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Borehole drilling and cone penetration test (CPT) are frequently employed site investigation methods for identifying subsurface stratification. However, these two methods have their respective pros and cons, and their corresponding soil type classification protocols are different. Therefore, an approach that can jointly interpret raw data from both investigation methods and provide unified soil classification results is in great demand. Motivated by the aforementioned point, this paper presents a novel semi-supervised clustering based stratification identification approach using information from both boreholes and CPT logs. The proposed approach is established on a hidden Markov random field (HMRF) framework so that the supervision constraints could be introduced by using borehole data during the clustering of CPT sounding samples. Further, the presented approach employs a Monte Carlo Expectation Maximization (MCEM) algorithm to perform the clustering process, which enables estimating the subsurface stratification in a probabilistic manner. The performances of the proposed approach are evaluated using real-world site investigation data. The test results indicate that the proposed approach is effective and robust for identifying subsurface stratification.

This paper presents a new probabilistic site characterization approach for both soil classification and property estimation using sounding data from multiple cone penetration tests (CPTs) at a project site. A hidden Markov random field (HMRF) model based Bayesian clustering approach is developed, which can describe not only the heterogeneity of properties in statistically homogeneous soil layers, but also the correlation between spatial distributions of different soil layers. The latter has not been well considered in the existing CPT interpretation methods. A Monte Carlo Markov chain based expectation maximization (MCMC-EM) algorithm is adopted to calibrate the established HMRF model, so that both the subsurface soil/rock stratification and the pertinent soil properties can be estimated in a probabilistic manner. The proposed CPT interpretation approach is validated and demonstrated using a series of numerical examples, including using real CPT data. It is shown that the proposed method is able to accurately identify soil layers, pinpoint their boundaries, and provide reasonable estimates of the associated soil properties. In addition, comparative studies show that combining analysis of CPT data from multiple soundings, rather than interpreting them separately, can significantly enhance the accuracy of interpretation and simplify the subsequent task of interpreting stratigraphic profiles.

Subsurface formations with multiple soil/rock strata are a common geological condition for shield-driven tunnel (i.e., tunnel constructed using shield-driven machines) construction. The excavation face, under such conditions, often encounters a frequently changing stratigraphic configuration that consists of various lithological units. Furthermore, due to a lack of direct and continuous observations of the subsurface region, it is difficult to predict the stratigraphic profile along the entire excavation path with a high degree of certainty. Such a widely changing and uncertain excavation environment may lead to wide variation in the state of stress and deformation of the tunnel structure along the longitudinal direction. This poses a challenge for design engineers in obtaining accurate performance evaluations or reasonable design outcomes for tunnel construction in subsurface ground with multiple strata. This paper aims to address this challenge by presenting a stochastic geological modeling framework for uncertainty quantification of stratigraphic profiles using sparsely located observation information from geotechnical site investigations. In the proposed modeling framework, the underground soil stratigraphic profile is regarded as a Markov random field with specific energy functions, which is able to describe the inherent anisotropic and non-stationary spatial correlation of lithological units in the subsurface stratigraphic structure. By incorporating the developed stochastic geological modeling framework with a finite element simulation of the tunnel excavation, a probabilistic analysis approach is established to evaluate the effects of stratigraphic uncertainty on the structural performance of a shield-driven tunnel.

Stratigraphic (or lithological) uncertainty refers to the uncertainty of boundaries between different soil layers and lithological units, which has received increasing attention in geotechnical engineering. In this paper, an effective stochastic geological modeling framework is proposed based on Markov random field theory, which is conditional on site investigation data, such as observations of soil types from ground surface, borehole logs, and strata orientation from geophysical tests. The proposed modeling method is capable of accounting for the inherent heterogeneous and anisotropic characteristics of geological structure. In this method, two modeling approaches are introduced to simulate subsurface geological structures to accommodate different confidence levels on geological structure type (i.e., layered vs. others). The sensitivity analysis for two modeling approaches is conducted to reveal the influence of mesh density and the model parameter on the simulation results. Illustrative examples using borehole data are presented to elucidate the ability to quantify the geological structure uncertainty. Furthermore, the applicability of two modeling approaches and the behavior of the proposed model under different model parameters are discussed in detail. Finally, Bayesian inferential framework is introduced to allow for the estimation of the posterior distribution of model parameter, when additional or subsequent borehole information becomes available. Practical guidance of using the proposed stochastic geological modeling technique for engineering practice is given.

