Geosynthetic-reinforced pile-supported embankments with caps in a triangular pattern over soft clay

Given the limit studies on the behavior of GRPS embankments with different numbers of geosynthetic layers and pile caps in a triangular pattern, this paper conducted a series of three-dimensional (3-D) numerical analyses. The numerical model was verified based on a well-instrumented large-scale test. A 3-D soil arch model was proposed for pile caps in a triangular pattern, in which the crown of the upper boundary was approximately 1.4 times the clear spacing of pile caps. Inclusion of geosynthetic reinforcement reduced the soil arching effect but increased the total load carried by the piles. For the case with three geosynthetic layers, the lower layer had a significant effect on load transfer than the middle and upper layers, but each layer had an almost proportional effect on mitigating the differential settlement on the top of the gravel cushion. The maximum strains in the reinforcement concentrated on the geosynthetic strips bridging over two adjacent square cap corners.     

Experimental study on the load bearing behavior of geosynthetic reinforced soil bridge abutments with different facing conditions

This paper presents an experimental study on reduced-scale model tests of geosynthetic reinforced soil (GRS) bridge abutments with modular block facing, full-height panel facing, and geosynthetic wrapped facing to investigate the influence of facing conditions on the load bearing behavior. The GRS abutment models were constructed using sand backfill and geogrid reinforcement. Test results indicate that footing settlements and facing displacements under the same applied vertical stress generally increase from full-height panel facing abutment, to modular block facing abutment, to geosynthetic wrapped facing abutment. Measured incremental vertical and lateral soil stresses for the two GRS abutments with flexible facing are generally similar, while the GRS abutment with rigid facing has larger stresses. For the GRS abutments with flexible facing, maximum reinforcement tensile strain in each layer typically occurs under the footing for the upper reinforcement layers and near the facing connections for the lower layers. For the full-height panel facing abutment, maximum reinforcement tensile strains generally occur near the facing connections.     

Numerical study on maximum reinforcement tensile forces in geosynthetic reinforced soil bridge abutments

This paper presents a numerical study of maximum reinforcement tensile forces for geosynthetic reinforced soil (GRS) bridge abutments. The backfill soil was characterized using a nonlinear elasto-plastic constitutive model that incorporates a hyperbolic stress-strain relationship with strain softening behavior and the Mohr-Coulomb failure criterion. The geogrid reinforcement was characterized using a hyperbolic load-strain-time constitutive model. The GRS bridge abutments were numerically constructed in stages, including soil compaction effects, and then loaded in stages to the service load condition (i.e., applied vertical stress?=?200?kPa) and finally to the failure condition (i.e., vertical strain?=?5%). A parametric study was conducted to investigate the effects of geogrid reinforcement, backfill soil, and abutment geometry on reinforcement tensile forces at the service load condition and failure condition. Results indicate that reinforcement vertical spacing and backfill soil friction angle have the most significant effects on magnitudes of maximum tensile forces at the service load condition. The locus of maximum tensile forces at the failure condition was found to be Y-shaped. Geogrid reinforcement parameters have little effect on the Y-shaped locus of the maximum tensile forces when no secondary reinforcement layers are included, backfill soil shear strength parameters have moderate effects, and abutment geometry parameters have significant effects.     

Numerical evaluation of the performance of a Geosynthetic Reinforced Soil-Integrated Bridge System (GRS-IBS) under different loading conditions

This paper presents the results of a finite element (FE) numerical analysis that was developed to simulate the fully-instrumented Geosynthetic Reinforced Soil Integrated Bridge System (GRS-IBS) at the Maree Michel Bridge in Louisiana. Four different loading conditions were considered in this paper to evaluate the performance of GRS-IBS abutment due to dead loading, tandem axle truck loading, service loading, and abnormal loading. The two-dimensional FE computer program PLAXIS 2D 2016 was selected to model the GRS-IBS abutment. The hardening soil model proposed by Schanz et al., (1999) that was initially introduced by Duncan and Chang (1970) was used to simulate the granular backfill materials; a linear-elastic model with Mohr-Coulomb frictional criterion was used to simulate the interface between the geosynthetic and backfill material. Both the geosynthetic and the facing block were modeled using linear elastic model. The Mohr-Coulomb constitutive model was used to simulate the foundation soil. The FE numerical results were compared with the field measurements of monitoring program, in which a good agreement was obtained between the FE numerical results and the field measurements. The range of maximum reinforcement strain was between 0.4% and 1.5%, depending on the location of the reinforcement layer and the loading condition. The maximum lateral deformation at the face was between 2 and 9 mm (0.08%–0.4% lateral strain), depending on the loading condition. The maximum settlement of the GRS-IBS under service loading was 10 mm (0.3% vertical strain), which is about two times the field measurements (～5 mm). This is most probably due to the behavior of over consolidated soil caused by the old bridge. The axial reinforcement force predicted by FHWA (Adams et al., 2011b) design methods were 1.5–2.5 times higher than those predicted by the FE analysis and the field measurements, depending on the loading condition and reinforcement location. However, the interface shear strength between the reinforcement and the backfill materials predicted by Mohr-Coulomb method was very close to those predicted by the FE.     

