Modeling Permanent Deformation of Unbound Granular Materials under Repeated Loads

Finite-element analysis on a pavement structure under traffic loads has been a viable option for researchers and designers in highway pavement design and analysis. Most of the constitutive drivers used were nonlinear elastic models defined by empirical resilient modulus equations. Few isotropic/kinematic hardening elastoplastic models were used but applying thousands of repeated load cycles became computationally expensive. In this paper, a cyclic plasticity model based on fuzzy plasticity theory is presented to model the long-term behavior of unbound granular materials under repeated loads. The discussion focuses on the model parameters that control long-term behavior such as elastic shakedown. The performance of the constitutive model is presented by comparing modeled and measured permanent strain at various numbers of load cycles. Calculated resilient modulus from the complete stress-strain curve is also discussed.     

基于均匀化理论的复合材料安定性分析方法

周期性非均质复合材料具有微观结构特征,需要均匀化理论进行宏观和微观的多尺度分析来研究其性能表现。针对其耐久强度性能,应用塑性极限安定下限定理,特别分析了其在长期交变载荷下的安定状态。结合工程应用目标,提出一种全新的代表性单元边界条件,结合圆锥二次优化算法进行数值计算,可以从材料微结构和组分性能出发,经过弹性应力场求解确定位移边界载荷数值,最终由优化求解得到复合材料板材的面内塑性性能容许域。所求得的应力域以单向应力为基,可根据结构宏观的单向应力状态变化幅值直接进行安定状态与否的判定。通过文中的多个算例,验证了所编写的软件及计算流程的可行性及数值准确性,展示了该方法在工程模型中的应用场合和工程实践意义。      

Load Bearing Capacity of Reinforced Concrete Beams Subjected to Dynamic Cyclic Loads

A kinematic method is developed to determine the shakedown limits of elastic-perfectly plastic steel-reinforced concrete beams under quasi-static and dynamic cyclic loads. This procedure, like the respective kinematic approach of plastic limit analysis, is visual and easy to use in engineering applications. The load parameters (amplitudes, frequency) versus yield moment diagrams, constructed from possible collapse modes, should assist in choosing the reinforcement scheme and amounts of reinforcement to meet the load bearing requirements for the structures.     

Spectral Analysis and Parametric Study of Stochastic Pavement Loads

This paper investigates the effects of vehicle parameters, speed, and surface roughness on the power spectral density (PSD) of stochastic pavement loads. Pavement surface roughness is modeled as a zero-mean stationary random field. A quarter-vehicle model is established to simulate the vibrations of heavy and passenger vehicles with typical parameters. Tire damping is also included in the consideration of stochastic pavement loads; this was assumed to be zero in many previous investigations. The PSD roughness proposed by the ISO is adopted in the simulation of the loads. An important indicator of the stochastic loads, the so-called energy cumulative distribution function, is introduced to describe the frequency distribution of load energy. The results show that passenger vehicles produce more high-frequency loads than heavy vehicles, while more of the loads generated by heavy vehicle are primarily distributed in the low-frequency region. It is also found that the effect of tire damping on stochastic pavement loads is not negligible especially if the loads of interest are concentrated in the high-frequency region. The results of the study may be useful in optimum design of vehicle suspensions and prediction of dynamic pavement response.     

Analysis and Implementation of Resilient Modulus Models for Granular Solids

Constitutive equations based upon stress dependent moduli, like K-θ and Uzan-Witczak, are widely used to characterize the resilient response of granular materials for the analysis and design of pavement systems. These constitutive models are motivated by the observation that the granular layers used in pavement structures shake down to (nonlinear) elastic response under construction loads and will, therefore, respond elastically under service loads typically felt by these systems. Due to their simplicity, their great success in organizing the response data from cyclic triaxial tests, and their success relative to competing material models in predicting the behavior observed in the field, these resilient modulus constitutive models have been implemented in many computer programs used by researchers and design engineers. This paper provides an analysis of the nonlinear solution algorithms that have been used in implementing these models in a conventional nonlinear 3D finite-element framework. The analysis shows that these conventional algorithms are destined to fail at higher load levels. The paper offers two competitive methods for global analysis with these models. A comparative study of eight possible implementations of the algorithms described in the paper is made through two simulation examples.     

