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This paper presents a novel perspective to understanding the spatial and statistical patterns of a cone penetration dataset and identifying soil stratification using these patterns. Both local consistency in physical space (i.e., along depth) and statistical similarity in feature space (i.e., logQt–logFrspace, where Qtis the normalized tip resistance and Fris the normalized friction ratio, or the Robertson chart) between data points are considered simultaneously. The proposed approach, in essence, consists of two parts: (i) a pattern detection approach using the Bayesian inferential framework and (ii) a pattern interpretation protocol using the Robertson chart. The first part is the mathematical core of the proposed approach, which infers both spatial pattern in physical space and statistical pattern in feature space from the input dataset; the second part converts the abstract patterns into intuitive spatial configurations of multiple soil layers having different soil behavior types. The advantages of the proposed approach include probabilistic soil classification and identification of soil stratification in an automatic and fully unsupervised manner. The proposed approach has been implemented in MATLAB R2015b and Python 3.6, and tested using various datasets including both synthetic and real-world cone penetration test soundings. The results show that the proposed approach can accurately and automatically detect soil layers with quantified uncertainty and reasonable computational cost.

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.

The premature failure of repaired concrete structures has become a big concern for civil engineers in recent years. While premature failure can be greatly reduced through the selection of an appropriate repair material, civil engineers must take into account a large number of conflicting criteria for candidate repair materials to make the final decision. In this paper, a procedure coupled with the VIKOR method is proposed to obtain the best repair material for concrete structures. This procedure can aid civil engineers in modeling and selecting suitable repair materials according to a set of predefined criteria. A case study is included to validate the accuracy of the outcomes of the proposed procedure. Since weights play a significant role in the ranking of results for the repair materials, sensitivity analysis is conducted using three different methods for assigning weights to find more reliable results. Keywords: Repair material, Concrete, Decision making, MCDM

A reliability-based method was developed for predicting the initiation time and the probability of flexural failure for continuous slab bridges with load-induced cracks exposed to chloride environment resulting from de-icing salts. A practical methodology was used for predicting the diffusion coefficient of chloride ingress into the pre-existing load-induced cracks in concrete. The reduction in the cross-sectional area of the reinforcement due to corrosion was included in the model. The proposed methodology accounts for uncertainties in the strength demand, structural capacity, and corrosion models, as well as uncertainties in environmental conditions, material properties, and structural geometry. All probabilistic data on uncertainties were estimated from the information contained in previous experimental and statistical studies. As an application of the proposed model, a three-span continuous slab bridge in Ohio is presented for demonstration of the developed methodology. A comparison of results clearly shows the importance of considering the effects of the load-induced cracks for correct prediction of the initiation of corrosion time and the critical time to maintain structural integrity.

With the development of intelligent and automated information system in the information era, the need for more efficient decision making method is growing. An effective method used to rank concrete bridge projects affected by reinforcement corrosion damage will help decision makers of bridge management agencies to better understand the different degrees of urgency for each project. The priority ranking process of different bridge repair projects is complex, since it is hard for decision makers to directly decide which bridge has higher priority when considering many criteria at the same time. The ranking of the different bridge repairing projects can be similar to solving multiple criteria decision making (MCDM) problems. The VIKOR (VlseKriterijumska Optimizcija I Kaompromisno Resenje in Serbian) method is a distance-to-target method which is developed and used to solve MCDM problems in material selection research. Since weights play a significant role in the priority ranking problems, objective weights based on Entropy concept and Target-based standard deviation method and dependent weights are also applied in this study. Several important criteria, which have not been considered in previous literatures, are proposed and the influence of these criteria to the bridge condition is checked and verified by using data information in NBI databased. A numerical example is proposed to illustrate the application of proposed method. Therefore, in this research a new ranking system methodology based on weighted VIKOR method with proposed criteria for ranking bridge projects is presented. Keywords: VIKOR method, Decision making, Concrete bridge, MCDM

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.