Toppling failure of rock slopes is a complicated mode due to a combination of both continuous and discontinuous deformation, especially in dealing with anti-dip rock slopes. In this paper, a novel continuum-based discrete element method (CDEM), which is useful in modeling the entire progressive process from continuous to discontinuous deformation, is proposed to analyze the deformation characteristics, the failure mechanism and the evolution process of a large-scale open pit slope with a typical anti-dip structure. To simulate the slope deformation, the shear strength reduction method (SSR) is adopted to represent the strength degradation of rock mass in the deterioration process. The simulated results are validated using data obtained from a field investigation and continuous monitoring by employing an advanced remote sensing technique called ground-based interferometric synthetic aperture radar (GB-InSAR). To analyze the evolution trend of the anti-dip slope, the subsequent toppling failure mode is predicted using the validated CDEM models. Based on a case study of a slope at the Fushun open pit mine (in Fushun, China), the unique geological structure with various joints and discontinuities, ground-water, intense rainfall, and mining activities are identified as the main triggers for different failure stages. The comparison between the field data and the simulation shows that CDEM accurately depicts the rock deformation and the failure pattern of the studied slope. The proposed numerical modeling techniques can be used for predicting failures of other similar excavated rock slopes. The simulated evolution process and the recorded deformation patterns help engineers to gain a better understanding of rock mass movement of anti-dip slopes, and the presented methodology could be utilized for similar studies and engineering designs. (C) 2015 Elsevier B.V. All rights reserved.

This paper describes the use of a clustering approach based on hidden Markov random field to extract potential homogeneous segments from a large length right-of-way of a pipeline structure with heterogeneous soil properties. This approach extends the conventional finite mixture model so that the spatial correlation of external corrosion sites can be taken into consideration. An algorithm is established for classifying corrosion defects using soil properties from an in-situ survey and location information from in-line inspection reports. The categorized corrosion defects reveal the hidden patterns of corrosion degradation in different segments along a pipeline structure. Stochastic simulation is employed to test this clustering approach. An example involving a 110-km pipeline interval is employed to illustrate the implementation of the clustering approach. The results indicate that the process of external corrosion propagation in a buried pipeline is position-dependent and is highly related to the soil environment. In addition, the results show that this phenomenon can be interpreted by segmentation using the proposed clustering method. A clustering-based inspection strategy is discussed as a way to apply the present approach.

In the petroleum industry, oil and gas pipeline operators routinely employ non-destructive in-line inspection (ILI) tools to perform integrity assessment, in which corrosion defects are detected, located and sized. However, the inspection technology is not perfect, and its accuracy is influenced by intrinsic measurement error of the ILI device as well as measurement noise. The quality of the inspection result should be assessed, and the inspection device should be calibrated before further assessment is performed. In the present work, a calibration model for an ultrasonic ILI device is proposed based on physical principles, and both systematic error and random error are able to be estimated. In addition to the errors from inspection devices, the soil environment introduces various uncertainties into the corrosion propagation. This paper presents a methodology to infer the actual corrosion defect depth based on detection theory and to account for the effect of soil property variation by combining cluster analysis with a Bayesian inferential framework. A numerical study on calibration uncertainty shows the influence of the number of field verifications. The proposed model framework is applied to a 110-km pipeline system to illustrate its application.

In reliability analysis, the crude Monte Carlo method is known to be computationally demanding. To improve computational efficiency, this paper presents an importance sampling based algorithm that can be applied to conduct efficient reliability evaluation for axially loaded piles. The spatial variability of soil properties along the pile length is considered by random field modeling, in which a mean, a variance, and a correlation length are used to statistically characterize a random field. The local averaging subdivision technique is employed to generate random fields. In each realization, the random fields are used as inputs to the well-established load transfer method to evaluate the load–displacement behavior of an axially loaded pile. Failure is defined as the event where the vertical movement at the pile top exceeds the allowable displacement. By sampling more heavily from the region of interest and then scaling the indicator function back by a ratio of probability densities, a faster rate of convergence can be achieved in the proposed importance sampling algorithm while maintaining the same accuracy as in the crude Monte Carlo method. Two examples are given to demonstrate the accuracy and the efficiency of the proposed method. It is shown that the estimate based on the proposed importance sampling method is unbiased. Furthermore, the size of samples can be greatly reduced in the developed method.

