Required Reinforcement Strength Research Articles

Modified pseudo-dynamic analysis of slope considering logarithmic spiral failure surface with numerical solution

ABSTRACT A methodology for the analysis of soil slope made up of c-ϕ soil using a modified pseudo-dynamic approach is tried to develop here. In this study, the slope is divided into a number of vertical slices and the failure surface of the slope is assumed to be logarithmic spiral. The suggested modified pseudo-dynamic approach satisfies the zero-stress boundary condition at the free ground surface and considers the damping properties of the materials. Results of the present analysis are presented in tabular form. The effects of the variation of different parameters like horizontal and vertical seismic acceleration, slope angle, soil friction angle, damping ratio, frequency ratio, cohesion and surcharge on the FOS are shown graphically. Consequently, required reinforcement strength is evaluated to ensure the safety of the slope under seismic loading conditions. The results obtained from the present method are compared with the results of the available literature and also a numerical validation of the model is given using PLAXIS 2D.

Seismic stability for reinforced 3D slope in unsaturated soils with pseudo-dynamic approach

Within the framework of limit analysis, the seismic stability of reinforced 3D slope in unsaturated soils is investigated, and the effects of nonhomogeneous and anisotropic soils are considered. In geotechnical engineering, reinforcement is commonly used to improve slope stability. Due to complex geological processes, soils are nonhomogeneous and anisotropic. Because of matric suction, the unsaturated property is considered in engineering. Using the analytical approach, a set of formula is proposed, which can evaluate the seismic stability of reinforced 3D slope in unsaturated soils. This work uses a pseudo-dynamic approach to consider the earthquake action, solves the work rates at two levels of time and space, and finally adopts a layer-wise summation means to get the outcomes done by seismic force. According to the energy balance relationship, analytical expressions are obtained in this study for the required reinforcement strength. The sensitivity analysis is conducted on some parameters, such as reinforcement distribution patterns, slope angle and so on. For three different patterns, the downwardly triangular distribution (DTD) pattern gets the best results, the upwardly triangular distribution (UTD) pattern obtains the worst outcomes, and the uniformly distribution (UD) pattern is between the UTD and DTD pattern.

Pseudo-static analysis of reinforced earth retaining walls

The investigation of the internal stability of reinforced earth retaining walls under dynamic loading is an important issue for the seismic design. This paper presents a thorough study of the seismic behavior of earth retaining walls, using the upper bound theorem of limit analysis in combination with the discretization technique. This combination permits to generate the failure mechanism of reinforced structures point by point. The pseudo-static approach is adopted to model the seismic effect. The proposed extended methodology is validated using the conventional limit analysis results obtained by Michalowski (Comput Geotech 23:1–17, 1998a. https://doi.org/10.1016/S0266-352X(98)00016-0 ), showing therefore its effectiveness. A parametric study is then conducted to point out the effects of key parameters on the required reinforcement strength.

Upper bound seismic limit analysis of geosynthetic-reinforced unsaturated soil walls

The assessment of the internal stability of geosynthetic-reinforced earth retaining walls has historically been investigated in previous studies assuming dry backfills. However, the majority of the failures of these structures are caused by the water presence. The studies including the water presence in the backfill are scarce and often consider saturated backfills. In reality, most soils are unsaturated in nature and the matric suction plays an important role in the wall's stability. This paper investigates the internal seismic stability of geosynthetic-reinforced unsaturated earth retaining walls. The groundwater level can be located at any reinforced backfill depth. Several nonlinear equations relating the unsaturated soil shear strength to the matric suction and different backfill type of soils are considered in this study. The log-spiral failure mechanism generated by the point-to-point method is considered. The upper-bound theorem of the limit analysis is used to evaluate the strength required to maintain the reinforced soil walls stability and the seismic loading are represented by the pseudo-dynamic approach. A parametric study showed that the required reinforcement strength is influenced by several parameters such as the soil friction angle, the horizontal seismic coefficient, the water table level, the matric suction distribution as well as the soil types and the unsaturated soils shear strength.