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 study, a model is developed to assess external corrosion in buried pipelines based on the uni- fication of Bayesian inferential structure derived from Markov chain Monte Carlo techniques using clustered inspection data. This proposed stochastic model com- bines clustering algorithms that can ascertain the simi- larity of corrosion defects and Monte Carlo simulation that can give an accurate probability density function es- timation of the corrosion rate. The metal loss rate is cho- sen as the indicator of corrosion damage propagation, obeying a generalized extreme value (GEV) distribution. Bayesian theory was employed to update the probability distribution of metal loss rate as well as the GEV param- eters in order to account for the model uncertainty. The proposed model was validated with direct and indirect inspection data extracted from a 110-km buried pipeline system.

A simplified approach was proposed to analyze the negative skin friction calculation of special-shaped pile considering pile-soil interaction under surcharge. Based on the concentric cylinder shearing theory, considering the changes of pile shape (such as, taper angle and diameters of pile base, etc.), the load-transfer of special-shaped pile was built. The accuracy of the developed simplified approach was verified by numerical simulation model with the same condition. Then, the influence factors, such as, taper angles, the diameter of pile base, surcharge, and pile-soil interface parameters were analyzed and discussed. The results show that the developed simplified approach can calculate NSF of special-shaped pile under surcharge effectively. A limited parametric study indicates that in many practical situations special-shaped piles (such as belled wedge pile shown in this work) offer a design option that is more economical than traditional uniform cross-section piles.

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.

Analysis of laterally loaded piles or drilled shafts is a complex soil–structure interaction problem for which the p–y method has been widely accepted as a computational tool for predicting the load-displacement behavior. This paper presents a sampling-based method that can be applied to reliability analysis of the load-deflection behavior for laterally loaded piles. Various sources of uncertainties arising from soil properties, analysis model, and p–y criteria can be taken into account in the proposed method. In particular, soil properties needed as input for determining site-specific p–y curves were modeled as random fields. To statistically characterize the random field of a soil parameter, the field mean, the field variance, and the correlation structure are required. The performance of a pile under lateral loading is evaluated using a different set of random samples in each realization. The probability of failure, in which failure is defined as the event of not meeting the prescribed performa...

In order to calculate negative skin friction (NSF) of pile group embedded in a consolidating soil, the dragload calculating formulas of single pile were established by considering Davis one-dimensional nonlinear consolidation soils settlement and hyperbolic load-transfer of pile-soil interface. Based on effective influence area theory, a simple semiempirical mathematical model of analysis for predicting the group effect of pile group under dragload was described. The accuracy and reliability of mathematical models built in this paper were verified by practical engineering comparative analysis. Case studies were studied, and the prediction values were found to be in good agreement with those of measured values. Then, the influences factors, such as, soil consolidation degree, the initial volume compressibility coefficient, and the stiffness of bearing soil, were analyzed and discussed. The results show that the mathematical models considering nonlinear soil consolidation and group effect can reflect the practical NSF of pile group effectively and accurately. The results of this paper can provide reference for practical pile group embedded in consolidating soil under NSF design and calculation.

Understanding of cracking behavior of cover concrete is important for assessment of the remaining service life of corrosion-affected concrete structures. Predicting initiation of concrete cracking is commonly based on the evolution of stresses caused by the volume expansion of corrosion products on reinforcing bars. This paper presents an analytical method that is capable of providing the solution to two-dimensional (2D) elastic stress field caused by nonuniform volume expansion around the corroding reinforcing bars. The developed method features the formulation of a displacement model, which is applied as a boundary condition to simulate the effect of nonuniform corrosion on the deformation of the surrounding concrete. A closed-form solution to the stress field is obtained using the complex variable method of Muskhelishvili. Validation of the solution is supported by a comparison with finite-element-based simulation results. The solution reveals the evolution of stresses surrounding two typical locations...

