Undrained Limit States of Shallow Foundations Acting in Consort

There is no established procedure for the calculation of bearing capacity of a shallow foundation system comprising cojoined footings. Ad hoc approaches are relied on and may simply involve summing the ultimate limit states of the individual footings as if they acted independently; neglecting additional capacity of the system available from the kinematic constraint provided by the structural connection between the footings. In this study, the undrained capacity under general loading of rigidly connected two-footing systems at various separations has been investigated with finite-element analyses. Results are presented in terms of ultimate limit states under pure vertical (V), horizontal (H), and moment (M) loading, and failure envelopes defining limiting load states under combined VH, VM, HM, and VHM loads. Kinematic failure mechanisms observed in the finite-element analyses are presented and in cases used to provide the basis for upper bound solutions.     

Undrained Stability of Footings on Slopes

Solutions for the ultimate bearing capacity of footings on purely cohesive slopes are obtained by applying finite element upper and lower bound methods. In a footing-on-slope system, the ultimate bearing capacity of the footing may be governed by either foundation failure or global slope failure. The combination of these two factors makes the problem difficult to solve using traditional methods. The importance of a dimensionless strength ratio in determining the footing capacity is broadly discussed, and design charts are presented for a wide range of parameters. In addition, the effect of footing roughness and surface surcharge are briefly quantified.     

Three-Dimensional Analysis of Nonhomogeneous Slopes

Presented is a method of three-dimensional slope stability analysis for homogeneous and nonhomogeneous symmetrical slopes based on the upper-bound theorem of the limit analysis approach. A rigid-block translational toe, above-the-toe or below-the-toe collapse mechanism is considered, with energy dissipation taking place along planar velocity discontinuities. The approach can be considered as a modification and extension of the procedure proposed by Michalowski in 1989. An effective iterative algorithm is applied to find the optimum (least) upper bound in constrained or unconstrained problems. The present procedure removes some essential limitations of limit analysis methods in two- and three-dimensional stability analysis of nonhomogeneous slopes.     

Undrained Stability of Braced Excavations in Clay

Short-term undrained stability often controls the design of braced excavations in soft clays. This paper summarizes the formulation of numerical limit analyses that compute rigorous upper and lower bounds on the exact stability number and include anisotropic yielding, typical of K0-consolidated clays and bending failure of the wall. Calculations for braced cuts bound the actual failure conditions within ±5%, and highlight limitations of existing basal stability equations. The analyses clarify how wall embedment and bending capacity improve the stability of well braced excavations. Careful selection of mobilized strengths at shear strains in the range 0.6–1.0% are necessary to match the predictions of anisotropic limit analyses with nonlinear finite-element predictions of failure for the embedded walls. Two example applications from recent projects in Boston highlight the practicality of the numerical limit analyses for modeling realistic soil profiles and lateral earth support systems, but also focus attention on the need for careful selection of undrained strength parameters. Credible estimates of stability have also been obtained in reanalyzing a series of case studies reported in literature using isotropic strength parameters derived from field vane or laboratory simple shear tests.     

Collapse of Masonry Buttresses

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

Undrained Capacity of Plate Anchors under General Loading

Under general conditions of loading, a plate anchor is subjected to six degrees of freedom of loading, three force components and three moment components. Prediction of the anchor performance under general conditions of loading requires realistic estimates of the anchor pullout capacity for each individual load component as well as the interaction effects when these loads are applied in combination. This paper presents an analysis of plate anchor capacity under these general conditions of loading. The study considers a range of plate width-to-length ratios ranging from 1:1 to 2:1. The anchor capacity estimates and interaction relationships were developed based on finite-element studies and upper bound plastic limit analyses. Interaction relationships developed from the numerical and analytical studies were fitted to a simple six degrees-of-freedom yield locus equation.     

Stability Analysis of Complex Soil Slopes using Limit Analysis

The limit equilibrium method is commonly used for slope stability analysis. Limit equilibrium solutions, however, are not rigorous because neither static nor kinematic admissibility conditions are satisfied. Limit analysis takes advantage of the lower- and upper-bound theorems of plasticity theory to provide rigorous bounds on the true solution of a stability problem. In this study, finite-element models are used to construct both statically admissible stress fields for lower-bound analysis and kinematically admissible velocity fields for upper-bound analysis of soil slopes. While limit analysis of relatively simple slopes, typically homogeneous and of simple geometry, has been done previously, limit analysis of slopes with complex geometries, soil profiles, and groundwater patterns could not be effectively done in the past. In this paper, the theoretical basis and procedure for limit analysis of such slopes is presented. Various examples of slopes are selected from the literature and analyzed using both limit equilibrium and limit analysis. Factors of safety from limit equilibrium and limit analysis are compared. A comparison is also made, for each example, between the critical slip surfaces from limit equilibrium with the velocity field and plastic zone from the upper-bound solution and with the stress field from the lower-bound solution.     

