Assessment of Multispan Masonry Arch Bridges. I: Simplified Approach

A stepwise iterative procedure for the nonlinear analysis of multispan arch bridges, suitable for implementation by standard programming of commercial finite element codes, is discussed. Relying on the plane section hypothesis, masonry is assumed elastic-perfectly plastic in compression and no tensile resistant; a collapse condition is found when an ultimate strain is reached. The iterative procedure is that of an elastic prevision and subsequent nonlinear correction of the nodal forces: tensile stresses are not allowed in the mortar joint by adapting the effective height of the arch to its compressed part, while the plastic response is represented by additional external fictitious forces accounting for the compressive plastic plateau. The procedure is first tested by comparison with experimental data and then applied to sample bridges, pointing out how the collapse mechanism and the ultimate load depend on the geometric and mechanical parameters.     

Assessment of Multispan Masonry Arch Bridges. II: Examples and Applications

Modern approaches to multispan masonry bridges are approximate in many ways: load distribution, masonry degradation, fill-to-barrel, span-to-span, and span-to-pier interaction are taken into account by means of approximate models or are neglected. At the end of the assessment procedure, the approximation to the load carrying capacity of the bridge cannot be easily quantified. In Part I of this paper, an extension of the classical approach to masonry arches was formulated taking into account the nonlinear response of masonry, a limit to compressive inelastic strains, and assuming simplifying but conservative assumptions. The procedure allows the analysis of multispan masonry bridges considering the nonlinear response of arches and barrels and the mutual interaction. The response of two- and three-span prototypes is compared to that of a single arch; then the procedure is applied to a six- 18.5-m span in-service viaduct. A detailed comparison with the single-span-bridge approach is discussed. Specific attention is paid to the evolution of the collapse mechanism and to the effect of load distribution, addressing the concentrated loads versus distributed equivalent loads problem and showing how the limit to compressive inelastic strains, i.e., to masonry ductility, may be of great importance to the structural analysis of masonry bridges.     

Radar Testing of a Masonry Composite Structure with Sand and Water Backfill

As part of an ongoing program into the noninvasive geometrical characterization of masonry arch bridges, a laboratory study of radar propagation through masonry has been undertaken. A 2.4 m long × 1 m wide × 1.5 m high experimental test rig was built in the laboratory with brick walls on three sides and a wooden gate on the fourth narrow side. The objective was to construct a composite test rig that would replicate certain of the environments that ground-penetrating radar might encounter when being used to test a masonry arch bridge. Tests were undertaken using 500, 900, and 1,000 MHz bow-tie antennas with the masonry box filled with fresh water and then saline water with different concentrations of sodium chloride. Further tests were undertaken with the masonry box filled with dry sand and wet sand. Finally the test rig was modified to simulate a composite masonry structure and tests were performed both on the hollow- and sand-filled models. The results from this work are reported herein indicating the reliability and ease of identifying various targets. It was found that radar signals were severely attenuated when the saline concentration exceeded 0.05% by mass. Better penetration of the radar signals was obtained when the masonry box was filled with dry sand rather than wet sand. In the case of the hollow cellular masonry structure, refraction effects were more evident.     

Analysis of Arch Dams Using Coupled Trial Load and Block Element Methods

This paper presents the use of the trial load method and the block element method with elastoviscoplastic discontinuities for analysis of arch dams. The arch dam is considered as an arch-cantilever system and the foundation as a block element system. With the displacement compatibility condition at the contact surface of the dam and the foundation (including abutment), the governing equations of the arch dam and foundation are established. These methods are used for the analysis of the double curvature arch dam with complex geology conditions of the Xiaowan Hydroelectric Project in China. The deformation and stress states in both the dam body and the foundation are determined. Furthermore, the stability safety factors of the foundation and the abutment are calculated at the same time, which allows for an optimal design of the arch dam considering the strength, the deformation and the stability of the dam and foundation.     