One important category of transportation infrastructure is underground pipelines. Corrosion of these buried pipeline systems may cause pipeline failures with the attendant hazards of property loss and fatalities. Therefore, developing the capability to estimate the soil corrosivity is important for designing and preserving materials and for risk assessment. The deterioration rate of metal is highly influenced by the physicochemical characteristics of a material and the environment of its surroundings. In this study, the field data obtained from the southeast region of Mexico was examined using various data mining techniques to determine the usefulness of these techniques for clustering soil corrosivity level. Specifically, the soil was classified into different corrosivity level clusters by k-means and Gaussian mixture model (GMM). In terms of physical space, GMM shows better separability; therefore, the distributions of the material loss of the buried petroleum pipeline walls were estimated via the empirical density within GMM clusters. The soil corrosivity levels of the clusters were determined based on the medians of metal loss. The proposed clustering method was demonstrated to be capable of classifying the soil into different levels of corrosivity severity.

In this paper, a limiting equilibrium based methodology, incorporating the method of slices and arching effects of the drilled shafts, is developed for optimizing the use of multiple rows of drilled shafts. This proposed method is focusing on the number of rows, the location of each row, the dimension and spacing of the drilled shafts. Three design criteria are used for optimization: target global factor of safety, the constructability and service limit. A PC-based program called M-UASLOPE has been coded to allow for handling of complex slope geometry, soil profile, and ground water conditions. A design example is presented to illustrate the application of the M-UASLOPE program in the optimized design of multiple rows of drilled shafts for stabilizing the example slope.

In most limit state design codes, the serviceability limit checks for drilled shafts still use deterministic approaches. Moreover, different limit states are usually considered separately. This paper develops a probabilistic framework to assess the serviceability performance with the consideration of soil spatial variability in reliability analysis. Specifically, the performance of a drilled shaft is defined in terms of the vertical settlement, lateral deflection, and angular distortion at the top of the shaft, corresponding to three limit states in the reliability analysis. Failure is defined as the event that the displacements exceed the corresponding tolerable displacements. The spatial variability of soil properties is considered using random field modeling. To illustrate the proposed framework, this study assesses the reliability of each limit state and the system reliability of a numerical example of a drilled shaft. The results show the system reliability should be considered for the serviceability performance. The importance measures of the random variables indicate that the external loads, the performance criteria, the model errors of load transfer curves and soil strength parameter are the most important factors in reliability analysis. Moreover, it is shown that the correlation length and coefficient of variation of soil strength can exert significant impacts on the calculated failure probability.

In this paper, a method for estimating yield acceleration of a slope reinforced with a row of equally spaced drilled shafts under a seismic excitation is presented. The method is based on a concept of soil arching due to rigid inclusions of drilled shafts on slope, which in turn reduces the driving force on the down-slope side of drilled shafts. Considering soil arching effects and earthquake-induced inertia forces, a limiting equilibrium based formulation was derived. A computer program was coded to allow for calculations of yield acceleration of a drilled shafts reinforced slope with complex slope geometry and soil profiles. Once yield acceleration is determined, then Newmark's method can be evoked to estimate permanent displacement of a slope reinforced with a row of drilled shafts under an earthquake excitation. A total of seven cases were presented to show that the proposed Newmark type calculation is adequate when compared to 3-D finite element analysis results.

The fundamental solutions of axisymmetric elastodynamic problem for the multilayered half-space due to an impulsive ring source acting within a layered elastic media are derived in time domain with the aid of Laplace–Hankel mixed transform and transfer matrix techniques. In addition, an effective numerical procedure, which utilizes the fast Hankel transform algorithm, is also proposed to calculate these solutions. Illustrative examples have been given to demonstrate that the fundamental solutions can be readily evaluated and the numerical results are of high accuracy. The present solutions can be directly applied to determine the transient wave fields caused by a seismic source and show the potential application to the elastodynamic problems solved by the boundary element method.

Understanding the anchor-soil interface behavior is essential to the determination of the anchor pullout capacity and prediction of the deformation of the anchor-reinforced system under working load conditions. Numerous anchor pullout tests under both lab and field conditions have generally yielded extremely high apparent interface strength, which cannot be explained by the conventional interface friction theory between the anchor material and the soil. In this paper, the mechanism and the phenomena of the anchor-soil interaction were studied, and the soil dilatancy due to shearing was regarded as the main factor contributing to the increase of the anchor-soil interface friction. Considering this effect, along with the adoption of a cylindrical shear deformation pattern of the soil, anchor-soil interface models have been developed for hardening and softening behavior, respectively. Using the developed interface model, the forward and backward calculation algorithms have been formulated and applied to predict the anchor performance for the given interface parameters and to determine the interface parameters from the given anchor pullout test, respectively. Furthermore, the prediction of the anchor pullout performance was compared favorably with two hypothetical cases, two laboratory test results, and one field case.

