Seismic Deformation of Bar Mat Mechanically Stabilized Earth Walls. II: A Multiblock Model

A relatively simple rigid plastic multiblock computational model has been developed to predict the permanent seismic displacement of mechanically stabilized earth (MSE) walls. The model formulation was based on many observations made from a series of centrifuge tests carried out on many different configurations of MSE walls. The proposed model is similar to the sliding block method of Newmark. The approach accounted for the variation in acceleration within the backfill and the nonuniform nature of the permanent wall face deformation. The predictive capability of the proposed model has been verified using centrifuge test results obtained for four MSE walls each subjected to three earthquake excitations with strength varying between 0.48 and 0.9g. The analytical model captures many aspects of the characteristic deformation behavior of MSE walls observed in the centrifuge tests. In each of the eleven wall displacement cases studied, the backfill friction angle that yielded a good match between the computed and measured maximum wall displacement was consistent with the corresponding laboratory measured values.     

Reliability-Based Design for External Stability of Narrow Mechanically Stabilized Earth Walls: Calibration from Centrifuge Tests

A narrow mechanically stabilized earth (MSE) wall is defined as a MSE wall placed adjacent to an existing stable wall, with a width less than that established in current guidelines. Because of space constraints and interactions with the existing stable wall, various studies have suggested that the mechanics of narrow walls differ from those of conventional walls. This paper presents the reliability-based design (RBD) for external stability (i.e., sliding and overturning) of narrow MSE walls with wall aspects L/H ranging from 0.2 to 0.7. The reduction in earth pressure pertaining to narrow walls is considered by multiplying a reduction factor by the conventional earth pressure. The probability distribution of the reduction factor is calibrated based on Bayesian analysis by using the results of a series of centrifuge tests on narrow walls. The stability against bearing capacity failure and the effect of water pressure within MSE walls are not calibrated in this study because they are not modeled in the centrifuge tests. An RBD method considering variability in soil parameters, wall dimensions, and traffic loads is applied to establish the relationship between target failure probability and the required safety factor. A design example is provided to illustrate the design procedure.     

Reliability-Based Design for External Stability of Mechanically Stabilized Earth Walls

A two-phase approach was used to develop a reliability-based design (RBD) method for external stability of mechanically stabilized earth (MSE) walls. In the first phase, a parametric study was conducted using Monte Carlo simulation to identify parameters that affect the probability of external failure of MSE walls. Three modes of failure were considered: sliding, overturning, and bearing capacity. External stability was assessed by treating the reinforced soil as a rigid mass using the same procedures employed for conventional gravity-type wall systems. Results from the parametric study indicate that the mean and coefficient of variation of the backfill friction angle are significant for sliding, the mean and coefficient of variation of the friction angle of the backfill and coefficient of variation of the unit weight of the backfill are significant for overturning, and the mean and coefficient of variation of the friction angle of the foundation soil and the mean of the backfill friction angle are significant for bearing capacity. In the second phase, a series of additional simulations was conducted where the significant parameters identified in the parametric study were varied over a broad range. Results of these simulations were used to develop a set of RBD charts for external stability of MSE walls. A comparison indicates that similar reinforcement lengths are obtained using RBD and conventional methods and that the inherent probability of external failure in conventional deterministic design is ? 0.001. This probability of external failure is similar to inherent probability of failure reported by other investigators for similar geotechnical structures.     

Reliability-Based Design for Internal Stability of Mechanically Stabilized Earth Walls

A parametric study was conducted using Monte Carlo simulation to assess how uncertainty in design parameters affects the probability of internal failure of mechanically stabilized earth (MSE) walls. Bishop’s simplified method was used to conduct the internal stability analyses. The results of the analyses indicate that the mean and coefficient of variation of the backfill friction angle, mean and coefficient of variation of the tensile strength of reinforcement, mean unit weight of the backfill, mean surcharge, mean reinforcement vertical spacing, and mean reinforcement length have a significant effect on the probability of internal failure of MSE walls. Based on the results of the parametric study, a series of additional simulations were conducted where the significant parameters were varied over a broad range. The results of these simulations were used to develop a set of reliability-based design (RBD) charts for internal stability of MSE walls. A method to adapt these charts to address model bias and model uncertainty is also presented. A MSE wall was designed using the RBD method and two other deterministic design methods. The required tensile strength of the reinforcement obtained from the RBD method fell between the strengths determined from the deterministic methods.     