Integral Abutment-Backfill Behavior on Sand Soil—Pushover Analysis Approach

This paper presents a study on the behavior of the abutment-backfill system under positive thermal variation in integral bridges built on sand. A structural model of a typical integral bridge is built, considering the nonlinear behavior of the piles and soil-bridge interaction effects. Static pushover analyses of the bridge are conducted to study the effect of various geometric, structural, and geotechnical parameters on the performance of the abutment-backfill system under positive thermal variations. The shape and intensity of the backfill pressure are found to be affected by the height of the abutment. Furthermore, the internal forces in the abutments are found to be functions of the thermal-induced longitudinal movement of the abutment, the properties of the pile, and the density of the sand around the piles. Using the pushover analysis results, design equations are formulated to determine the maximum forces in the abutments and the maximum length of integral bridges based on the strength of the abutments. Integral bridges with piles encased in loose sand and oriented to bend about their weak axis, abutment heights less than 4?m, and noncompacted backfill are recommended to limit the magnitude of the forces in the abutments.     

State-of-the-Art of Integral Abutment Bridges: Design and Practice

The superstructure for integral abutment bridges is cast integrally with abutments that are supported by a single row of piles. Thermal expansion or contraction and concrete creep and shrinkage induce bending stresses in the piles. Very limited design and construction guidelines are available and no unified design procedures exist nationwide; hence, there is a lack of enthusiasm to adopt integral abutment bridges for long spans. Current design and construction practices of integral abutment bridges have been reviewed. Important design parameters are identified with an emphasis on temperature, creep, and shrinkage effects of concrete bridge decks, varying soil strata, and the pile-soil interaction. A parametric study is described regarding the effects of a predrilled hole, the type of fill in the predrilled hole, elevation of the water table, soil type, and pile orientation. The results from the parametric study should aid in the selection and design of piles for integral abutment bridges.     

Behavior of Brick Masonry Vaults Strengthened by FRP Laminates

The results of experimental research on brick masonry vaults strengthened at their extrados or at their intrados by fiber-reinforced polymer (FRP) strips is presented here. The presence of the fibers prevents the typical brittle collapse that occurs in a plain arch because of the formation of four hinges; therefore, depending on the position and amount of the reinforcement in the strengthened vaults, three mechanisms are possible: (1) masonry crushing, (2) detachment of the fibers; and (3) sliding along a mortar joint due to the shear stresses. Some first theoretical approaches describing some of these mechanisms are discussed, and the formulation of further models based on the local interaction among the constituent materials is proposed. Six masonry vaults strengthened by glass FRPs or carbon FRPs have been tested. The results have pointed out the enhancement in strength and ductility of the strengthened vaults and the influence in the ultimate strength of the width of the strips and of the bond between the laminate and the masonry.     

Homogenization of Masonry Using Numerical Simulations

Homogenization is one of the most important steps in the numerical analysis of masonry structures where the continuum method is used. In the present study, equivalent elastic properties, strength envelope, and different failure patterns of masonry material are homogenized by numerically simulating responses of a representative volume element (RVE) under different stress conditions. The RVE is modeled with distinctive consideration of the material properties of mortar and brick. In the numerical simulation, various displacement boundaries are applied on the RVE surfaces to derive the stress-strain relation under different conditions. The equivalent overall material properties of the RVE are averaged by integrating the stresses and strains over the entire area. Failure of masonry is defined by three different modes, namely, tensile failure of mortar (Mode I), shear failure of mortar or combined shear failure of brick and mortar (Mode II), and compressive failure of brick (Mode III). The homogenized elastic properties and failure model can be used to analyze large-scale masonry structures.     