Drilled shafts have been used as an effective means to stabilize a soil slope with marginal safety factor. A limit equilibrium based slope stability analysis technique is presented in this paper that would allow for the determination of the safety factor of the reinforced slope and the forces acting on the drilled shafts. Specifically, the finite element analysis generated load transfer characteristic curves were incorporated into the traditional method of slice approach to account for the soil arching effects. Mathematical formulation of the proposed analysis method is given in detail, followed by validation of the approach with other analysis methods. Examples of the slopes with or without the drilled shafts are given to illustrate the reasonableness of the solution provided by the proposed approach. The efficiency of using drilled shafts to stabilize a slope is discussed by examing the influence of the shaft location, shaft size and spacing on the calculated safety factor. Finally, a practical case involving the use of the proposed approach is presented.

Embankment dams are important and costly civil engineering structures that provide an essential infrastructure for the management of water. One of the critical aspects of dam design is the analysis of stability and safety of the earth structure under various operating and environmental conditions. Traditionally, a deterministic approach is used for such analysis. However, the determination of variables such as soil strength parameters, pore pressure and other pertinent properties involves uncertainties, which cannot be handled in the traditional deterministic methods. It is, therefore, highly desirable to develop a reliability based analytical/numerical methodology for stability analysis of dams taking into account these uncertainties. Reliability and probability theories are developed in this paper for assessing the reliability index and the corresponding probability of failure of multi-layered embankment dams and slopes. Two definitions were used to calculate the reliability index (i.e. the normal distribution and the log–normal distribution). The computer program reslop was developed and validated by the Congress Street open cut failure case. The developed approach was used to study the stability of the King Talal embankment dam. The results are discussed and conclusions drawn.

Anchor has been successively used as an in-situ soil reinforcement for more than two decades. The design of anchors is traditionally performed based only on its pull-out capacity, which ignores the interface interaction between anchor and soil due to relative displacement. This paper provides the analytical solutions based on the linear elastic-perfectly plastic model for the interface between the anchor and soil. The derived analytical solutions include the case of soil movements along the anchor axis and the case of soil movements normal to the anchor axis. It shows that the anchor pull-out behavior is only a special case of the general solution for the anchor subjected to the soil movement along its axis. The parametric study for both actively loaded and passively loaded anchor has been extensively carried out, which provides insights into the interface interaction between the anchor and soil and general guidelines in design of an anchor system.

Combining the conventional method of slices for slope stability analysis with the previously derived analytical solutions for the anchor-soil interaction, a displacement-based approach for the stability analysis of anchor reinforced slope has been developed. The procedure for evaluating the working forces in the anchor, the global factor of safety, and the limits of the anchor working force is described in detail. Furthermore, the effects of reinforcement on the slope stability due to different parameters, such as soil properties, anchor characteristics and anchor-soil interface properties were studied. The numerical results demonstrate the progressively mobilized anchor forces and their distribution along a vertical section of the slope, and the expected global factor of safety at each stage of soil movement along the slip surface. Also, for a given anchor reinforced slope, the anchor working limit is generated along a vertical section of the slope, which controls the anchor resistance to the slope and limits the potential soil movement. Based on the results of the analysis, the general guideline for the design of an anchor reinforced slope is discussed.

The development of simple and computationally efficient analytical models for predicting the time-dependent initiation and propagation of cracks in linear viscoelastic materials is of paramount importance in practical structural design using polymeric materials. A crack tip model similar to that of Schapery is adapted (R. A. Schapery, A theory of crack initiation and growth in viscoelastic media I. Theoretical development. International Journal of Fracture, 1975, 11(1), 141–159), in which the failure zone is assumed to be of highly-damaged material preceding the physical crack tip. In the spirit of Wnuk's total energy release formulation of elasto-plastic solid (M. P. Wnuk, Subcritical growth of fracture (inelastic fatigue). International Journal of Fracture Mechanics, 1971, 7(4), 383–407), the theoretical expression for the total energy release rate of viscoelastic materials has been derived through the application of the correspondence principle. The derived theory has been applied to three specific case studies: (i) an infinite plate with central crack subjected to remote tension, (ii) an edge crack in a semi-infinite plate subjected to a pair of equal and opposite concentrated forces, and (iii) a pre-notched three-point bending beam. The significance of the influence of the plastic energy dissipation (due to viscoelasticity) on the crack initiation and propagation in these three cases has been examined and discussed in this paper.

