Embedded Length Research Articles

Analysis of post-failure response of sands using a critical state micropolar plasticity model

Accurate estimations of pre-failure deformations and post-failure responses of geostructures require that the simulation tool possesses at least three main ingredients: 1) a constitutive model that is able to describe the macroscopic stress-strain-strength behavior of soils subjected to complex stress/strain paths over a wide range of confining pressures and densities, 2) an embedded length scale that accounts for the intricate physical phenomena that occur at the grain size scale in the soil, and 3) a computational platform that allows the analysis to be carried out beyond the development of an initially contained failure zone in the soil. In this paper, a two-scale micropolar plasticity model will be used to incorporate all these ingredients. The model is implemented in a finite element platform that is based on the mechanics of micropolar continua. Appropriate finite elements are developed to couple displacement, micro-rotations, and pore-water pressure in form of and (n > m) elements for analysis of dry and saturated soils. Performance of the model is assessed in a biaxial compression test on a slightly heterogeneous specimen of sand. The role of micropolar component of the model on capturing the post-failure response of the soil is demonstrated.

Minimum Embedded Length of Cyclic Horizontally Loaded Monopiles

Monopiles are used as foundation structures for offshore wind energy towers. To ensure stable behavior of the monopile under cyclic loading conditions, a minimum embedded length is usually required. For this, different design criteria are used, some of which result in very large embedded depths for large-diameter monopiles. The suitability of these criteria is tested by means of numerical simulations. To account for cyclic loading, a new approach called the stiffness degradation method is applied. The results of a parametric study show that the design criteria used can indeed ensure optimum pile performance under static and cyclic loads. It is recommended that the requirement of a critical pile length, which leads to the minimum pile deflection under extreme load, is used as a design criterion. For the cases considered, this requirement results in only slightly greater cyclic deformations compared to the optimum case of very long piles. A further optimization of the required monopile length with respect to cyclic loading is possible, but requires specific consideration of cyclic behavior, as is done in this paper. DOI: 10.1061/(ASCE)GT.1943-5606.0000602. © 2012 American Society of Civil Engineers. CE Database subject headings: Piles; Cyclic loads; Numerical analysis; Finite element method; Offshore structures. Author keywords: Piles; Monopiles; Cyclic loads; Numerical analysis; Finite element method; Offshore structures.

Study on embedded length of piles for slope reinforced with one row of piles

The embedded length of anti-slide piles for slope is analyzed by three-dimensional elastoplastic shear strength reduction method. The effect of embedded pile length on the factor of safety and pile behavior is analyzed. Furthermore, the effects of pile spacing, pile head conditions, pile bending stiffness and soil properties on length and behavior of pile are also analyzed. The results show that the pile spacing and the pile head conditions have significant influences on the critical embedded length of pile. It is found that the critical embedded length of pile, beyond which the factor of safety does not increase, increases with the decrease in pile spacing. The smaller the pile spacing is, the larger the integrity of the reinforced slope will be. A theoretical analysis of the slip surface is also conducted, and the slip surface determined by the pressure on piles, considering the influences of both soil and piles for slope, is in agreement with the ones in previous studies.

Analysis of internal stresses induced by strain recovery in a single SMA fiber–matrix composite

Due to the shape memory effect (SME) of shape memory alloy (SMA) fiber and the different thermal expansion coefficients between the constituent materials, internal stresses are induced when a single prestrained SMA fiber–matrix composite is heated. To avoid interfacial debonding between the SMA fiber and the epoxy matrix and to take full advantage of the properties of SMAs, it is necessary to investigate the internal stress distribution profiles. In the present study, stress functions which satisfy the equilibrium equations in SMA fiber and matrix are employed to analyze the stress distributions in SMA composite. The principle of minimum complementary energy is utilized to solve the stress functions and the internal stress distributions are obtained. The parameter effect is also investigated and some useful results are obtained. The finite element simulation illustrates the validity of the theoretical results. The results indicate that the maximum interfacial shear stress is located at both embedded ends of the composite and the maximum axial stress on the fiber appears at the midpoint of the entire embedded length.

A molecular dynamics study of the mechanical properties of graphene nanoribbon-embedded gold composites

Molecular dynamics simulations were performed to investigate the mechanical properties of a single-crystal gold nanosheet and graphene nanoribbon-embedded gold (GNR/Au) composites for various embedded locations, temperatures, and lengths. The computational results show that the Young's modulus, tensile strength, and fracture strain of GNR/Au composites are much larger than those of pure gold. The mechanical properties of GNR/Au composites deteriorate drastically due to C-C bond breaking. Thermal fluctuation and an increase in length can decrease the mechanical properties of GNR/Au composites.