Parametric Study of Concrete Integral Abutment Bridges

A parametric study was conducted to extend the results of an experimental program on a concrete integral abutment (IA) bridge in Rochester, MN to other integral abutment bridges with different design variables including pile type, size, orientation, depth of fixity, and type of surrounding soil, fixity of the connection between the abutment pile cap and abutment diaphragm, bridge span and length, and size and orientation of the wingwalls. The numerical results indicated that bridge length and soil types surrounding the piles had a significant impact on the behavior of IA bridges. To select pile type and orientation, there is a need to balance the stresses in the piles with the stresses in the superstructure for long IA bridges or IA bridges in stiff soils. Plastic hinge formation is possible at the pile section near the pile head for combined critical variables, such as long span, compliant piles in weak axis bending, deep girders, and stiff soils. Because large pile curvatures or stresses may be caused due to the rotation of the pile cap during temperature increases, hinged connections between the abutment pile cap and diaphragm are not recommended for the practice of IA bridges. Cast-in-place piles are recommended only for short-span IA bridges because their relatively large bending stiffness can cause large superstructure concrete stresses during temperature changes.     

Analytical Investigation of Lateral Strength of Masonry Infilled RC Frames Retrofitted with CFRP

In this study, two reinforced concrete frames with hollow clay tile masonry infill walls, retrofitted with diagonally applied carbon fiber-reinforced polymer (CFRP), which were tested previously, were analytically investigated. A simple material model for the masonry infill wall strengthened with CFRP is suggested. The lateral strength of each rehabilitated frame was obtained by pushover analysis of four different models using a commercially available finite-element program, and the results were compared with the test results. We also determined the lateral strength of the CFRP-applied masonry infill walls, and compared the results with the results obtained from existing analytical models. Drift capacity of the masonry infill walls strengthened with CFRP was also investigated, and the drift capacity of the masonry infill walls strengthened with diagonally applied CFRP was recommended. It is concluded that the strength of the masonry infilled frames strengthened with diagonally applied CFRP can be satisfactorily predicted with the suggested procedure. The ultimate drift capacity of the masonry infill walls strengthened with diagonally applied CFRP strips was conservatively predicted to be 1.0%.     

Pathophysiology of peritoneal fluid eosinophilia in peritoneal dialysis patients

This study deals with the stress distribution in concrete deck slabs on composite steel beams used with integral abutment bridges. The applied loading is composed of one or more side-by-side HS20-44 trucks. The finite-element method is used to analyze two bridge structures with different numbers of beams, beam spacings, and supporting piles. The transverse and longitudinal slab stresses in the deck slab are investigated in the positive and negative bending regions near and away from the integral abutment. The slab stresses in the integral abutment bridges are compared with the corresponding stresses induced in the slab of equivalent jointed bridges. The results indicate that integral abutment bridges distribute the loads in the deck slab more uniformly than their jointed counterparts. The maximum stresses in the transverse direction of the slab can be 25–50% lower in the integral bridges than in their corresponding simply supported ones.     

Modeling Out-of-Plane Behavior of URM Walls Retrofitted with Fiber Composites

Although masonry is one of the oldest construction materials, its behavior has not been investigated as extensively as other construction materials. Out-of-plane failures are common in unreinforced masonry (URM) buildings constructed in seismic regions. Seven half-scale brick masonry walls were constructed, externally strengthened with vertical glass-fabric composite strips, and subjected to static cyclic out-of-plane loading. The flexural behavior of the tested specimens is characterized by three main stages corresponding to the first visible bed-joint crack, the first delamination, and the ultimate load. The main parameters being investigated in this study are the amount of composite, the height-to-thickness ratio h∕t, the tensile strain in composites, and the mode of failure. Based on the trends observed in the experimental phase, it was concluded that the behavior of the walls is best predicted with a linear elastic approach. It was also concluded that the ultimate strength method overestimates the flexural capacity and the ultimate deflection of the wall. Preliminary design recommendations are also proposed for tensile strain in the composite, maximum deflection, and maximum reinforcement ratio.     

Cabin John Bridge: Role of Alfred L. Rives, C.E.

