of a modified version of exponential algorithm. The model is validated through comparison with experimental results. Some numerical examples are also presented, where the roles of concrete ageing and strength variation with time are investigated.     

Model of FRP-Confined Concrete Cylinders in Axial Compression

This paper introduces a dilatancy-based analytical model of the response of an axially loaded concrete cylinder, confined with a fiber-reinforced polymer (FRP) composite jacket. Model construction is based on the experimentally based observation that the relation between axial secant stiffness and the lateral (dilatancy) strain is effectively unique for cylinders with the same unconfined concrete strength, although the confinement levels may differ. Model development incorporates strength degradation of the concrete with dilatancy (lateral dilation); this feature allows one to demonstrate that the performance of FRP-confined concrete is consistent with the strength envelope obtained from triaxial tests. Model validation is accomplished by comparisons with existing test database and the new results on large-scale concrete cylinders. The results of the validation reveal good agreement with key response functions and parameters. The present study illustrates basic constitutive equations to model FRP-confined concrete in a more rational manner.     

Improved Lattice Model for Concrete Fracture

An improved regular lattice network model is developed and validated for fracture of concrete structures. The improvements pertain to the inclusion of the tension softening response of the matrix phase, and of the modelling of structural response by incrementing the deformation rather than the load. A further development is the use of a regular square rather than a triangular lattice network to speed up the computations. These improvements eliminate the need for the introduction of arbitrary scaling parameters in the beam element failure criteria. Validation checks on notched three-point bend concrete specimens confirm the predictive capabilities of the improved lattice model with regard to both the load-deformation behavior and the energy dissipation mechanisms.     

Elastoplastic Damage Behavior of a Mortar Subjected to Compression and Desiccation

This paper deals with experimental investigation and numerical modeling of drying effects on the mechanical behavior of cement-based materials. First, the main results from an experimental study on the mechanical behavior (failure strength, induced damage, and plastic deformation) of a mortar subjected to the desiccation process are presented. Then, a coupled elastoplastic damage model is proposed to describe the mechanical behavior of cement-based materials subjected to tensile and compressive stresses. A particular emphasis is put on the pressure sensitivity of plastic flow and damage evolution. Capillary effects on mechanical behavior due to desiccation have been taken into account in the framework of partially saturated porous media. Finally, numerical simulations and experimental data are compared in order to verify the capacity of the model to reproduce the basic characteristics of the mortar in saturated and unsaturated conditions.     

Elasto-Plastic Bonding of Embedded Optical Fiber Sensors in Concrete

Fiberoptic sensors are increasingly employed for sensing and measurement of strains in structural materials. The glass core of the optical fiber senses the strain through intensity fluctuations, interference, or frequency modulation. Brittleness of the glass core limits practical usage, and therefore, the glass core of optical fibers is coated with low modulus softer protective coatings. The protective coating alters the strain transduction capabilities of the sensor. It absorbs a portion of the strain, and hence only a segment of structural strain is sensed. The study reported here corrects for this error through development of a theoretical model to account for the loss of strain in the protective coating of the optical fiber. The model considers the coating as an elasto-plastic material and formulates strain transfer coefficients for elastic, elasto-plastic, and plastic phases of coating deformation. The theoretical findings were verified through laboratory experimentation. The experimental program involved fabrication of interferometric optical fiber sensors, embedment within mortar samples, and tensile tests in a closed-loop servo-hydraulic testing machine. The elasto-plastic strain transfer coefficients developed in this study were employed for correction of optical fiber sensor data and results were compared with conventional extensometers.     

Continuous Relaxation Spectrum for Concrete Creep and its Incorporation into Microplane Model M4

Efficient numerical finite-element analysis of creeping concrete structures requires the use of Kelvin or Maxwell chain models, which are most conveniently identified from a continuous retardation or relaxation spectrum, the spectrum in turn being determined from the given compliance or relaxation function. The method of doing that within the context of solidification theory for creep with aging was previously worked out by Ba?ant and Xi in 1995 but only for the case of a continuous retardation spectrum based on the Kelvin chain. The present paper is motivated by the need to incorporate concrete creep into the recently published Microplane Model M4 for nonlinear triaxial behavior of concrete, including tensile fracturing and behavior under compression. In that context, the Maxwell chain is more effective than the Kelvin chain, because of the kinematic constraint of the microplanes used in M4. The paper shows how to determine the continuous relaxation spectrum for the Maxwell chain, based on the solidification theory for aging creep of concrete. An extension to the more recent microprestress-solidification theory is also outlined and numerical examples are presented.     

Behavior of Compacted Lunar Simulants Using New Vacuum Triaxial Device

Development and study of mechanical properties of engineering materials from locally available materials in space is a vital endeavor toward establishment of bases on the Moon and other planets. The objectives of this study are to create a lunar simulant locally from a basaltic rock, and to design and develop a new vacuum triaxial test device that can permit testing of compacted lunar simulant under cyclic loading with different levels of initial vacuum. Then, triaxial testing is performed in the device itself without removing the compacted specimen; this is achieved by a special mechanism installed within the device. Preliminary constrained compression and triaxial shear tests are performed to identify effects of initial confinements and vacuums. The results are used to define deformation and strength parameters. At this time, vacuum levels up to 10?4 are possible; subsequent research should involve higher vacuum levels, e.g., 10?14?torr as they occur on the Moon. The research can have significant potential toward development of methodology so as to develop compacted materials for various construction applications, and also toward stress‐strain‐strength testing of lunar simulants with different vacuum levels.     