Seismic Design of Flexible Cantilevered Retaining Walls

In this paper, the seismic behavior of embedded cantilevered retaining walls in a coarse-grained soil is studied with a number of numerical analyses, using a nonlinear hysteretic model coupled with a Mohr-Coulomb failure criterion. Two different seismic inputs are used, consisting of acceleration time histories recorded at rock outcrops in Italy. The numerical analyses are aimed to investigate the dynamic behavior of this class of retaining walls, and to interpret this behavior with a pseudostatic approach, in order to provide guidance for design. The role of the wall stiffness on the dynamic response of the system is investigated first. Then, the seismic performance of the retaining walls under severe seismic loading is investigated, exploring the possibility of designing the system in such a way that during the earthquake the strengths of both the soil and the retaining walls are mobilized. In this way, an economic design criterion may be developed, that relies on the ductility of the system, as it is customary in the seismic design of structures.     

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.     

Blast Resistance of FRP-Strengthened Masonry Walls. I: Approximate Analysis and Field Explosion Tests

An approximate analysis method is proposed to determine the blast resistance of fiber-reinforced polymer (FRP)-strengthened masonry walls. The method relates the static to dynamic response by incorporating the strain rate effect on the material strength and a dynamic load factor for the applied peak load. Based on the method, 18 full-scale masonry walls reinforced with three different FRP systems were designed and subjected to field explosions, using charges of 27-ton TNT in one test and 5-ton TNT in the other. For each test, the walls were placed at three different standoff distances and orientations to the blast source. The response of the strengthened walls under blast was monitored by high-speed data acquisition systems. Post-test observations indicated no visible damage, crack, or debonding in any of the walls, thus confirming the effectiveness of the FRP retrofit technique in blast protection. The data presented are valuable for validation of analytical or numerical models.     

Seismic Performance and Deformation of Levees: Four Case Studies

During the 1989 Loma Prieta earthquake the Pajaro River levees near Watsonville, Calif., spread laterally at multiple locations. Four of these locations are discussed in this paper. At one location, an industrial facility was also damaged and a dispute arose as to whether lateral spreading of the adjacent levee was the cause. Stability analyses were made of the industrial site for conditions before, during, and after the earthquake. To confirm the findings, analyses were also made of three other nearby locations where the actual deformation was documented and the subsurface conditions are well defined. The calculated levee deformations at the four locations are quite consistent with the observed movements (up to 60 cm). This experience provides increased confidence in the methods of analysis described, for the characterized subsurface conditions, and the range of ground motions experienced. Additional analyses made using the more recently developed multilinear regression lateral-spreading model (e.g., Youd et al. in 1999) yielded inconsistent results.     

Analyzing the Reinforcement Loads of Geosynthetic-Reinforced Soil Walls Subject to Seismic Loading during the Service Life

It is more rational to analyze permanent geosynthetic reinforced soil (GRS) walls against seismic loading based on their behavior during service life, but it has seldom been attempted. Calibrated finite-element procedure was used to investigate the reinforcement loads of GRS walls subject to seismic loading during service life, the results of which were compared to those predicted by Federal Highway Administration (FHwA) guideline. Parametric studies were carried out to investigate the effects of various wall parameters and characteristics of earthquake excitations. It is found that due to the isotach behavior of geosynthetics, the reinforcement loads during earthquake that occurs 10 years after construction were similar to those if the earthquake occurs at the end of construction. The FHwA method predicted roughly the maximum reinforcement load but it could not consider strain softening of soil and characteristics of earthquakes. The horizontal locations of maximum reinforcement load in lower reinforcement layers were farther away from the facing units than Rankine’s surface, which is believed to come from the potential compound failure.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. I: As Built

The seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States is evaluated. Nonlinear time history analyses are conducted using synthetic ground motion for three cities for 475 and 2,475-year return period earthquakes (10 and 2% probability of exceedance in 50 years). The results indicate that the seismic response for the 475-year return period earthquake would lead to an essentially linear response in typical bridges. However, the seismic response for a 2,475-year return period earthquake resulted in significant demands on nonductile columns, fixed and expansion bearings, and abutments. In particular, pounding between decks in the MSSS bridge would result in significant damage to steel bearings and would lead to the toppling of rocker bearings, which may result in unseating of the bridge deck.     