Most of the rock medium possesses intrinsic grain orientation or preferred bedding and joint directions, thus requiring the use of at least transverse isotropy to describe its elastic behavior. This paper presents a series of charts, based on extensive finite element parametric studies along with nonlinear regression analysis of FE simulation results, for estimating the subgrade reaction modulus (or initial tangent to the p-y curve) using five elastic constants of a transversely isotropic rock mass. The proper characterization of subgrade reaction modulus is critical for accurate prediction of the elastic lateral deflection of a rock socketed drilled shaft under the applied lateral loads. The sensitivity of the response of a laterally loaded drilled shaft to the degree of anisotropy and orientation of the plane of anisotropy (bedding plane direction of the rock medium) was demonstrated in this paper for an actual lateral load testing case in Ohio. It is highly recommended to use five elastic constants to estimate subgrade reaction modulus of rock medium exhibiting high degree of cross anisotropy.

Drilled shafts socketed in rock mass have been used frequently as a foundation system to support both vertical and lateral loads. Traditionally, the lateral interaction between the drilled shaft and the surrounding rock medium has been characterized by means of nonlinear p-y curves; however, there is a lack of well verified p-y criterion for rock mass. In this paper, a hyperbolic p-y criterion is developed based on both theoretical derivations and numerical (finite element) parametric analysis results. The methods for determining pertinent rock parameters needed for constructing the proposed p-y curves are presented in the paper. Two full-scale lateral load tests on large diameter, fully instrumented drilled shafts socketed in rock conducted by the writers, together with additional four load test results reported by Gabr et al. were used to validate the applicability of the proposed hyperbolic p-y curves for rock mass. The comparisons between the computed shaft responses (both deflections and bending mome...

The permeability coefficient of a rock mass depends mainly on the aperture of the joint and the porosity of the block, which may alter with time when creep of the rock mass is taken into account. Therefore, a coupled creep and seepage model for hybrid media is proposed in this paper. Large-scale and strongly permeable joints are simulated according to their spatial distributions, while other discontinuities are treated as equivalent continuum. Based on the fundamental mechanism of creep effects on the permeability of the rock mass, together with empirical equations for hydraulic conductivity, coupled creep and seepage equations for filled joints, rough joints, and equivalent continuum are proposed. By application of these equations, governing equations for the coupled creep and seepage model are deduced. A simplified numerical solution is proposed to solve the coupled creep and seepage model. The coupled model is shown to simulate the evolvement of seepage, deformation, and stress field in a gravity dam. By comparing the results derived by coupled and uncoupled models, it is concluded that the coupling between creep and seepage should be taken into account when performing engineering design of large dams.

An innovative bridge construction utilizing on-site posttensioned precast concrete beams that are compressed together with full depth grouted shear keys and transverse posttensioning is the subject of this paper. In particular, the performance of the shear keys with regard to load transfer and water tightness constitutes the main issues of investigation. This paper presents the results of a live load testing program and associated finite-element analysis results of the as-built bridge. Live truck load test results help provide insights on the lateral (transverse direction) load distribution characteristics among the interconnected beams. The measured lateral distribution of the applied truck load among adjacent beams showed that the load was transferred primarily to the beams close to the truck load position, validating the effectiveness of the shear key details in transporting loads.

Precast concrete multibeam deck systems are widely used to replace deteriorated bridge decks. The system's rapid erection substantially reduces traffic disruptions. The transverse precompression force provided by the posttensioning tendons is an important design consideration to ensure adequate load transfer between contiguous beams and to reduce potential differential cracking at shear key joint locations. This paper presents an analysis method, based on grillage analogy, for calculating the required transverse posttensioning stress for a deck built with precast concrete multibeams. The effects of skew--as well as other influencing factors, such as deck width, thickness, and span length--on the required posttensioning stress were studied. Results of the study indicate that the effect of skew is significant when the skew angle is greater than 30 deg. Results compare well with the AASHTO's LRFD specifications for right-angle decks; however, the required posttensioning stress is decreased with an increase in skew angle.