Stability and Collapse of Semirigidly Connected Portal Frames

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

Mitigating Risk from Abnormal Loads and Progressive Collapse

A progressive collapse initiates as a result of local structural damage and develops, in a chain reaction mechanism, into a failure that is disproportionate to the initiating local damage. Such collapses can be initiated by many causes. Changes in building practices to address low probability/high consequence events and to lessen building vulnerability to progressive collapse currently are receiving considerable attention in the professional engineering community and in standard-writing groups in the United States, Canada, and Western Europe. Procedures for identifying and screening specific threat scenarios, for assessing the capability of a building to withstand local damage without a general structural collapse developing, and for assessing and mitigating the risk of progressive collapse can be developed using concepts of probabilistic risk assessment. This paper provides a framework for addressing issues related to low probability/high consequence events in building practice, summarizes strategies for progressive collapse risk mitigation, and identifies challenges for implementing general provisions in national standards such as ASCE Standard 7, Minimum design loads for buildings and other structures.     

Three-Dimensional Lower Bound Solutions for Stability of Plate Anchors in Clay

Soil anchors are commonly used as foundation systems for structures that require uplift or lateral resistance. These types of structures include transmission towers, sheet pile walls, and buried pipelines. Although anchors are typically complex in shape (e.g., drag or helical anchors), many previous analyses idealize the anchor as a continuous strip under plane strain conditions. This assumption provides numerical advantages and the problem can be solved in two dimensions. In contrast to recent numerical studies, this paper applies three-dimensional numerical limit analysis to evaluate the effect of anchor shape on the pullout capacity of horizontal anchors in undrained clay. The anchor is idealized as either square, circular, or rectangular in shape. Estimates of the ultimate pullout load are obtained by using a newly developed three-dimensional numerical procedure based on a finite-element formulation of the lower bound theorem of limit analysis. This formulation assumes a perfectly plastic soil model with a Tresca yield criterion. Results are presented in the familiar form of break-out factors based on various anchor shapes and embedment depths, and are also compared with existing numerical and empirical solutions.     

Evaluation of Undrained Shear Strength Using Full-Flow Penetrometers

Full-flow penetrometers (the T-bar and ball) are increasingly used on sites with thick deposits of soft clays, particularly prevalent offshore. Full-flow penetration tests were performed at five international well-characterized soft clay test sites to assess the use of full-flow penetrometers to estimate undrained shear strength. Field vane shear data were used as the reference undrained strength. Statistical analyses of strength factors indicates that full-flow penetrometers provide an estimate of undrained shear strength at a similar level of reliability compared to the piezocone. Relationships for estimating the strength factor and soil sensitivity using only full-flow penetrometer data obtained during initial penetration and extraction are developed. A strong dependence of the strength factor on sensitivity was identified and can be used for the estimation of undrained strength. The effectiveness and use of the developed correlations are demonstrated through their application at an additional test site.     

Displacements of Multiblock Geotechnical Structures Subjected to Seismic Excitation

A method is presented for calculations of irreversible displacements of multiblock structures subjected to seismic excitation. Use is made of the kinematic approach of limit analysis. To make the analysis tractable a hodograph representing distribution of accelerations in the structure is introduced. Distinction is made between soils conforming to the associative and nonassociative flow rules, and the importance of this distinction is demonstrated. The yield acceleration calculated for slopes comprised of soils conforming to the nonassociative flow rule is lower than that for a soil with the same strength parameters, but its deformation governed by the associative flow rule. Consequently, the displacements predicted for the former are larger. An example of a slope is demonstrated, but the method presented is applicable to other structures, such as retaining walls and embankments.     

Vertical Stability of Anchored Concrete Soldier–Pile Walls in Clay

The problem of vertical stability in flexible anchored retaining walls is analyzed and the pattern of the behavior under conditions of poor vertical support is described, on the basis of results from case histories, small-scale tests, and numerical modeling. The possibility of shear stress mobilization in the soil-to-wall interface of anchored concrete soldier–pile retaining walls is discussed. A finite element procedure to model excavations supported by soldier–pile retaining walls is described and applied to a numerical case study. Finite element analyses are performed, emphasizing the consequences of vertical instability due to buckling of the soldier piles and the role of interface resistance in vertical equilibrium. The understanding of some results of the numerical analyses, which are highly influenced by the complexity of the interaction between the different parts of the structure, is obtained by reassessing the vertical equilibrium issue in the light of limit analysis. This approach makes it possible to estimate the pile resistance corresponding to the limit situation of excavation collapse. The finite element model is used to confirm this resistance. Some conclusions are drawn.     

Undrained Bearing Capacity of Square and Rectangular Footings

The uniaxial vertical bearing capacity of square and rectangular footings resting on homogeneous undrained clay is investigated with finite element analyses, using both Tresca and von Mises soil models. Results are compared with predictions from conventional bearing capacity theory and available analytical and numerical solutions. By calibrating the finite element results against known exact solutions, best estimates of bearing capacity for rough-based rectangular footings are derived, with the shape factor fitted by a simple quadratic function of the footing aspect ratio. For a square footing, the bearing capacity is approximately 5% lower than that based on Skempton’s shape factor of 1.2.     