Limit equilibrium analysis within the framework of method of slices is one of the most commonly used methods for analyzing the stability of a slope. Since the equilibrium condition, along with failure criterion, is insufficient to render the problem to be determinate, various assumptions were evoked. In the past, the problem of indeterminacy was solved either by iteration method together with the assumption of the same mobilization of shear strength along the potentially sliding surface and by making assumptions regarding the direction of interslice forces. In this paper, a direct method for determining the interslice forces is proposed via the hypothesis of least resistance. A simple equation is derived for determining the inclination angle of the interslice force. It is shown that the inclination is dependent upon the geometry and soil properties of a given slope. Use of the derived equation for calculating the factor of safety of a given slope is computationally efficient. Results obtained from this method are compared with that of the existing methods. The numerical cases studied indicated that the factor of safety as well as the interslice forces and line of thrust obtained from the proposed method is close to those obtained from the existing methods. There is no convergency problem in the proposed method. The proposed method eliminates the need to make assumptions on the interslice force direction or location.

Fatigue cracking due to repeated loading has been recognized as an important distress problem in asphalt concrete (AC) pavements. The development of fatigue laws to describe the AC beams has been carried out through two main approaches: a phenomenological approach and a fracture mechanics based approach. However, both approaches, at the present time, employ regression constants that cannot truly reflect basic material properties. The primary purpose of this paper is to develop a fracture-mechanics-based fatigue law which utilizes fundamental material parameters including fracture toughness, flexure tensile strength, as well as two other physically quantifiable model parameters: damage parameter, α, and critical plastic zone length, δc. The development of a two-stage plastic zone model is presented, followed by the derivation of a fatigue crack growth law. The significance of the damage parameter, α, and critical plastic zone length, δc is emphasized, with a detailed discussion of the method to determine these parameters. The developed fatigue model is used to predict fatigue life of AC beams fabricated from a wide spectrum of mixture designs. The developed fatigue model predicts a much faster crack growth rate compared to the Paris law, and appears to be more sensitive to the ratio of the initial stress intensity factor over its critical value (Ko/Kc)

The interaction between a penetrating shaft and the surrounding soil media under impact loading is a frequently encountered phenomenon in geotechnical engineering. Examples of such dynamic soil/shaft interaction would include dynamic pile driving, standard penetration testing (SPT), and dynamic driven rod test. Presented in this paper is a novel approach, based on the principle of dynamic system identification, which enables identification of dynamic soil-pile interaction model parameters. The analytical transfer function, relating the output stress waveforms to the input stress waveforms in the soil/shaft system, is derived using the Laplace and Fourier Transform techniques and the one-dimensional wave propagation theories. A numerical solution algorithm based on a variation of gradient method is coded into a micro-computer based program to solve the frequency-dependent soil-pile interaction parameters (Smith model): soil damping and soil spring stiffness. To further reduce the amount of computational effort required in the solution of the frequency-dependent dynamic soil properties, it is suggested that the solution be obtained for the first-mode natural frequency of the measured stress waves. The results obtained from this simplified solution algorithm, when compared with both numerical simulations and controlled laboratory tests, are reasonably acceptable. The proposed parameter identification technique offers a viable alternative data interpretation procedure for deducing pertinent Smith model parameters used frequently in pile driving analysis. (A)

The capability of identifying both location and severity of damages of faulted elements in a structural system is greatly needed under the present demands of constantly maintaining the safety of civil engineering structures. Presented in this paper is a methodology based on vibration theory that can be used for the detection of faults in a beam of either uniform or nonuniform cross section and under a variety of boundary conditions, including simple support, cantilever support, and beam on elastic foundation. Theoretical developments of the methodology are presented first, followed by numerical experiments to demonstrate the feasibility of the method. Numerical experiments include various damage scenarios such as those faults occurring in a beam section as well as in a subgrade foundation. Furthermore, damage scenarios involving both single fault and multiple faults are also presented. The defect of the supporting subgrade foundation can be modeled either as degrading subgrade stiffness or increasing damping values. Numerical experiments demonstrate the feasibility of the developed NDT methodology which warrants the next stage of field study.