Novel experimental techniques to assess the time-dependent deformations of geosynthetics under soil confinement

A new experimental approach to assess the impact of soil confinement on the long-term behavior of geosynthetics is presented in this paper.The experimental technique described herein includes a novel laboratory apparatus and the use of different types of tests that allow generation of experimental data suitable for evaluation of the time-dependent behavior of geosynthetics under soil confinement.The soil-geosynthetic interaction equipment involves a rigid box capable of accommodating a cubic soil mass under plane strain conditions.A geosynthetic specimen placed horizontally at the mid-height of the soil mass is subjected to sustained vertical pressures that,in turn,induce reinforcement axial loads applied from the soil to the geosynthetic.Unlike previously reported studies on geosynthetic behavior under soil confinement,the equipment was found to be particularly versatile.With minor setup modifications,not only interaction tests but also in-isolation geosynthetic stress relaxation tests and soil-only tests under a constant strain rate can be conducted using the same device.Also,the time histories of the reinforcement loads and corresponding strains are generated throughout the test.Results from typical tests conducted using sand and a polypropylene woven geotextile are presented to illustrate the proposed experimental approach.The testing procedure was found to provide adequate measurements during tests,including good repeatability of test results.The soilegeosynthetic interaction tests were found to lead to increasing geotextile strains with time and decreasing reinforcement tension with time.The test results highlighted the importance of measuring not only the time history of displacements but also that of reinforcement loads during testing.The approach of using different types of tests to analyze the soilegeosynthetic interaction behavior is an innovation that provides relevant insight into the impact of soil confinement on the time-dependent deformations of geosynthetics.     

Shaking table tests on geosynthetic encased columns in soft clay

This paper presents the results of an experimental research on the behavior of geosynthetic encased stone columns and ordinary stone columns embedded in soft clay under dynamic base shaking. For this purpose, a novel laminar box is designed and developed to run a total of eight sets of 1-G shaking table tests on four different model soil profiles: Soft clay bed, ordinary stone column installed clay bed, and clay beds with geosynthetic encased columns with two different reinforcement stiffnesses. The geosynthetic encased columns are heavily instrumented with strain rosettes to quantify the reinforcement strains developing under the action of dynamic loads. The responses of the columns are studied through the deformation modes of the encased columns and the magnitude and distribution of reinforcement strains under dynamic loading. The response of the granular inclusion enhanced soft subsoil and embankment soil and the identification of the dynamic soil properties of the entire soil body are also discussed in this article. Finally, to determine the effect of dynamic loading on the vertical load carrying capacity, stress-controlled column load tests are undertaken both on seismically loaded and undisturbed columns.     

Development of geomembrane strains in waste containment facility liners with waste settlement

The development of tensile strains in geomembrane liners due to loading and waste settlement in waste containment facilities is examined using a numerical model. Two different constitutive models are used to simulate the waste: (a) a modified Cam-Clay model and (b) a Mohr-Coulomb model. The numerical analyses indicate the role of the slope inclination on the maximum geomembrane liner strains for both short-term loading (immediately post closure) and long-term waste settlement. A geosynthetic reinforcement layer over the geomembrane liner is shown to reduce the maximum geomembrane liner strains, but the strain level of the geosynthetic reinforcement itself may become an engineering concern on steeper slopes (i.e., greater than 3H:1V) for cases and conditions examined in this paper. The paper considers some factors (e.g., slope inclination, use of a high stiffness geosynthetic over the geomembrane liner) and notes others (e.g., the designer selection of interface characteristics below and above the geomembrane, use of a slip layer above the geomembrane) that warrant consideration and further investigation to ensure good long-term performance of geomembrane liners in waste containment facilities.     