Piles are often embedded in a layered soil profile, such as sand or clay layer underlain by rock. Several existing solutions are available for laterally loaded piles in a layered soil system. However, these solutions are only applicable to constant soil stiffness for each layer. In this paper, a variational approach is employed to numerically solve the problem of laterally loaded piles in layered soils using beam on an elastic foundation model. The soil stiffness can be either constant with depth or linearly varying with depth. The numerical solution is validated against an existing solution for linearly varying soil stiffness in a single soil layer system and an existing solution for a two-layer soil system with constant soil stiffness. Case studies using the proposed solution for field lateral load tests on full size drilled shafts embedded in weak rock with an overlying sand layer are presented. The simplicity and the relative ease of using the solution make it a good alternative approach for estimating the deflection and moment responses of a laterally loaded pile in a two-layer soil profile.

A statistical database is developed to describe the increase in pile axial capacity with time, known as set-up, when piles are driven into clay. Based on the collected pile testing data, pile set-up is significant and continues to develop for a long time after pile installation. The statistical database shows that normal distribution can be used to properly describe the probabilistic characteristics of predicted set-up capacity by the Skov and Denver equation. The main objective of this paper is to incorporate the set-up effect into a reliability-based load and resistance factor design (LRFD) of driven piles. The statistical parameters for set-up effect combined with the previously documented statistics of load and resistance can be systematically accounted for in the framework of reliability-based analysis using the first-order reliability method (FORM). Separate resistance factors are obtained to account for different degrees of uncertainties associated with measured short-term capacity and predicted set-up capacity at various reliability levels. The incorporation of set-up effect in LRFD can improve the prediction of design capacity of driven piles. Thus, pile length or numbers of pile could be reduced and economical design of driven piles could be achieved.Key words: driven piles, set-up, reliability, load and resistance factor design (LRFD), first-order reliability method (FORM).

Quality control criteria for driven piles are developed using the framework of acceptance-sampling analysis based on the statistical data of static and dynamic load tests. The static and dynamic load tests are often carried out for quality control and verification of load-carrying capacity of driven piles. The number of load tests and the acceptance criterion of measured capacities are discussed in this technical note. The relationship between the number of load tests and the criterion on acceptance of measured capacity is elucidated. It is shown that the measured capacity required to assure adequate quality control decreases with an increase in the number of load tests. Either the number of load tests or the target measured capacity or both needs to be increased in order to obtain a higher target reliability index. The number of load tests associated with the acceptance criteria of the measured capacities is recommended in this technical note for the static and dynamic pile test methods to achieve different levels of reliability.

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.

Drilled shafts have been widely used as an effective means for slope stabilization. In this paper, a design procedure for stabilizing an unstable slope with a row of equally spaced drilled shafts is presented. The limiting equilibrium–based slope-stability analysis method, modified to incorporate the drilled-shaft-induced arching effects through a semiempirical load-transfer factor, is formulated and coded into a general slope-stability computer program, UASLOPE, for complex slope geometry, soil profile, and groundwater table conditions. The UASLOPE program is validated with three-dimensional (3D) finite-element simulation results concerning factor of safety of the drilled-shaft/slope system and net force imparted on drilled shafts. Regression analysis performed on more than 40 cases of 3D finite-element simulation results has led to a semiempirical predictive equation for the drilled-shaft-induced load-transfer factor, from which the phenomenon of soil arching in a drilled-shaft/slope system is e...

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.