Internal stability analysis of reinforced convex highway embankments considering seismic loading

The seismic internal stability of reinforced, convex embankments that are three-dimensional in nature is analyzed. A limit equilibrium based three-dimensional rotational failure mechanism is adopted to calculate the required reinforcement strength to maintain the stability of convex embankments. The results are presented in the form of stability charts and the effects of various parameters on the three-dimensional solution are investigated. The calculation of the required strength and length of reinforcement is demonstrated by two examples using an approach consistent with AASHTO (2012). Comparing the strengths obtained under two and three-dimensional conditions, the results show that the two-dimensional results are more conservative with respect to the strength of reinforcement, but could be unconservative considering the required length of reinforcement, especially for reinforced convex embankments with gentle turning angles. The influence of seismicity causes greater three-dimensional effects when the reinforced convex embankment is vertical, but less so when the slope inclination is gentle.

Seismic analysis of geosynthetic-reinforced retaining wall in cohesive soils

Although a cohesionless backfill is recommended for geosynthetic reinforced earth retaining walls, cohesive soil have been widely used in many regions across the globe for economic reasons. This type of backfill exposes the soil to the crack formation that leads to reduce the stability of the system. In this paper, to investigate the internal seismic stability of reinforced earth retaining walls with cracks, the discretization method combined with the upper bound theorem of limit analysis are used. The potential failure mechanism is generated using the point-to-point method. Two types of cracks are considered, a pre-existing crack and a crack formation as a part of the failure mechanism. The use of the discretization method allows the consideration of the vertical spatial variability of the soil properties. A pseudo-dynamic approach is implemented which allows the account of the dynamic characteristics of the ground shaking. The presented method is validated using the conventional limit analysis results of an existing study conducted under static conditions. Once the proposed technique to consider the cracks is validated, a parametric study is conducted to highlight the key parameters effects on the lower bound of the required reinforcement strength.

Seismic internal stability assessment of geosynthetic reinforced earth retaining wall in cohesive soil using limit analysis

Assessment of internal seismic stability of geosynthetic reinforced cohesive soil retaining walls with likelihood for developing cracks in the failure mechanism is typically done with the limit equilibrium method. However, in this paper, the kinematic theorem of limit analysis combined with the discretization method are used to implement the crack formation in the collapse mechanism in the internal seismic assessment of geosynthetic reinforced soil retaining walls within the framework of the pseudo-static approach. The presence of the crack leads to an increase of the required reinforcement strength that prevent the failure of the structure.

Seismic stability of 3D soil slope reinforced by geosynthetic with nonlinear failure criterion

This work conducts a seismic stability of a three-dimensional (3D) geosynthetic-reinforced slope in soils following the linear and nonlinear Mohr-Coulomb failure criterion. Three categories of reinforcement distribution patterns and four kinds of clays are considered. Within the framework of limit analysis and the generalized tangent technique, expressions of required reinforcement strength and the stability factor under different distribution patterns are derived from the energy balance equations. Comparisons are conducted to verify the validity of new expressions. Parametric analysis is conducted to explore the impacts of seismic force, soil strength nonlinearity, 3D character of slope and reinforcement strength on slope stability. It is found from the results that the downwardly-strong triangular (DTD) distribution pattern is the most effective choice for slope reinforcement, while the upwardly-strong triangular (UTD) pattern is the worst. One should intensify the density of reinforcement layers at the bottom of the slope to achieve a better slope stability condition. Besides, soil strength nonlinearity and seismic forces both have non-negligible negative effects on slope stability.