Debonding initiation in a NiTi shape memory wire–epoxy matrix composite. Influence of martensitic transformation

The effect of martensitic transformation on the debonding initiation in single shape memory NiTi wire–epoxy matrix composite was studied. Three different heat treatment cycles were performed in order to obtain wires with different transformation characteristics. The composite samples were prepared using NiTi wires and steel wire for comparison. The single-wire specimens were subjected to the pull-out test. The in situ observations of the interfacial debonding and sliding behaviour during the test were carried out. In the pull-out tests, the embedded length is usually small and the interfacial shear strength (IFSS) can be estimated by dividing the maximum force to the lateral surface. But for evaluating the phase transformation effect, a long embedded length is required. In this case, a new method must be developed to estimate the IFSS. In the present study, a new method has been developed for the long embedded wire length samples using an analytical model. The IFSS was determined by implementing the experimental results into the model. It has been observed that the debonding stress for NiTi wire is significantly less than that for steel wire. It can be associated with the difference between the elastic modulus of the wires. The interfacial shear strength was then determined for these systems. It has been experimentally found that, when there is no phase transformation the IFSS is about 9 MPa while it is about 14 MPa when the martensitic transformation/reorientation occurs in the reinforced wire.

Behavior of monopile foundations under cyclic lateral load

This paper describes the development and application of design charts for monopile foundations of offshore wind turbines in sandy soil under long-term cyclic lateral load. It outlines a numerical model, working with a numerical concept, which makes the calculation of accumulated displacements based on cyclic triaxial test results possible, and it describes important factors affecting the deformation response of a monopile to cyclic lateral loads. The effects of pile length, diameter and loading state on the accumulation rate of lateral deformation are presented and design charts are given, in which a normalized ultimate lateral resistance of a pile is used. For monopiles with very large diameter, the suitability of the “zero-toe-kick” and “vertical tangent” design critera for determining the required embedded length is discussed.

Micromechanical modeling of the microbond test to quantify the interfacial properties of fiber-reinforced composites

The present study has focused on achieving a micromechanical understanding of the microbond test, which involves pulling a fiber out of a bead of matrix (i.e. droplet) through a knife-edge, in order to quantify the interfacial fracture properties of fiber-reinforced composites. According to the microbond test results for carbon-fiber and epoxy-resin system, matrix cracking occurred during the fiber pullout, in addition to the debonding at the fiber–matrix interface. Therefore, in evaluating the fracture properties of the fiber–matrix interface, we should pay attention to the coupling effects of matrix failure and interfacial debonding on the test results. Then, we discuss how to best extract the interfacial properties while excluding the influence of matrix plasticity and cracking, using numerical simulations. The key mechanism demonstrated here is that the pullout force, in the cases where the influence of matrix cracking is negligible, appears as the upper limit among the experimental data of the pullout force for a constant initial embedded length of the fiber in the matrix. For this reason, the upper-limit data all over the range of embedded fiber length in experiments can be reasonably evaluated by the simulation focusing on the debonding process with matrix plasticity. This evaluation technique is effective as a way of extracting interfacial properties appropriately from microbond test results.

Effect of filler content on the adhesion strength between UD fiber reinforced and particulate filled composites

Fiber reinforced composites (FRCs) are increasingly replacing metals in many engineering and medical applications. Recently, splints, post-orthodontic retainers and various load bearing substructures in fixed partial dentures (FPD) are manufactured using special dental grade FRC prepregs. In these applications, FRC substructures are covered with particulate filled dental composites to improve esthetics and patient comfort as well as to maintain good oral hygiene by reducing plaque accumulation. In this paper, effect of the composition of the particulate filled esthetic composite veneer (PFC) on the shear strength of adhesion between the FRC framework and the PFC was investigated. Light-cured, unidirectional S2-glass fiber reinforced composite rods were used to model the FRC dental substructures. A series of PFCs with filler content varying from 0 to 46 vol.% was prepared. Nominal shear adhesion strength, τ a, was measured using a modified pull-out test. Resin matrix for both, FRC and PFC was based on the same dimethacrylate monomer mixture. No adhesive was used and the FRC and PFC were joined together during polymerization. Scanning electron microscope (SEM) was used to inspect the loci of failure of the adhesive joint. The stress field within the test specimen was simulated using finite element analysis (FEA) code. Increasing filler content in the PFC resulted in an increase of the measured nominal shear adhesion strength, τ a, between FRC and PFC. With increasing embedded length of the FRC rod in the PFC cylinder, the τ a became almost independent of PFC composition, and, joint failure was altered from cohesive failure in the PFC to adhesive and/or interlaminar failure in the FRC. The results suggested that the fracture toughness of the PFC composite is of pivotal importance for preventing PFC layer from chipping-off the FRC load bearing framework and, hence, it is critical for long lasting passive dental appliances such as splints, retainers and FPDs. In addition, the interfacial shear strength of the fiber–matrix interface in the FRC controls the crack path in the FRC/PFC joint. Increasing the fiber–matrix adhesion can change the failure from interlaminar in the FRC to adhesive failure running along the FRC/PFC interface or even to cohesive fracture propagating in the PFC.