3D numerical study of the performance of geosynthetic-reinforced and pile-supported embankments

Geosynthetic-reinforced and pile-supported (GRPS) systems provide an economic and effective solution for embankments. The load transfer mechanisms are tridimensional ones and depend on the interaction between linked elements, such as piles, soil, and geosynthetics. This paper presents an extensive parametric study using three-dimensional numerical calculations for geosynthetic-reinforced and pile-supported embankments. The numerical analysis is conducted for both cohesive and non-cohesive embankment soils to emphasize the fill soil cohesion effect on the load and settlement efficacy of GRPS embankments. The influence of the embankment height, soft ground elastic modulus, improvement area ratio, geosynthetic tensile stiffness and fill soil properties are also investigated on the arching efficacy, GR membrane efficacy, differential settlement, geosynthetic tension, and settlement reduction performance. The numerical results indicated that the GRPS system shows a good performance for reducing the embankment settlements. The ratio of the embankment height to the pile spacing, subsoil stiffness, and fill soil properties are the most important design parameters to be considered in a GRPS design. The results also suggested that the fill soil cohesion strengthens the soil arching effect, and increases the loading efficacy. However, the soil arching mobilization is not necessarily at the peak state but could be reached at the critical state. Finally, the geosynthetic strains are not uniform along the geosynthetic, and the maximum geosynthetic strain occurs at the pile edge. The geosynthetic deformed shape is a curve that is closer to a circular shape than a parabolic one.     

An experimental evaluation of the behavior of footings on geosynthetic-reinforced sand

This research was performed to investigate the behavior of geosynthetic-reinforced sandy soil foundations and to study the effect of different parameters contributing to their performance using laboratory model tests. The parameters investigated in this study included top layer spacing, number of reinforcement layers, vertical spacing between layers, tensile modulus and type of geosynthetic reinforcement, embedment depth, and shape of footing. The effect of geosynthetic reinforcement on the vertical stress distribution in the sand and the strain distribution along the reinforcement were also investigated. The test results demonstrated the potential benefit of using geosynthetic-reinforced sand foundations. The test results also showed that the reinforcement configuration/layout has a very significant effect on the behavior of reinforced sand foundation. With two or more layers of reinforcement, the settlement can be reduced by 20% at all footing pressure levels. Sand reinforced by the composite of geogrid and geotextile performed better than those reinforced by geogrid or geotextile alone. The inclusion of reinforcement can redistribute the applied footing load to a more uniform pattern, hence reducing the stress concentration, which will result reduced settlement. Finally, the results of model tests were compared with the analytical solution developed by the authors in previous studies; and the analytical solution gave a good predication of the experimental results of footing on geosynthetic reinforced sand.     

A new generation of soil-geosynthetic interaction experimentation

A new device was developed to comprehensively assess the interaction between soil and reinforcement as well as the interaction between neighboring reinforcement layers in a reinforced soil mass, under both working and ultimate interface shear stress conditions. An understanding of these two interactions is required to assess the mechanical behavior of a geosynthetic-reinforced soil mass considering varying vertical reinforcement spacings. Specifically, the new device allows direct visualization of the kinematic response of soil particles adjacent to the geosynthetic reinforcement layers, which facilitates evaluation of the soil displacement field via digital image analysis. Evaluation of the soil displacement field allows quantification of the extent of the shear influence zone around a tensioned reinforcement layer. Ultimately, the device facilitates investigating the load transfer mechanisms that occur not only at the soil-reinforcement interface, but also at distances farther from the interface, thereby providing additional insight into the effect of vertical reinforcement spacing on a reinforced soil mass. Finally, the device allows monitoring of dilatancy within the reinforced soil mass upon shear stress generation at the interface between soil and reinforcement. Overall, the device was found to provide the measurements needed to adequately predict the strains developing both in reinforcement layers tensioned by direct application of external loads as well as in reinforcement layers tensioned by the shear transfer induced by adjacent geosynthetic reinforcements. Ultimately, the proposed experimentation technique allows generation of data required to evaluate the load transfer mechanisms amongst soil and reinforcement layers in reinforced soil structures. The strain magnitude in the neighboring reinforcements was found to exceed a magnitude of 10% of the strain magnitude obtained in the active reinforcement. The zone of shear stress transfer from the soil-reinforcement interface was found to exceed 0.2 m on each side of the active reinforcement.     