Stability and Collapse of Semirigidly Connected Portal Frames

A numerical procedure for the nonlinear elastic‐plastic instability analysis and collapse of semirigidly connected portal frames, with elastic rotational restraints at the supports, is presented. The procedure is based on nonlinear kinematic relations and linearly elastic material behavior except at the plastic regions (concentrated plasticity). The nonlinear flexible connections are represented by polynomial models. A computational technique for incorporating the stability and strength into the analysis is described in detail. It is found that several important parameters affect the failure modes and consequently the critical loads. These parameters are the slenderness ratio, support restraints, type of connections, and the loading conditions. It is also demonstrated that the connection flexibility has considerable effect on the critical load and the deformation. It is further concluded that for design application the assumption of linear (instead of nolinear, polynomial) connection behavior is adequate for portal frames only if the loading conditions do not produce a significant amount of bending moment at the joints.     

Shakedown Approaches to Rut Depth Prediction in Low-Volume Roads

Rutting, due to permanent deformations of unbound materials, is one of the principal damage modes of low traffic pavements. Flexible pavement design methods remain empirical; they do not take into account the inelastic behavior of pavement materials and do not predict the rutting under cyclic loading. A finite-element program, based on the concept of the shakedown theory developed by Zarka for metallic structures under cyclic loadings, has been used to estimate the permanent deformations of unbound granular materials subjected to traffic loading. Based on repeated load triaxial tests, a general procedure has been developed for the determination of the material parameters of the constitutive model. Finally, the results of a finite-element modeling of the long-term behavior of a flexible pavement with the simplified method are presented and compared to the results of a full-scale flexible pavement experiment performed by Laboratoire Central des Ponts et Chaussées. Finally, the calculation of the rut depth evolution with time is carried out.     

Unified DSC Constitutive Model for Pavement Materials with Numerical Implementation

Need for unified and mechanistic constitutive models for pavement materials for evaluation of various distresses has been recognized; however, such models are not yet available. There have been efforts to develop unified models; however, they have been based usually on ad hoc combinations of models for special properties such as elastic, plastic, creep and fracture, often without appropriate connections to various coupled responses of bound and unbound materials, they may result and in a large number of parameters, often without physical meanings. The disturbed state concept (DSC) provides a modeling approach that includes various responses such as elastic, plastic, creep, microcracking and fracture, softening and healing under mechanical and environmental (thermal, moisture, etc.) within a single unified and coupled framework. A brief review is presented to identify the advantages of the DSC compared to other available models. The DSC has been validated and applied to a wide range of materials: geologic, asphalt, concrete, ceramic, metal alloys, and silicon. It allows for evaluation of various distresses such as permanent deformations (rutting), microcracking and fracture, reflection cracking, thermal cracking, and healing. The DSC is implemented in two- and three-dimensional finite-element (FE) procedures, which allow static, repetitive, and dynamic loads including elastic, plastic, creep, microcracking leading to fracture and failure. A number of examples are solved for various distresses considering flexible (asphalt) pavements; however, the DSC model is applicable to rigid (concrete) pavements also. It is felt that the DSC and the FE computer programs provide unique and novel approaches for pavement engineering. It is desirable to perform further research and applications including validation with respect to simulated and field behavior of pavements.     