Modeling of energy absorption of short fiber composite considering interfacial properties of fiber/matrix

A generalized mathematical model of energy absorption of randomly oriented short fiber composite is developed on the basis of result of single-fiber pull-out test and some assumptions obtained from experimental investigation of the fracture of the composite of Aramid short fiber. Concept of the pull-out test is incorporated to the model, such that the fibers intersecting a fracture plane (where the fracture of composite occurs) would pull out or fracture like single-fiber pull-out test. The energy contribution of each fiber in the fracture plane is calculated for different embedded length and orientation to estimate the total fracture energy. According to the model, it is found that energy absorption depends upon the intrinsic properties of the fiber and matrix, volume fraction, critical embedded length of the fiber, fiber length and orientation of the fibers in the matrix. Analytical results obtained by the model are compared with the experimental results of Aramid short fiber composite.

Discussion of “Axial Load Tests on Bored Piles and Pile Groups in Cemented Sands” by Nabil F. Ismael

The writer reported results of static loading tests in tension and compression on two small-scale, single, bored piles in compact, dry to moist, slightly cemented sand. The tension test was performed on a pile with a diameter of 200 mm and an embedment length of 2.65 m and the compression test was performed on a pile with a diameter of 100 mm and an embedment length of 2.25 m. The load‐movement response in the tension test was that of a gradual rise rather than a plunging failure ~Fig. 7 of the original article!. The writer defined the capacity of the tension pile to the maximum load applied in the tension test—157 kN at a pile head movement of 20 mm. The maximum movement in the compression test was 12 mm and no plunging failure occurred ~Fig. 8 of the original article!. By applying ‘‘the slope tangent method’’ to the shape of this load‐movement curve, the writer determined the capacity of the compression pile to be 90 kN. The compression-pile head movement at this load was 7 mm. For the tension test, the writer calculated the 157 kN capacity to correspond to an average unit shaft resistance of 91.5 kPa. The writer then applied this average value to the 90 kN capacity of the compression tested pile, establishing a 66 kN total shaft resistance for this pile. The balance of the capacity, 24 kN, was assigned as pile toe resistance. The writer based his analysis on a simple total stress analysis, applying constant unit shaft resistance along the piles. The discusser believes that an effective stress analysis is better suited to the analysis of the test results. In contrast to the total stress method, the effective stress analysis accounts for the difference in embedment depth of the piles; the embedded length of the compression pile is 85% of that of the tension pile. Accordingly, for the unit shaft resistance in an effective stress analysis to be equal for the two piles, the average shaft resistance of the compression pile must also be 85% of that of the tension pile. Moreover, the writer’s values of shaft resistance in the two tests were determined at different pile head movements. Considering the load‐movement dependency, in the discusser’s opinion, correlation of the shaft resistance measured for the tension pile to the shaft resistance measured for the compression pile should be made at equal pile movements. In the tension test at a pile head movement equal to the movement at the 90 kN compression test capacity, 7 mm, the tension load was 125 kN, as opposed to 157 kN for the maximum movement. Combining the aspects of

Analysis of pull-out and failure of unidirectional bundles in a laminated carbon/carbon composite

The carbon/carbon composites for braking applications, processed by Messier Bugatti, Division Carbone Industrie (Villeurbanne) are laminates of [0/60/−60] n stacking, needled in the through-thickness direction. The unidirectional plies are made of adjacent meshes of square cross-section which exhibit some porosity between them because of the CVI processing route. The goal of the present paper is the study of the fracture behaviour of an individual mesh, and the analysis of the interfacial properties between the mesh and its surroundings. Tensile tests have been performed on special specimens where the mesh, embedded in the composite bulk over a given embedded length, can be loaded. For a long embedded length ( d > 3.6 mm), the mesh is broken and the ultimate stress is 260±80 MPa. For a shorter embedded length, the mesh debonds first with a mean interfacial shear stress of 18±8 MPa. The post-debonding extraction is controlled by friction, starting with an interfacial shear stress of 8±3 MPa. The pull-out curves are analysed and modelled by using the Amontons–Coulomb law.