The Cabin John Bridge (CJB), located just outside Washington, D.C., is a masonry arch with a central angle of 110°, an intrados radius of 40.9 m (134 ft), and a span of 67 m (220 ft). Construction of the bridge began in 1857 but was not completed until late in 1863 because of suspensions due to lack of appropriations and the Civil War. The CJB is part of the Washington Aqueduct (WA) and is still the longest single-span masonry arch in the United States. The bridge was designated a National Historic Civil Engineering Landmark by the ASCE in 1972. The paper provides context for the bridge design and explains the construction technologies that were used. In the process, French and British influences on American masonry arch design practices at mid-19th century are revealed. The respective roles of Captain Montgomery C. Meigs, the chief engineer of the WA, and Alfred Landon Rives, his assistant engineer, are critically assessed. The paper provides, for the first time, relevant facts on Rives’ education and engineering career. The performance of the bridge over 145 years is reviewed and discussed.     

Load Rating of Masonry Arch Bridges

A masonry arch bridge can be analyzed by frame analysis methods by considering a unit width of the arch ring and the overlying fill. The arch ring is divided into at least 10 segments, each of which is given cross-sectional properties corresponding to the properties of the material in the arch ring. The dead load of the arch ring and the overlying fill are considered as nodal loads, and the axle loads are applied to the frame as linearly varying pressures, based on a simplified distribution of pressures through the fill. The supports are considered to be rigid in the vertical direction and elastic springs in the horizontal direction. The elastic spring constant varies depending on the type of foundation and the condition of the springings. Based on this application of dead and live loads to the structure, the axial thrust and moment can be found throughout the arch ring, and compared to an estimate of the capacity of the arch ring. This procedure can be used to find an appropriate load rating for the structure service level. An example rating of a bridge in Adams County, Pa., is provided, along with the results of a validation field test of the structure.     

Experimental Methods for Estimating In Situ Tensile Force in Tie-Rods

Several methods have been proposed for estimating the actual tensile forces in metallic tie-rods inserted into the masonry arches and vaults of historic buildings. Static and dynamic methods based on the experimental measurement of the vertical displacements caused by concentrated loads, accelerations, and the fundamental frequencies and periods of free vibrations have been applied to arrive at a more precise evaluation of the axial tensile forces acting on the tie-rod under examination. Each of these methods, with its corresponding experimental procedure, presents different advantages and disadvantages with regard to operating procedures, equipment requirements, and accuracy range in the determination of tie-rod stress. In this paper the writers propose a simple method and experimental procedure based on a single static test. The reference structural system consists of a bending moment-resistant tie beam with unknown restraint conditions at its ends. Therefore, the proposed method does not require any assumptions when modeling the rod's extremities, nor does it discount the increase in pull induced by the transverse load as irrelevant. The relevant experimental data are represented by three vertical displacements under a concentrated load and the strain variations measured in three sections of the rod. The reliability of the method has been verified through laboratory tests using tie-rods set within a sufficiently stiff metal framework in which the tension is known through continuous monitoring by means of a load cell. The correlation of the measurements with the actual tensile strength was checked; laboratory tests show good agreement between the analytical estimates and experimental measurements.     

Tensile Strength Characteristics of Unsaturated Sands

Tensile strength characteristics of unsaturated sands are examined through a combined theoretical and experimental study. The characteristics of tensile strength in all three water retention regimes of pendular, funicular, and capillary are examined. A simple direct tensile strength apparatus is employed to determine tensile strength for sands with a broad range of particle sizes from silty sand to fine sand and medium sand over a full range of degree of saturation. Tensile strength characteristic curves (TSCC) are established experimentally for these sands and are used to validate the existing theories for tensile strength in the pendular regime. The TSCC for sand characteristically exhibits two zeros at 0 and near 100% saturation, and two peak values occurring in the pendular and capillary regimes, respectively. A minimum tensile strength is observed in the dense fine sand, indicating that either water bridges or pore pressure contributes exclusively to the tensile strength in the funicular regime of this sand. The maximum tensile strength for the silty sand is 1,448?Pa, the fine sand is 1,416?Pa, and the medium sand is 890?Pa. Comparison between the soil–water characteristic curves obtained for these sands indicates that the peak tensile strength in the capillary regime is highly correlated to the air-entry pressure. Photographs of the failure surfaces clearly delineate distinct geometric characteristics for different water retention regimes. Analysis of the patterns of failure surfaces in different water retention regimes indicates that the effective stress principle is valid for tensile stress failure in unsaturated sands.     