Residual Deformation of Geosynthetic-Reinforced Sand in Plane Strain Compression Affected by Viscous Properties of Geosynthetic Reinforcement

A series of plane strain compression (PSC) tests were performed on large sand specimens unreinforced or reinforced with prototype geosynthetic reinforcements, either of two geogrid types and one geocomposite type. Local tensile strains in the reinforcement were measured by using two types of strain gauges. Sustained loading (SL) under fixed boundary stress conditions and cyclic loading (CL) tests were performed during otherwise monotonic loading at a constant strain rate to evaluate the development of creep deformation by SL and residual deformation by CL of geosynthetic-reinforced sand and also residual strains in the reinforcement by these loading histories. It is shown that the creep deformation of geosynthetic-reinforced sand develops due to the viscous properties of both sand and geosynthetic reinforcement, while the residual deformation of geosynthetic-reinforced sand during CL (defined at the peak stress state during CL) consists of two components: i) the one by the viscous properties of sand and reinforcement; and ii) the other by rate-independent cyclic loading effects with sand. The development of residual deformation of geosynthetic-reinforced sand by SL and CL histories had no negative effects on the subsequent stress-strain behaviour and the compressive strength was maintained as the original value or even became larger by such SL and CL histories. The local tensile strains in the geosynthetic reinforcement arranged in the sand specimen subjected to SL decreased noticeably with time, due mainly to lateral compressive creep strains in sand during SL of geosynthetic-reinforced sand. This result indicates that, with geosynthetic-reinforced soil structures designed to have a sufficiently high safety factor under static loading conditions because of seismic design, it is overly conservative to assume that the tensile load in the geosynthetic reinforcement is maintained constant for long life time. Moreover, during CL of geosynthetic-reinforced sand, the residual tensile strains in the geosynthetic reinforcement did not increase like global strains in the geosynthetic-reinforced sand that increased significantly during CL. These different trends of behaviour were also due to the creep compressive strains in the lateral direction of sand that developed during CL of geosynthetic-reinforced sand.     

Soil-reinforcement interaction: Stress regime evolution in geosynthetic-reinforced soils

Understanding the stress regime that develops in the vicinity of reinforcements in reinforced soil masses may prove crucial to understanding, quantifying, and modeling the behavior of a reinforced soil structures. This paper presents analyses conducted to describe the evolution of stress and strain fields in a reinforced soil unit cell, which occur as shear stresses are induced at the soil-reinforcement interface. The analyses were carried out based on thorough measurements obtained when conducting soil-reinforcement interaction tests using a new large-scale device developed to specifically assess geosynthetic-reinforced soil behavior considering varying reinforcement vertical spacings. These experiments involved testing a geosynthetic-reinforced mass with three reinforcement layers: an actively tensioned layer and two passively tensioned neighboring layers. Shear stresses from the actively tensioned reinforcement were conveyed to the passively tensioned reinforcement layers through the intermediate soil medium. The experimental measurements considered in the analyses presented herein include tensile strains developed in the reinforcement layers and the displacement field of soil particles adjacent to the reinforcement layers. The analyses provided insights into the lateral confining effect of geosynthetic reinforcements on reinforced soils. It was concluded that the change in the lateral earth pressure increases with increasing reinforcement tensile strain and reinforcement vertical spacing, and it decreases with increasing vertical stress.     

Two-dimensional soil arching evolution in geosynthetic-reinforced pile-supported embankments over voids

Soil arching and tensioned membrane effects are two main load transfer mechanisms for geosynthetic-reinforced pile-supported (GRPS) embankments over soft soils or voids. Evidences show that the tensioned membrane effect interacts with the soil arching effect. To investigate the soil arching evolution under different geosynthetic reinforcement stiffness and embankment height, a series of discrete element method (DEM) simulations of GRPS embankments were carried out based on physical model tests. The results indicate that the deformation pattern in the GRPS embankments changed from a concentric ellipse arch pattern to an equal settlement pattern with the increase of the embankment height. High stiffness geosynthetic hindered the development of soil arching and required more subsoil settlement to enable the development of maximum soil arching. However, soil arching in the GRPS embankments with low stiffness reinforcement degraded after reaching maximum soil arching. Appropriate stiffness reinforcement ensured the development and stability of maximum soil arching. According to the stress states on the pile top, a concentric ellipse soil arch model is proposed in this paper to describe the soil arching behavior in the GRPS embankments over voids. The predicted heights of soil arches and load efficacies on the piles agreed well with the DEM simulations and the test results from the literature.     