Effect of fiber treatment on bending strength of aramid short fiber reinforced polyester

Effect of fiber treatment on the bending strength of the aramid short fiber composite is studied in this paper. Interfacial shear strength and fiber strength are determined for different fiber treatments by performing single-fiber pull-out test. Effect of the fiber treatments on the property of the composite depends both on the interfacial shear strength and the fiber strength, simultaneously. Thus, to evaluate quantitatively the effect of the treatments on the strength of the composite a parameter embedded is introduced that covers both the interfacial shear strength and the fiber strength. It is a parameter that defines the maximum embedded length during pull-out test, above which the shear force in the fiber/matrix interface exceeds the value of fracturing force of the fiber. The result shows that decrease of the critical embedded length causes increase in the bending strength of the composite, for the cases of the treatments employed in this research. Finally, an empirical equation is developed to calculate the bending strength of the aramid short fiber composite for the fiber treatments employed in this research.

Permanent Strains of Piles in Sand due to Cyclic Lateral Loads

The strain superposition concept, proposed for ballast study, is applied here to evaluate strain accumulation for laterally loaded piles in sand. It is shown that the soil properties, types of pile installation, cyclic loading types, pile embedded length, and pile/soil relative stiffness ratio are important factors that influence the pile behavior under mixed lateral loads. These factors are quantified by means of a degradation factor, t, which is derived from the results of 20 full-scale pile load tests and then verified using 6 additional full-scale pile load tests.

Free vibrations of tapered piles embedded partially in Winkler type foundations

The numerical methods for calculating the natural frequencies and the mode shapes of the tapered piles embedded partially in the Winkler type foundations are developed. The ordinary differential equation governing the free vibrations of such piles and the boundary conditions are derived, in which three types of linear tapered piles the with rectangular cross-sections i.e. breadth, depth and square tapers are considered. This equation subjected to the boundary conditions is solved numerically. The Runge-Kutta method and the determinant search method combined with Regula-Falsi method are used for integrating the differential equation and determining the eigenvalues(natural frequencies), respectively. In the numerical examples, the two lowest natural frequencies for six kind of end constraints are presented as the functions of four non-dimensional system parameters: the embedded length parameter, the foundation parameter, the section ratio, and the load parameter. The effects of taper types on the natural frequencies are reported. In addition, the typical mode shapes of free vibrations of piles are presented in the figure.

Buckling of Piles with General Power Distribution of Lateral Subgrade Reaction

A model for evaluating the critical buckling capacity of long slender friction piles is developed with lateral soil support included based on the concept of the subgrade reaction. A general power distribution of the coefficient of the subgrade reaction (kh), with depth, is utilized in the model. The lateral force-deflection (P-y) behavior is assumed to be linear. A parametric study was conducted to demonstrate the effect of ω value, defining the distribution of the horizontal subgrade reaction, on the evaluated buckling capacity. In the case of the free top and fully embedded condition with embedment length (h) greater than 10 m, a 59% increase in the buckling capacity (Pcr) was predicted as ω was increased from 0 (constant horizontal subgrade reaction distribution) to 1 (linearly increasing horizontal subgrade reaction). Results also indicated that the boundary conditions at the pile tip have a minimal effect on Pcr when the nondimensional embedded length (h′) exceeded 3.3 for the free top, 5.6 for the fixed-sway top, and 7.6 for the pinned-top condition. A comparison between a pile load test result reported in the literature and the model presented in this paper favorably verified the applicability of the developed model.