An energy approach previously developed as an alternative to the conventional dynamic pile­ driving control methods (e.g., ENR and Gates formula) has been formulated in a probabilistic framework. The Smith-model parameters incorporated in the energy approach, including the damping factor and the quake, were treated as random variables whose mean values, standard deviations, and probability distribution functions were determined from a statistical analysis of a database of 204 pile cases. The Smith parameters for each pile case were derived from the back-calCUlation process in relation to the Case Pile Wave Analysis Program (CAPWAP) signal-match procedure. The first-order second-moment (FOSM) method was used in the probabilistic energy approach to compute the mean value and standard deviation of the pile capacity. A detailed description is given of the database, the statistical analysis results, and the mathematical formulation of the probabilistic energy approach. The developed probability approach was applied to the 204 pile cases. The agreement between the computed pile-capacity and the static load test results is either slightly better than or equally as good as the comparison between the traditional CAPWAP deduced pile-capacity and the static pile-load test results. The required inputs in the probabilistic energy approach are the energy delivered to the pile head during each hammer blow, the blow count per 0.3 m of pile penetration, the maximum velocity at the pile head, and the pile dim~nsions and elastic properties. The required instrument for this method is much simpler compared to that reqUired by the Case and CAPWAP methods, leading it to be an attractive and economic method for pile-driving control in the field.

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)

A simple method is proposed for determination of fracture energy of materials exhibiting quasi-brittle behavior during mode I cracking. A series of graphs showing the relationship between the nondimensional peak load and the nondimensional beam size are generated for a three-point beam configuration using a new and computationally efficient finite-element program. The method only requires the measurement of the peak load of a single-size beam specimen. It is preferred that the beam specimens have a small preexisting notch to ensure mode I cracking in a three-point bending test. The other required material properties for the use of nondimensionalized graphs include Young's modulus and tensile strength. Since the three-point bending test can be easily carried out in the laboratory, the proposed method offers a practical, yet expedient, way of characterizing the nonlinear fracture properties of materials that follow the linear stress-separation behavior in the process zone.

The phenomena that occur during the early age of concrete curing are complex, as the coupling between chemical-thermal-hydration and mechanical effects must be considered. Among the main attributes that govern the nonlinear behavior of early-age concrete are stiffness evolution, the development of thermal strains, creep, and cracking. To properly accommodate these effects in a finite-element analysis of the large structure such as a concrete dam, efficient computational strategies are needed. In this paper, a finite-element numerical algorithm is developed for analyzing thermomechanical damage in young concrete. Thermal analysis procedures include consideration of heat generation (hydration) and dissipation within mass concrete, including the effects of ambient temperature. The stress-deformation-damage analysis procedures include temperature-induced, creep, and autogenous deformations. Development of concrete properties, including Young’s modulus, tensile strength, and limiting tensile strain is described by experimentally obtained functions. Damage in concrete is considered to be the result of crushing, cracking, and a mixed failure mode. Failure criteria for each failure mode, along with constitutive relationships for prefailure and postfailure states are developed for both loading and unloading conditions. The developed finite-element program is used to simulate the construction of the first four layers of a concrete dam. The cracking damage predicted by the finite-element analysis is shown to qualitatively match with field observations.

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.

The linear fictitious crack model with linear softening law is a very important special case of the general fictitious crack model proposed by Hillerborg. When the traction‐separation softening curve is assumed linear, the peak load can be determined through the proposed linear eigenvalue problem formalism, referred to as the boundary eigenvalue problem. A detailed description is given of the finite element implementation of the proposed algorithm. It is shown that the first eigenvector can be used to calculate the peak load of the linear fictitious crack model. Furthermore, the first eigenvalue can be related to the critical nondimensional specimen size. Finally, it is elucidated that in the linear fictitious crack model, the peak‐load solutions can be presented in a nondimensional fashion with proper consideration of material properties and specimen sizes. The nondimensional peak‐load solution graphs can be used effectively for quantifying the size effect in the linear fictitious crack model.