Compound Shear-Flexural Capacity of Reinforced Concrete–Topped Precast Prestressed Bridge Decks

Modern concrete bridge decks commonly consist of stay-in-place (SIP) precast panels seated on precast concrete beams and topped with cast-in-place (CIP) reinforced concrete. Such composite bridge decks have been experimentally tested by various researchers to assess structural performance. However, a failure theory that describes the failure mechanism and accurately predicts the corresponding load has not been previously derived. When monotonically increasing patch loads are applied, delamination occurs between the CIP concrete and SIP panels, with a compound shear-flexure mechanism resulting. An additive model of flexural yield line failure in the lower SIP precast prestressed panels and punching shear in the upper CIP-reinforced concrete portion of the deck system is derived. Analyses are compared to full-scale experimental results of a tandem wheel load straddling adjacent SIP panels and a trailing wheel load on a single panel. Alone, both yield line and punching-shear theories gave poor predictions of the observed failure load; however, the proposed compound shear-flexure failure mechanism load capacities are within 2% accuracy of the experimentally observed loads. Better estimation using the proposed theory of composite SIP-CIP deck system capacities will aid in improving the design efficiency of these systems.     

Service Life Predictions for Hot Bulk Forming Tools

Hot bulk forming tools are subject to high thermal and mechanical alternating loads which can induce the formation of fatigue cracks in the highly stressed regions of the tool. It this way, premature tool failure occurs with which increased tool costs are associated. It is therefore vitally important to calculate the tool life output during the process design to improve the efficiency. Thermomechanical fatigue tests using the hot‐working tool steel X38CrMoV5‐3 are carried out as the basis for service life predictions in order to characterise the material behaviour subject to cyclic loading. In the tests, the thermal and mechanical loads operating in the tool steel during a forging process are reproduced. In this way, a strain controlled S‐N curve is determined for a specific temperature interval by varying the applied mechanical load. Thus it is possible to consider the damage mechanisms in the material, which operate during the forming process, for computing the service life. Based on the experimentally determined strain controlled S‐N curve, the computation of a fatigue failure is carried out for a practical example with tool fracture. By comparing the material's experimentally determined load carrying capacity with the loading computed by employing the elastic‐plastic material behaviour, the number of forging cycles is ascertained up to incipient cracking. The simulation model introduced here permits an improved prediction of the fatigue crack formation by integrating the cyclic material behaviour subject to similar conditions found in the forging process.     

Experimental and Modeling Studies of Permanent Strains of Subgrade Soils

Mechanistic-empirical pavement design guide for flexible pavements as per the AASHTO design guide requires characterization of subgrade soils using the resilient modulus (MR) property. This property, however, does not fully account for the plastic or permanent strain or rutting of subgrade soils, which often distress the overlying pavements. Soils such as silts exhibit moderate to high resilient moduli properties but they still undergo large permanent deformations under repeated loading. This explains the fallacy in the current pavement material characterization practice. A comprehensive research study was performed to measure permanent deformation properties of subgrade soils by subjecting various soils under repeated cycles of deviatoric loads. This paper describes test procedure followed and results obtained on three soils including clay, silt, and sandy soils. The influence of compaction moisture content, confining pressure, and deviatoric stresses applied on the measured permanent deformations of all three soils are addressed. A four-parameter permanent strain model formulation as a function of stress states in soils and the number of loading cycles was used to model and analyze the present test results. The model constants of all three soils were first determined and these results were used to explain the effects of various soil properties on permanent deformations of soils. Validation studies were performed to address the adequacy of the formulated model to predict rutting or permanent strains in soils.     

Implementation of a Critical State Two-Surface Model to Evaluate the Response of Geosynthetic Reinforced Pavements

A finite-element model was developed using ABAQUS software package to investigate the effect of placing geosynthetic reinforcement within the base course layer on the response of a flexible pavement structure. A critical state two-surface constitutive model was first modified to represent the behavior of base course materials under the unsaturated field conditions. The modified model was then implemented into ABAQUS through a user defined subroutine, UMAT. The implemented model was validated using the results of laboratory triaxial tests. Finite-element analyses were then conducted on different unreinforced and geosynthetic reinforced flexible pavement sections. The results of this study demonstrated the ability of the modified critical state two-surface constitutive model to predict, with good accuracy, the response of the considered base course material at its optimum field conditions when subjected to cyclic as well as static loads. The results of the finite-element analyses showed that the geosynthetic reinforcement reduced the lateral strains within the base course and subgrade layers. Furthermore, the inclusion of the geosynthetic layer resulted in a significant reduction in the vertical and shear strains at the top of the subgrade layer. The improvement of the geosynthetic layer was found to be more pronounced in the development of the plastic strains rather than the resilient strains. The reinforcement benefits were enhanced as its elastic modulus increased.     