On failure phenomenon in single-fibre pull-out tests

This letter seeks to provide a theoretical explanation of a commonly observed failure phenomenon in the single-fibre pull-out test, namely the presence of a matrix cone at the emergent end of the extracted fibre. The single fibre pull-out test is commonly used [1,2] to characterize fibre reinforced polymer composites. This is because the test is simple to conduct and can be Used for almost any fibre-matrix composite system. An advantage [1] of the pull-out test is that in addition to the interfacial bond strength and interfacial toughness, other interfacial properties, such as the matrix shrinkage pressure on the fibre, the interfacial shear stress and the work done in pulling the fibre from the matrix, can be determined. The last factor is important, since the significant increase in fracture toughness of fibrous composites has been attributed to the fibre pull-out process during failure. Four types of failure [3] may occur in the specimen during a single-fibre pull-out test. These are: (i) specimen failure due to matrix failure away from the fibre-matrix interface, (ii) specimen failure by fibre fracture along the external free length of the fibre, (iii) partial debonding followed by specimen failure due to fibre fracture within the embedded length of the fibre and (iv) specimen failure due to complete debonding and extraction of the debonded fibre from the matrix. The first three types of failure represent unsuccessful pull-out tests. Data from specimens that exhibit these types of failure should not be included in pull-out analysis. Only specimens that exhibit failure of type (iv) represent successful pull-out tests. Thus, only data from such specimens should be utilized for analysis. This letter concerns specimens that exhibit this type of failure. A matrix "cone" is frequently observed at the emergent end of the extracted fibre after specimen failure. Such a typical matrix cone on the extracted fibre of a glass fibre/epoxy matrix pull-out specimen is shown in Fig. l a. The region below the matrix cone is the exposed debonded fibre surface. The point at which the cone is widest represents the original location of the edge of the matrix block that was bonded to the fibre. The part of the matrix cone above this location represents the menscus formed by the epoxy on the glass fibre. The matrix cone of an extracted fibre from a specimen with short embedded length is shown in Fig. lb. All of the features described above for a specimen with larger embedded length can be seen clearly in Fig. lb. Such matrix cones have been reported in the literature for both thermoset-based [3, 4] and thermoplastic-based [5] single-fibre pull-out specimens. None of the existing models [6-8] can account for the formation of such a matrix cone during type (iv) failure of a single-fibre pull-out specimen. It will be shown in this letter that radial and circumferential stresses in the matrix are responsible for the formation of the matrix cone. Radial stresses O'rm are usually neglected in the existing models, which predict a maximum finite value of the interfacial shear stress ~'i at the fibre emergent end since oS~ is much smaller [6] "ri. Therefore O~m is expected to have little effect on debonding crack initiation at the emergent end of the single-fibre pull-out specimen. However, the prediction of a finite maximum

Pull-out tests with fibre-metal systems

Fibre pull-out experiments have been carried out to compare the behaviour of reactive and non-reactive fibre-reinforced metal systems. The test samples were made by melting the metal matrix in vacuum and lowering the fibre a known depth into the liquid. In all cases some brittleness appeared to develop, since final interface failure, except with steel-99% AI, was sudden, and the values of the debonding force were quite scattered in all cases. Otherwise the results agreed with earlier observations, i.e. a linear increase in debonding force with increasing embedded length until the force was high enough to break the fibre rather than debond it. Some yielding was noticeable before failure. An elasticity analysis suggested that high shear stresses were needed in some cases to initiate yielding. However, the interface strengths, as indicated by the debonding forces, were no more than about twice the shear yield stresses of the matrices, as indicated by compressive tests on the metals. A reaction layer was obse...

Two results on linear embeddings of complete binary trees

Given a binary tree T with n vertices, we want to embed T onto a given set A of n points on the line so as to minimize the total embedded edge length. Polynomial-time algorithms for the two following special cases of this problem can be found in the literature: 1. when T is arbitrary but A = {1… n}. 2. when T is a complete binary tree and A is arbitrary. To the best of our knowledge, the complexity of the general problem is open. In this paper we deal with case (2). Bern et al. presented an algorithm for this case that runs in time O( n 5.76) and uses O( n 3.2) space. They also considered the naive embedding, which maps the root r of T into the middle point a of A, and then embeds, recursively, the left and right subtrees of r to the left and right of a, respectively. This is equivalent to embedding T from left to right according to the inorder traversal. They prove that this naive algorithm approximates the optimal solution within the factor of 3. The main results of this paper are: (i) the proof that the approximation ratio of this naive algorithm is exactly 7 3 , and (ii) a more efficient algorithm for computing minimum embeddings of complete binary trees. Our algorithm runs in time O ( n 1 + log 3) = O( n 2.59), and uses O ( n) space, where O ( f) = O( f log c n), for some constant c > 0.

Pull-out of a ductile fibre from a brittle matrix

Pull-out of a ductile fibre from a brittle matrix has been analysed using a shear lag model. Debonding at the fibre-matrix interface and yielding of the fibre occurred during the pull-out process. Both Poisson's contraction of the fibre and Coulomb friction of the debonded interface were considered. The debond length, which consists of an elastic zone length and a plastic zone length, was also analysed. When the fibre has a finite embedded length, it was found that necking prior to full pull-out of the fibre was required to optimize the toughening of a brittle matrix due to plastic deformation of the fibres. The essential material properties to achieve this are addressed.