Wave equation analysis and dynamic pile testing have been generally accepted by the engineering profession as effective techniques for construction control of driven piles. The accuracy of wave equation analysis, however, is dependent upon the assumed hammer performance and the correct input of dynamic soil-pile interaction model parameters. A host of proprietary numerical simulation programs have been developed to facilitate the calculation of pile capacity and pertinent soil-pile interaction model parameters based on the measured dynamic signals (force and velocity wave forms measured at a point near the pile top) during each hammer blow (usually at the end of initial driving or the beginning of re-strike). The numerical simulation techniques involve the adjustment of the model parameters based on the matching of the calculated signal with a reference signal. Either dynamic force or kinetic velocity is imposed at the top as a stimulus, while the other signal is used as a reference for matching purpose. In this paper, a new numerical simulation algorithm, utilizing both force and velocity as the given boundary stimuli, has been developed. The proposed algorithm differs from the existing numerical programs mainly in that it is cast in a system in which the signal matching process is performed at several points along the pile shaft. In this way, the soil-pile interaction model parameters can be more accurately determined. Furthermore, the proposed algorithm can determine the shaft resistance and toe resistance separately, thus helping the determination of the uplift capacity of driven piles.

An integrated technique based on the vibration theory to nondestructively identify multiple discrete cracks in a structure is presented. Two damage modeling techniques, one involving the use of massless, infinitesimal springs to represent discrete cracks and the other one employing the continuum damage concept, are integrated to provide a crack-detection technique that utilizes the global vibration characteristics of a structure but offers local information on each individual crack, including location and extent of the cracks. In the spring model, the Castigliano's theorem and the perturbation technique are used to derive a theoretical relationship between the eigenfrequency changes and the location and extent of the discrete cracks. In the continuum damage model, the effective stress concept coupled with the Hamilton's principle are used to derive the similar relationship that is cast in a continuum form. A unified g(β) function emerges from the two model approaches. The g(β) function can be determined through the mode shapes of an intact structure by means of the modal strain energy density. In the proposed integrated approach, the continuum damage model can be used first to identify the discretizing elements of a structure that contain cracks. Then, the spring damage model can be used to quantify the location and severity of the discrete crack in each damaged element. An example of a simply-supported beam containing two discrete cracks is given to illustrate the application and accuracy of the proposed approach.

T he conceptual differences between the conventional cohesive crack model and the cohesive crack model discussed in this paper are briefly reviewed. Based on the potential energy principle and the assumption of a linear softening law, a boundary eigenvalue problem is introduced. Under the critical condition, that is, when the smallest eigenvalue is one, the corresponding eigenfunction represents the non-unique part of the displacement solution, and the critical load can be determined via the eigenfunction. Based on this formulation and using a singular integral equation technique, the boundary eigenvalue problem is established for an infinite plane with a central cut under transverse tension. It is found that the obtained solution approaches Griffith theory in the large size limit. The implication of this result is discussed in comparison with the concept of the R-curve approach.

The elasto-viscoplasticity model presented in Part I is now examined in detail in this paper. The physical meaning of model parameters as well as appropriate procedures for their determinations are described herein. Based on this procedure, the model constants were determined for three groups of soils. Numerical simulations demonstrated the model's capability to capture the time-dependent behaviors, including creep (both drained and undrained), undrained stress relaxation, and drained tests with various effective stress paths. Quantitatively, the rate effect is shown to be captured by the model.

A unified elasto-viscoplasticity model is formulated for describing the stress-strainpore pressure-time behavior of saturated cohesive soils under general three-dimensional stress conditions. The limit surface and the conjugated static yield surface (elastic domain) form the basic framework from which the time- (aging and creep) and rate- effects can be conveniently accounted for by using a single internal state variable - preconsolidation pressure. The attendant evolution law for the internal state variable is formulated on the basis of phenomenological characteristics presented by Leroueil, et al, (1985) [1]. A detailed review of macroscopic characteristics of clays and mathematic derivations of the proposed viscoplasticity theory are presented in this paper.

A method based on measurements of natural frequencies of structures has been developed for the detection of crack location and quantification of damage magnitude in a uniform beam under simply supported or cantilever boundary conditions. The method adopts rotational massless springs in the beam element as a mechanical model to represent the local flexibility introduced by a crack. For a given natural frequency and a damage location, the characteristic equation can be solved to provide numerical value of the stiffness of the rotational spring. The intersection points of the values of the normalized crack stiffness K at various natural frequencies ω i along the axial direction of the beam represent the possible locations of the crack. Furthermore, the numerical value K has been shown to be directly related to the damage magnitude as Δ I⧸I , where Δ I is the reduction of section modulus and I is the original undamaged section modulus. Two numerical case studies are given to demonstrate the validity of the method.