台阶宽度对加筋土挡墙垂直应力的影响研究

 为了研究台阶式加筋土挡墙平台宽度对下墙墙体垂直应力大小及分布的影响,进行3组不同平台宽度的台阶式加筋土挡墙室内模型试验。试验结果表明：台阶式加筋土挡墙基底垂直应力随着填土高度的增加而增大,最大值出现在墙面板附近;随着墙间台阶宽度的增加,基底垂直应力沿筋长的分布形式由“V”字形逐渐过渡到倒“S”形;过大的台阶宽度对双级加筋土挡墙基底垂直应力的减载效果不明显;修正的FHWA方法和修正的Gray弹性解方法可较为准确计算基底垂直应力;随着墙顶荷载加载位置距墙面板距离的增加,基底垂直应力逐渐减小;墙顶施加荷载后下墙筋材中后部垂直应力增长较大,而拉筋始端垂直应力变化较小。     

Combined effect of PVDs and reinforcement on embankments over rate-sensitive soils

A numerical study of the behavior of geosynthetic-reinforced embankments constructed on soft rate-sensitive soil with and without prefabricated vertical drains (PVDs) is described. The time-dependent stress–strain-strength characteristic of rate-sensitive soil is taken into account using an elasto-viscoplastic constitutive model. The effects of reinforcement stiffness, construction rate, soil viscosity as well as PVD spacing are examined both during and following construction. A sensitivity analysis shows the effect of construction rate and PVD spacing on the short-term and long-term stability of reinforced embankments and the mobilized reinforcement strain. For rate-sensitive soils, the critical period with respect to the stability of the embankment occurs after the end of the construction due to a delayed, creep-induced, build-up of excess pore pressure in the viscous foundation soil. PVDs substantially reduce the effect of creep-induced excess pore pressure, and hence not only allow a faster rate of consolidation but also improve the long-term stability of the reinforced embankment. Furthermore, PVDs work together with geosynthetic reinforcement to minimize the differential settlement and lateral deformation of the foundation. The combined use of the geosynthetic reinforcement and PVDs enhances embankment performance substantially more than the use of either method of soil improvement alone.     

Static structural behavior of geogrid reinforced soil retaining walls with a deformation buffer zone

To understand the structural behavior of geogrid reinforced soil retaining walls (GRSW) with a deformation buffer zone (DBZ) under static loads, the model tests and the numerical simulations were conducted to obtain the wall face horizontal displacement, vertical and horizontal soil pressures, and geogrid strains. Results showed that compared with the common GRSW, the horizontal displacement of GRSW with DBZ decreased, and the horizontal soil pressure acting on the face panel of GRSW with DBZ increased. The vertical and horizontal soil pressures showed a nonlinear distribution along the reinforcement length, and the value was smaller near the face panel. The horizontal soil pressure acting on the face panel of GRSW with DBZ was greater than that of the common GRSW in the middle portion. The cumulative strain of the geogrid had a single-peak distribution along its length; the maximum strain of the geogrid was 0.45%, the maximum tension was approximately 29.12% of ultimate tensile strength.     

Effect of footing shape and load eccentricity on behavior of geosynthetic reinforced sand bed

This paper presents the results from a laboratory modeling tests and numerical studies carried out on circular and square footings assuming the same plan area that rests on geosynthetic reinforced sand bed. The effects of the depth of the first and second layers of reinforcement, number of reinforcement layers on bearing capacity of the footings in central and eccentral loadings are investigated. The results indicated that in unreinforced condition, the ultimate bearing capacity is almost equal for both of the footings; but with reinforcing and increasing the number of reinforcement layers the ultimate bearing capacity of circular footing increased in a higher rate compared to square footing in both central and eccentrial loadings. The beneficial effect of a geosynthetic inclusion is largely dependent on the shape of footings. Also, by increasing the number of reinforcement layers, the tilt of circular footing decreased more than square footing. The SR (settlement reduction) of the reinforced condition shows that settlement at ultimate bearing capacity is heavily dependent on load eccentricity and is not significantly different from that for the unreinforced one. Also, close match between the experimental and numerical load-settlement curves and trend lines shown that the modeling approach utilized in this study can be reasonably adapted for reinforced soil applications.     