A physical model using a massless rotational spring to represent the crack-induced local flexibility is adopted as a basis for developing a quantitative nondestructive evaluation (NDE) technique for assessing the damage in a beam structure. Expressions relating changes in eigenfrequencies of the structure and the quantitative damage index S\I\de\N are formulated via an influence matrix h. The coefficients in the h matrix can be determined from the knowledge of the modal shapes of the undamaged structure. The damage index matrix S\I\de\N can be solved by the resulting system of linear algebraic equations using the measured eigenfrequencies of existing structure. Methods of solution for the system of equations are discussed along with special cases where a pseudo-inverse technique is necessary to solve the system of equations. Series of case studies involving simply supported, cantilevered, and continuous beams are presented to demonstrate the validity of the formulation.

A mathematical formulation is proposed to describe equilibrium and stability behavior of the cohesive-crack model (model Ι\N cracking). Under the condition that no unloading occurs, total potential of the system can be defined, including energy dissipation in the process zone. Displacement and crack propagation can be formally solved from the potential energy. The properties of stable crack propagation are discussed using second-order potential-energy variation. The slope of load-deflection curve is determined as a function of the second-order variations of potential energy. Particularly, the second-order variation of the potential energy with respect to displacement is found to be critical at incipient crack instability, a feature very useful in calculating critical quantities such as peak load. Based on the proposed stability theory, an analytic model is derived for three-point beams to demonstrate the validity and usefulness of the formulation. The predictions of the analytical model compared excellently with numerical-simulation results. Comparison with experimental data is not attempted, since the cohesive crack model was already validated experimentally by Hillerborg in 1976 and Hillerborg et al., 1983 and many other authors.

The theoretical relationships between eigenfrequency changes and magnitudes and the locations of crack-induced damage are developed for beam structures with either simply supported or cantilever boundary conditions. For uniform beams, a physical model of a massless rotational spring is used to represent the local flexibility introduced by the crack. A characteristic equation is derived as a base for the development of the relationship. A symbolic computational package, MACSYMA, is used to facilitate the computations of the higher-order determinant and the corresponding derivatives involved in the characteristic equations. For nonuniform beams, the concept of receptance is used for a system linked with two coordinates (axial and rotational coordinates). Numerical experiments involving the use of a finite-element program, SAP, to determine the eigenfrequencies of both uniform and nonuniform beams with a variety of damage scenarios are used to validate the derived theoretical relationships. The comparisons between the predicted and simulated damage conditions are satisfactory. Two important assumptions are involved in the derived relationship: one is that the structure is considered to behave linearly, and the other one is that the elastic properties of the structure member are time-invariant. The application of the theoretical model is discussed at the end of the paper.

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 boundary element program based on a fictitious crack‐model (FCM) was used to study the size effect in concrete during mode‐I nonlinear fracturing. Series of numerical parametric studies were performed to examine the effects of specimen size, loading configuration (three‐point beam and double cantilever beam), and initial notch size on the nonlinear fracture characteristics. The results of numerical simulations confirmed the curve‐fitting procedure proposed by Bažant and his coworkers in their size‐effect law method. However, two notable exceptions were observed: (1) Small size specimens where bending strengthening may be pronounced; and (2) specimens with small initial notch. In addition to examining the range of applicability of Bažant's size‐effect law method, this paper provides empirical equations for determination of the maximum process‐zone length under three‐point bending or double cantilever beam (DCB) loading condition. Finally, the normalized R‐curves expressed in terms of the energy release r...

A simple analytical model has been developed for prediction of size‐dependent maximum loads of concrete‐beam specimens subjected to mode‐I rupture. The analytical model is cast within a framework of a fictitious crack model, but incorporating the following simplifying assumptions: (1) The tension‐softening law is linear; (2) the crack‐opening profile remains linear throughout the fracture process; (3) the resultant cohesive force is acted at an approximate, yet constant, location; (4) the stress distribution in the ligament of the beam specimens is described by a quadratic function; and (5) a simplified compliance equation is adopted to relate the crack opening to the applied loads. The model requires input of four material properties: Young's modulus, Poisson’s ratio, threshold separation, and tensile strength. Model predictions were compared with experimental data as well as numerical simulations. The favorable comparisons suggest that, instead of a number of simplifying assumptions made in the formulat...