Experiments to Relate Acoustic Emission Energy to Fracture Energy of Concrete

Acoustic emission (AE) was used to measure energy associated with fracture of standard concrete test specimens. The goal of the work was to identify ways in which AE could be used to quantify damage in generic laboratory structures for the purpose of tuning damage models. A series of mortar and concrete specimens of different compositions were tested for fracture energy Gf, while simultaneously being monitored for acoustic emission energy release. Reasonable correlation between the two quantities was observed for fine-grained specimens, however the relationship was not as good for coarse-grained specimens. Toughening mechanisms such as friction are suggested as being responsible for the poor relationship observed in the course-grained materials. It is further suggested that AE energy release can be related to actual crack formation energy but not to friction and other internal energy dissipation or toughening mechanisms.     

Behavior of Ellipsoids of Two Sizes

The influence of particle shape on granular material response is examined by using the discrete element method. Triaxial drained and undrained tests were performed on specimens of ellipsoids of two sizes. The triaxial test boundary conditions were simulated with a recently developed boundary mechanism. Different loading paths including axial compression, axial extension, lateral compression, and true extension were employed. The specimens were composed of 1,170 ellipsoids having two types of particles. The specimen is made up of 50% by weight of Type I particles that have an aspect ratio of 1.2. The aspect ratio of the Type II particles varies between 1.5 and 2. The specimens were consolidated isotropically before shearing. Comparing with the behavior of specimens of mono-size particles, a higher friction angle and a more complex particle shape effect were observed. The friction angles from the drained tests (axial extension, true extension, and lateral compression tests) were similar and the values are higher than that of the axial compression test. All simulated results are in good agreement with laboratory observation of sands.     

Numerical Modeling of Nonhomogeneous Behavior of Structured Soils during Triaxial Tests

The nonhomogeneous behavior of structured soils during triaxial tests has been studied using a finite element model based on the Structured Cam Clay constitutive model with Biot-type consolidation. The effect of inhomogeneities caused by the end restraint is studied by simulating drained triaxial tests for samples with a height to diameter ratio of 2. It was discovered that with the increase in degree of soil structure with respect to the same soil at the reconstituted state, the inhomogeineities caused by the end restraint will increase. By loading the sample at different strain rates and assuming different hydraulic boundary conditions, inhomogeneities caused by partial drainage were investigated. It was found that if drainage is allowed from all faces of the specimen, fully drained tests can be carried out at strain rates about ten times higher than those required when the drainage is allowed only in the vertical direction at the top and bottom of the specimen, confirming the findings of previous studies. Both end restraint and partial drainage can cause bulging of the triaxial specimen around mid-height. Inhomogeneities due to partial drainage influence the stress–strain behavior during destructuring, a characteristic feature of a structured soil. With an increase in the strain rate, the change in voids ratio during destructuration reduces, but, in contrast, the mean effective stress at which destructuration commences was found to increase. It is shown that the stress–strain behavior of the soil calculated for a triaxial specimen with inhomogeneities, based on global measurements of the triaxial response, does not represent the true constitutive behavior of the soil inside the test specimen. For most soils analyzed, the deviatoric stress based on the global measurements is about 25% less than that for the soil inside the test specimen, when the applied axial strain is about 30%. Therefore it can be concluded that the conventional global measurements of the sample response may not accurately reflect the true stress–strain behavior of a structured soil. This finding has major implications for the interpretation of laboratory triaxial tests on structured soils.     

Triaxial Test Simulations with Discrete Element Method and Hydrostatic Boundaries

A new boundary condition has been developed for the discrete element method. This boundary is different from the conventional periodic, rigid, or flexible boundries. This new boundary mechanism was developed to simulate triaxial tests. The new boundary, hydrostatic boundary, simulated the chamber fluid but not the rubber membrane. When a particle (ellipsoids in our simulations) contacts the hydrostatic boundary, pressure is developed. The interaction between the particle and the boundary is calculated analytically based on geometry. This hydrostatic boundary condition was implemented into an existing ellipsoidal discrete element code. Triaxial compression drained tests were performed with both periodic and hydrostatic boundaries. The result showed an increase in friction angle over the values observed from the periodic boundary mechanism. The result also closely resembles the experimental triaxial data. Thirteen specimens were generated and were used to investigate the following variables: particle shape, specimen size, and void ratio. A unique slope of the linear relationship between friction angle and void ratio was identified for monosize specimens of different particle shapes. It is found that the friction angle decreases as the aspect ratio increases provided that the void ratio of the two specimens is the same. The friction angle is linear proportional to the coordination number for monosize specimens regardless the specimen size. Also, the specimen size does not influence the behavior of two-size specimens.