Performance Evaluation of Short Span Reinforced Concrete Arch Bridges

In this paper, the static and seismic performance of some short span reinforced concrete arch bridges, before and after strengthening interventions, are evaluated. To verify whether retrofit strategies for the considered arch bridges, which were designed for resisting under permanent and service actions, were adequate for earthquake resistance, seismic analyses of the as-built model of the structures have been undertaken. To account for multiple input effects on arches, induced by out-of-phase motions at foundation levels as well as different boundary conditions at structural supports, the seismic response of the structures under correlated horizontal and vertical multiple excitations is calculated. The effects on arch bridges of conventionally used uniform input and partially correlated multiple inputs with phase shifts are compared. In all cases, the results are discussed with particular reference to the influence of structural configuration, secondary systems, cross-section thickness of the arch, and retrofit interventions.     

Computational Analysis of Masonry Structures with a Funicular Model

This paper presents a computational approach for the assessment of masonry structures based on the well known analogy between the equilibrium of arches and that of hanging strings or cables working in tension. According to the analogy, the hanging strings model the inverted shape of the equilibrium lines (or thrust lines) describing the locus of the equilibrium forces acting across the sections of the arch. The approach proposed combines two developments. First, a new cable element is proposed to numerically model the strings used to describe the equilibrium lines. The formulation proposed, obtained as a modification of the conventional equations for inextensible cables, is based on an exact analytical derivation. Compared to other available numerical approaches, it has the advantage of ensuring the exact equilibrium of the cable net after deformation. Second, complementary algorithms are proposed for the assessment of the strength of masonry structures by the application of the limit theorems of plasticity (static approach). These algorithms are intended to find optimized solutions complying with the so-called safe (or lower-bound) and uniqueness theorems. Two examples of application are described to illustrate the accuracy of the method and its ability to handle masonry structural systems.     

Simple Model for Bond Behavior of Masonry Elements Strengthened with FRP

The aim of the present paper is the development of a simple procedure for the analysis of the bond behavior of fiber-reinforced polymer (FRP) sheets or plates externally applied to masonry supports for the strengthening or repair of masonry constructions. The procedure allows evaluation of the bond strength and the fracture energy developed during the debonding process through simple formulas based on a few parameters, evaluated either by standard tests performed on the materials making up the support and the strengthening system or by theoretical considerations. A brief discussion on the main experimental evidence and the theoretical models provided by the literature is also reported in this paper. The comparison between the theoretical results obtained by applying the proposed procedure and the experimental data deduced from literature is carried out.     

Integral Abutment Bridges: Current Practice in United States and Canada

Integral abutment bridges have been gaining popularity among bridge owners as cost-effective alternatives to bridges with conventional joints. They reduce initial construction costs and long-term maintenance expenses, improve seismic resistance, and extend long-term serviceability. New York has been building them since the late 1970s, with a wide variety of details, and they have been performing well. For further improvement of New York's design practice, a comparative survey was undertaken across North America, focusing on design and construction of both substructures and superstructures. In all, 39 states and Canadian provinces responded, including 8 who said they had no experience with these bridges. Responses are analyzed and summarized in this paper. Overall, integral abutment bridges are performing as well as, if not better than, conventional bridges, but no uniform national standards exist for their design. Design practices and assumptions concerning limits of thermal movement, soil pressure, and pile design vary considerably among responding agencies. These decisions are based largely on past experience. Validity of these assumptions needs investigation by testing and analysis to ensure efficient and reliable design.