Locality of Truck Loads and Adequacy of Bridge Design Load

United States highway bridge design has advanced into the era of risk-based practice, milestoned by the American Association of State Highway and Transportation Officials Load and Resistance Factor Design Bridge Design Specifications. On the other hand, national and state design codes cannot specifically account for localized risk for each bridge site, which may have significantly different loading conditions from the national average. This issue is focused on here, as related to the adequacy of current bridge design loads for sites in the state of Michigan. The structural reliability indices are calculated for a randomly selected sample of new bridges from the Michigan inventory, including four major girder bridge types. Weigh-in-motion truck load data collected in Michigan are used to statistically characterize the truck load effect in the bridges’ primary members for moment and shear at critical cross sections. The reliability indices are found to vary significantly among the bridge sites and types investigated. Many of them indicate inadequate design load for the Detroit area.     

Innovative ANN Technique for Predicting Failure/Cracking Load of Masonry Wall Panel under Lateral Load

This paper introduces an artificial intelligent technique for predicting the failure/cracking loads of laterally loaded masonry wall panels based on their corresponding failure/cracking patterns derived from the laboratory experiments. First, a lattice is made on a wall panel based on the dimension of the wall panel. Then, the numerical values, 0 or 1, are assigned to the cells in the lattice in order to describe the failure/cracking pattern. Thus, a numerical matrix is formed to show the failure/cracking pattern of the wall panel. Since the matrices for the wall panels with various sizes have different dimensions, the gray level cooccurrence matrix is innovatively used to transfer these matrices into the matrices whose dimensions are the same. Next, the numerical modes of failure/cracking patterns of experimental wall panels and the corresponding normalized failure/cracking loads can be used as the input and output of the artificial neural network (ANN) training data, respectively. Finally, three types of ANN models for predicting the failure/cracking load of the unseen wall panel are achieved by repeatedly training and adjusting so as to optimize its parameters. In a wide significance, this study opens a novel way to establish the relationship between the failure/cracking pattern and the failure/cracking load of the wall panel.     

3D Finite Element Study on Load Transfer at Doweled Joints in Flat and Curled Rigid Pavements

This study examines load transfer across doweled joints in rigid pavements using 3D finite element analysis. A recently developed dowel modeling strategy is employed that allows the efficient and rigorous consideration of dowel/slab interaction. Parametric studies on the response of a typical, dowel‐retrofitted pavement system subjected to axle loads and varying degrees of slab curling are conducted. To examine the effect of slab support on pavement response, the studies consider two different foundation types: layered elastic with an asphalt‐treated base and a dense liquid foundation. The results of the studies are discussed with emphasis on the effect of slab curling and foundation type on joint load transfer and the potential for joint distress. While there are significant differences in response for the ATB‐supported slabs and the slabs founded on a dense liquid, slab curling does generally increase dowel shears and dowel/slab bearing stresses. However, further examination of the parametric study results that accounts for compressive fatigue of the concrete at the dowel/slab interface indicates that slab curling may not significantly increase the potential for damage to the slab concrete surrounding the dowels.     

Collapse of Masonry Buttresses

This paper investigates the collapse of masonry buttresses under concentrated lateral loads. A fracture forms at the collapse state, significantly decreasing the resistance to overturning. Conventional analysis assumes that a masonry buttress acts monolithically to resist lateral loads. The current paper demonstrates that this approach is clearly unsafe, and the possibility of a fracture at the collapse state must be considered in the design and assessment of masonry buttresses. By treating the masonry as a continuum, infinitely strong in compression, with no resistance to tension and no possibility for sliding, the writers demonstrate the form of the fracture and determine the critical failure load for typical buttress forms. This approach follows in the tradition of limit analysis of masonry structures as developed by Heyman. General methods are proposed for the overturning analysis of masonry buttresses, and calculation examples are provided. Finally, methods for evaluating the safety of existing buttresses are presented and discussed.     