Load-Displacement of Masonry Panels with Unbonded and Intermittently Bonded FRP. I: Analytical Model

An experimental study was carried out to develop and test innovative fiber-reinforced polymer (FRP) rehabilitation techniques that meet the stringent requirements of restoration of historical buildings and are cost-effective alternatives applicable to existing masonry structures. In these techniques, FRP reinforcement was either unbonded or intermittently bonded to the masonry wall. In order to analyze performance, extend the range of the investigated parameters, and define limitations, a simplified analytical model was developed to predict the postcracking lateral load-displacement response under biaxial bending. The response of the retrofitted walls cannot be modeled by conventional approaches. The proposed model is based on balancing internal and external work and rigid body mechanics. It is assumed that all postcracking deformations take place at cracks between wall subpanels. Postcracking displacements are calculated from rotation rather than curvature. The adequacy of the model was verified by comparisons with the experimental results and a good agreement was found. The model could be used as the basis for a design method.     

Numerical Simulation of Viscoplastic and Frictional Heating During Finite Deformation of Metal. Part I: Theory

This paper is concerned with the numerical simulation of hot metal forming, especially superplastic forming. In this first part, a complete thermo-viscoplastic formulation at finite strains is derived and a unified stress update algorithm for thermo-elastoplastic and thermo-elasto-viscoplastic constitutive equations is obtained. The resulting unified implicit algorithm is both efficient and very inexpensive. A staggered scheme is used for the global resolution of the thermomechanical problem. We will also describe the basis of our thermomechanical frictional contact model. Discussion of computational aspects and efficiencies will be assessed in the second part of this work.     

Seismic Response of Interior RC Beam-Column Joints Upgraded with FRP Sheets. I: Experimental Study

In this paper, efficiency and effectiveness of carbon fiber-reinforced polymers (CFRP) in upgrading the shear strength and ductility of seismically deficient beam-column joints have been studied. For this purpose, four reinforced concrete interior beam-column sub-assemblages were constructed with nonoptimal design parameters (inadequate joint shear strength with no transverse reinforcement) representing preseismic code design construction practice of joints and encompassing the vast majority of existing beam-column connections. Out of these four, two specimens were used as baseline specimens (control specimens) and the other two were strengthened with CFRP sheets under two different schemes (strengthened specimens). In the first scheme, CFRP sheets were epoxy bonded to the joint, beams, and part of the column regions. In the second scheme, however, sheets were epoxy bonded to the joint region only but they were effectively prevented against any possible debonding through mechanical anchorages. All four subassemblages were subjected to cyclic lateral load histories so as to provide the equivalent of severe earthquake damage. Further, the damaged control specimens were repaired after filling the cracks through epoxy and wrapping them with CFRP sheets under the same two above-mentioned schemes. These repaired specimens were subjected to the similar cyclic lateral load history and their response histories were obtained. Hence, a total of six specimens were tested: two control; two strengthened; and two repaired. Response histories of control, repaired, and strengthened specimens were then compared. The results were compared through hysteretic loops, load-displacement envelopes, column profiles (maximum horizontal displacements of column along its height), joint shear distortion, ductility, and stiffness degradation. The comparison shows that CFRP sheets improve the shear resistance of the joint and increase its ductility. Results of two chosen schemes of strengthening were also compared and the importance of beam upgrading was highlighted.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. II: Retrofitted

Part I of this two-part paper evaluated the seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States. The results showed that the bridges were vulnerable to damage resulting from impact between decks, and large ductility demands on nonductile columns. Furthermore, fixed and expansion bearings were likely to fail during strong ground motion. In this paper, several retrofit measures to improve the seismic performance of typical multispan simply supported and multispan continuous steel girder bridges are evaluated, including the use of elastomeric bearings, lead-rubber bearings, and restrainer cables. It is determined that lead-rubber bearings are the most effective retrofit measure for reducing the seismic vulnerability of typical bridges. While isolation provided by elastomeric bearings limits the forces into the columns, the added flexibility results in pounding between decks in the MSSS steel girder bridges. Restrainer cables, which are becoming a common retrofit measure, are effective in reducing the hinge opening in MSSS bridges with steel bearings. However, when used with elastomeric bearings, the restrainer cables negate the isolation effect of the bearings.