Collapse during Construction of a Precast Girder Bridge

This paper describes the collapse during construction of a precast concrete girder bridge crossing Highway 15, north of Montréal. The bearing conditions for the girders at the time of collapse are discussed. The tie rods that were used to restrain the movement of the girder top flanges were tested to determine their effective stiffness and strength. Rotational and sliding tests were also performed on the pot bearing units. These experimental results were used in an analytical study to confirm the sequence of collapse of the girders. Bracing requirements during construction for precast girder bridges supported on pot bearings are discussed.     

Dynamic Analysis of Gap Closing and Contact in the Mixed Lagrangian Framework: Toward Progressive Collapse Prediction

Previous research has shown many advantages of the mixed Lagrangian formulation (MLF) for the solution of dynamic problems. In particular, it has shown a very stable and robust behavior with respect to the time step size required for convergence, even in cases where plasticity and fracture were considered. This paper presents another step toward enabling the prediction of progressive collapse of structures using MLF. A new gap element is added to the framework by formulating an additional component in the Lagrangian function. It is shown that by carefully formulating the new component, the optimization problem to be solved in each time step of the MLF algorithm retains its form which is quadratic in the cases considered. Hence, a unified formulation is attained for all stages of the analysis whether contact forces are present or not. After presenting details of the formulation, the proposed method is used for the solution of two examples. These examples illustrate that relatively large time steps can be considered even for contact problems. Furthermore, the reasons for this capability of the algorithm are discussed in the paper.     

Undrained Lateral Pile Response in Sloping Ground

Three-dimensional finite element analyses were performed to study the behavior of piles in sloping ground under undrained lateral loading conditions. Piles of different diameter and length in sloping cohesive soils of different undrained shear strength and several ground slopes were considered. Based on the results of the finite element analyses, analytical formulations are derived for the ultimate load per unit length and the initial stiffness of hyperbolic p-y curves. New p-y criteria for static loading of piles in clay are proposed, which take into account the inclination of the slope and the adhesion of the pile-slope interface. These curves are used through a commercial subgrade reaction computer code to parametrically analyze the effect of slope inclination and pile adhesion on lateral displacements and bending moments. To validate the proposed p-y curves, a number of well documented lateral load tests are analyzed. Remarkable agreement is obtained between predicted and measured responses for a wide range of soil undrained shear strength and pile diameter, length, and stiffness.     

Simplified Trial Wedge Method for Soil Nailed Wall Analysis

This paper presents a new approach that allows soil nailed walls to be analyzed using a trial wedge method. Most soil nailed wall analysis methods are rooted in traditional slope stability solutions with curvilinear or bilinear slip surfaces. This has led to limited access to these methods due to the cost of commercial software. In addition, there are at least two well-documented test walls brought to failure that indicated evidence of relatively steep, approximately linear slip surfaces instead of the more complex surfaces assumed by most software packages. The simplified trial wedge method is intended as a relatively simple and inexpensive method for preliminary or supplemental design calculations for soil nailed walls. The method stems from the existing Federal Highway Administration analysis guidelines. Procedures are outlined for implementing the trial wedge method using a spreadsheet-based approach. The method is applied to two test walls that were intentionally brought to failure, the Amherst Test Wall in clay, and the Clouterre Test Wall No. 1 in sand. In each case, the trial wedge analysis produces results consistent with the failure mode of the wall.     

Collapse Study of an Unreinforced Masonry Bearing Wall Building Subjected to Internal Blast Loading

A blast test was conducted inside a conventional, two-story, unreinforced, brick, bearing wall building scheduled to be demolished. A credible explosive device was placed inside the building on the ground floor and was detonated to investigate whether or not the building would collapse. The measured blast pressures, key material properties of the structure, and the structural configuration were used as input parameters to a single-degree-of-freedom software program, the single-degree-of-freedom blast effects design spreadsheet (SBEDS), commonly used in the United States to model unreinforced masonry walls subjected to blast loading. The net effect of overburden loads on the ground-floor bearing walls, including uplift by blast pressures on the ground-floor ceiling, was considered when investigating the validity of an appropriate resistance function (available in SBEDS) that defines out-of-plane bearing wall response. Comparisons were made between analytical and experimental permanent wall deflections and two alternatives, a simple displacement-based criterion and a resistance criterion, were used to estimate the building’s state relative to its estimated collapse limit state. It was found that SBEDS was able to model the experimental deflections quite well if effective input parameters were carefully considered. As a result, analytical and experimental determinations of the structure’s state were also in good agreement.     

Stability Charts for the Collapse of Residual Soil in Karst

Collapse of the residual soil over bedrock cavities often occurs during construction in karst terrain, particularly when the thickness of the residuum is reduced during excavation. Even if an estimate of the strength of the residual soil is known, uncertainty with respect to the size/geometry of the subterranean voids makes a detailed analysis difficult, and straightforward methods to check the stability are needed. In this study, numerical analyses were performed to develop a stability chart expressed in terms of a dimensionless stability number and the geometry of a potential void in the residual soil. The stability charts include the effect of friction angle, and are also developed to allow the investigation of the effect of the inverted strength profile typically observed in karst terrain. Such stability numbers may be useful to estimate the stability of a given site based on the expected thickness of the soil overburden and the likely range of anticipated soil void diameters.