Axial Compression of Footings in Cohesionless Soils. I: Load-Settlement Behavior

The results of 167 full-scale field load tests were used to examine several issues related to the load-displacement behavior of footings in cohesionless soils under axial compression loading, including (1) method to interpret the “failure load” from the load-settlement curves; (2) correlations among interpreted loads and settlements; and (3) generalized load-settlement behavior. The L1-L2 method was found to be more appropriate than the “tangent intersection” and “10% of the footing width” methods for interpreting the failure load. The interpreted loads and displacements indicate that footing load-settlement behavior is less elastic and more nonlinear than that of drilled foundations. The results show that the footing behavior will be beyond the elastic limit for designs where a traditional factor of safety between 2 and 3 is used. A normalized curve was developed by approximating the load-settlement curve for each load test in the database by hyperbolic fitting, and the uncertainty in this curve was quantified. This normalized curve can be used in footing design that considers capacity and settlement together. Where possible or warranted, the normalized curve can be subdivided as a function of initial soil modulus.     

Mechanical Characterization of a Graphite∕Epoxy IsoTruss

Graphite∕epoxy IsoTruss specimens were filament wound and experimentally tested to failure under simple compression, tension, and torsion and compared with simple analytical predictions. Failed specimens were subsequently retested to gain further insight into the mechanical interaction of the various components of the IsoTruss. Simple analytical techniques were used to predict the approximate strength of the IsoTruss. A total of 15 five inch (12.7 cm) diameter, five-bay IsoTruss specimens were filament wound on a reusable, silicone inner mandrel. Nine 3-tow specimens with a nominal member cross-sectional area of 0.27 in.2 (1.7 cm2) and six 5-tow specimens with a corresponding area of 0.45 in.2 (2.9 cm2) were fabricated and tested. Axial and torsion loads, axial displacements, and rotations were synchronized with axial strain gauge data from the three main regions of the IsoTruss (axials, tetrahedrons, and the cross-zone). Additionally, four 3-tow IsoTruss specimens with various lengths tested in simple compression showed that global buckling does not affect a five inch (12.7 cm) IsoTruss six bays in length or less, and that the failure of a single bay has little or no effect on the capacity of the remaining IsoTruss to resist compressive loads. The results indicate the relative contributions of primary and secondary load members. The influence of the secondary load members increases after failure of a primary load member. The redundancy of the structure coupled with the influence of the secondary load members causes a ductile type failure to occur for all load types, but it is most pronounced in torsion. In all load types, failure was initially isolated to a single bay. Generally, reloaded specimens were only minimally affected by the prior damage. Finally, increased fiber interconnectivity at the nodes of the IsoTruss yields higher ultimate stresses and greater toughness in IsoTruss structures.     

Three-Dimensional Analysis of Performance of Laterally Loaded Sleeved Piles in Sloping Ground

Development of urban cities in hilly terrain often involves the construction of high-rise buildings supported by large diameter piles on steep cut slopes. Under lateral loads, the piles may induce slope failure, particularly at shallow depths. To minimize the transfer of lateral load from the buildings to the shallow depths of the slope, an annulus of compressible material, referred to as sleeving, is usually constructed between the piles and the adjacent soil. However, the influence of the sleeving on the pile performance in a sloping ground is not fully studied and understood. To investigate the influence, a 3D numerical analysis of sleeved and unsleeved piles on a cut slope is described in this paper. The influences of relative soil stiffness on the response of sleeved piles are also examined. The load transfer from the laterally loaded sleeved pile to the sloping ground is primarily through a shear load transfer mechanism in the vertical plane. Under small lateral loads, the sleeving can lead to a significant reduction in subgrade reaction on the sleeved pile segment and may considerably increase the pile deflection and bending moments. Under large lateral loads, the influence of the sleeving on pile performance appears to diminish because of the widespread plastic zones developed around the pile.