Geosynthetic reinforcement stiffness for analytical and numerical modelling of reinforced soil structures

Many analytical and numerical analysis and design methods for geosynthetic-reinforced soil structures require a single-value (constant) estimate of reinforcement stiffness. However, geosynthetic reinforcement products are rate-dependent polymeric materials meaning that they exhibit time and strain-dependent behaviour under load. Hence, the appropriate selection of a constant (elastic) stiffness value requires careful consideration. A simple hyperbolic stiffness model is shown to be a useful approximation to the constant-load isochronous creep-strain behaviour of these materials at low load levels applicable to operational (serviceability) conditions of geosynthetic-reinforced soil structures. A large database of 606 creep tests on 89 different geosynthetic reinforcement products falling within seven different product categories was collected. From these data, isochronous stiffness values were determined for different combinations of duration of loading and strain level. Data from products falling within the same category were collected together to provide approximations linking the isochronous load-strain (creep) stiffness to the ultimate tensile strength of the material. These approximations are useful for analytical and numerical modelling particularly when parametric studies are undertaken to identify the sensitivity of model outcomes to reinforcement stiffness. Finally, three different geosynthetic-reinforced soil application examples are provided to demonstrate the important role of tensile stiffness on analysis and design outcomes.     

Study of the behavior of mechanically stabilized earth (MSE) walls subjected to differential settlements

The limit equilibrium (LE) analysis has been used to design MSE walls. Presumably, the deflection of MSE walls can be limited to an acceptable range by ensuring sufficient factors of safety (FOSs) for both external and internal stabilities. However, unexpected ground movements, such as movements induced by excavations, volume changes of expansive soils, collapse of sinkholes, and consolidations of underlying soils, can induce excessive differential settlements that may influence both the stability and the serviceability of MSE walls. In this study, a numerical model, which was calibrated by triaxial tests and further by a specially-designed MSE wall tests, investigated the behavior of an MSE wall as well as the influence of various factors on the performance of the MSE wall when the wall facing settled relatively to the reinforced zone. The numerical results showed that the differential settlement would cause substantial vertical and horizontal movements for the MSE wall, as well as an increase in lateral earth pressure and geosynthetic reinforcement strain. The maximum horizontal movement and increase of the lateral earth pressure occurred at about 1.0 m above the toe. The differential settlement resulted in a critical plane that coincided with the plane of 45°+?/2. The maximum increase of the strain for each geogrid layer occurred in that plane, and the bottom layer had the greatest strain increase among all layers of reinforcement. The study further indicated that the surcharge, backfill friction angle, tensile stiffness of geogrid, reinforcement length and MSE wall height had noticeable influences on horizontal and vertical movements, and strain in geosynthetics. According to the results, the MSE wall that had a higher factor of safety would have less movements and geosynthetic strain increase. In contrast, only the friction angle, tensile stiffness and MSE wall height showed some degree of influence on the lateral earth pressure due to differential settlements.     

Influence of uncertainty in geosynthetic stiffness on deterministic and probabilistic analyses using analytical solutions for three reinforced soil problems

The paper examines the quantitative influence of uncertainty in the estimate of geosynthetic reinforcement stiffness on numerical outcomes using analytical solutions for a) the maximum outward facing deformation in mechanically stabilized earth (MSE) walls, b) maximum reinforcement tensile loads and strain in MSE walls under operational conditions, and c) the mobilized reinforcement stiffness in a geosynthetic layer used to reinforce a fill over a void. The stiffness of the reinforcement is modelled using an isochronous two-parameter hyperbolic load-strain model. A linear relationship between isochronous stiffness and the ultimate tensile strength of the reinforcement is used to estimate reinforcement stiffness when product-specific creep data are not available at time of design. Solution outcomes are presented deterministically and probabilistically. The quantitative link between nominal factor of safety used in deterministic working stress design practice and reliability index is provided. The latter is preferred in modern performance-based design to quantify margins of safety within a probabilistic framework. Finally, the paper highlights the practical benefit of using product-specific isochronous secant stiffness data when available, rather than estimates of isochronous stiffness values based on reinforcement type or pooled data.