Design of geosynthetic-reinforced slopes in cohesive backfills

Currently, geosynthetic reinforcements for slopes are calculated assuming the ground strength to be purely frictional, i.e. without any cohesion. However, accounting for the presence of even a modest amount of cohesion could allow using locally available cohesive soils as backfills to a greater extent and less overall reinforcement. But cohesive soils are subject to the formation of cracks that tend to reduce slope stability so their presence has to be accounted for in the design of the slope reinforcement. In the paper, limit analysis was employed to derive a semi-analytical method for uniform c−ϕ slopes that provides the amount of reinforcement needed as a function of ground cohesion, tensile strength, angle of shearing resistance and of the slope inclination. Both climate induced cracks as well as cracks that form as part of the slope collapse mechanism are accounted for. Design charts providing the value of the required reinforcement strength and embedment length are plotted for both uniform and linearly increasing reinforcement distributions.From the results, it emerges that accounting for the presence of cohesion allows significant savings on the reinforcement to be made, and that cracks are often significantly detrimental to slope stability so they cannot be overlooked in the design calculations.

Analysis of slope using modified pseudo-dynamic method

Seismic design of slope is an important aspect in earthquake-prone areas to resist devastation due to earthquake load. This study presents the seismic stability analysis of homogeneous soil slope in which modified pseudo-dynamic method adopting limit equilibrium approach has been used. Results are presented in tabular form, which will serve as essential design parameters. Parametric studies show effects of soil properties and seismic forces on safety of slope. In addition, the required reinforcement strength against failure under seismic loading is evaluated and presented in figures that are useful to design reinforced slope.

Required strength of geosynthetic in reinforced soil structures supporting spread footings in three dimensions

Little insight exists into the stability of reinforced slopes supporting spread footings. Existing research is largely focused on idealized, plane strain analyses that do not account for three-dimensional conditions. These conditions are significant because the geometries of both reinforced slopes and footings are three-dimensional in nature. In this study, the stability of reinforced slopes supporting spread footings is analyzed in three dimensions using a limit analysis approach and presented in a series of design charts. To better understand the impact of three-dimensional conditions, a parametric study is conducted to evaluate effects of various design parameters on required reinforcement strength.

Three-dimensional reinforced slopes: Evaluation of required reinforcement strength and embedment length using limit analysis

Virtually all analyses of reinforced earth structures are based on two-dimensional (2D) conditions, ignoring three-dimensional (3D) effects despite adhering to three-dimensional behavior in reality. In this study, the three-dimensional effects of three-dimensional conditions on reinforced earth structure stability are considered, and employed to determine the required strength and length of reinforcement using a Limit Analysis approach. The results of the three-dimensional stability analysis are compared with idealized two-dimensional results and examples from prior literature. As expected, use of two-dimensional stability analyses for reinforced soil slopes yield results that are more conservative than those considering three-dimensional effects. The effects of various parameters on the three-dimensional solution are investigated and design charts are proposed. The solutions demonstrate that for practical scenarios, three-dimensional effects may affect the required length of reinforcement more than the associated required tensile strength.

Closure to “Load-Carrying Capacity and Required Reinforcement Strength of Closely Spaced Soil-Geosynthetic Composites” by Jonathan T. H. Wu and Thang Q. Pham

Closure to “Load-Carrying Capacity and Required Reinforcement Strength of Closely Spaced Soil-Geosynthetic Composites” by Jonathan T. H. Wu and Thang Q. Pham

Required unfactored strength of geosynthetics in reinforced 3D slopes

The design of reinforced earth structures uses idealized two-dimensional (2D) geometry – classifying as a plane-strain analysis. This 2D idealization greatly simplifies design by ignoring stabilizing effects posed by three-dimensional (3D) characteristics. While the outcome of this 2D idealization is conservative in terms of required reinforcement strength, ignoring 3D end effects in back-calculations of experimental and field data may overestimate the contribution of the reinforcement to stability thus possibly leading to unconservative learned lessons related to design. The objective of this study is to explore 3D effects on the required strength of reinforcement in geosynthetic-reinforced earth structures (GRESs) using a modified 3D limit equilibrium (LE) slope stability analysis. To determine the stability of GRESs, a rotational, 3D failure mechanism, derived from variational LE analysis, is applied using a log-spiral surface generalized to 3D conditions. In order to determine the long-term strength of geosynthetics required to ensure sufficient internal stability, the moment equilibrium approach is applied and its respective equations solved. In order to conveniently assess the end effects on the required total strength of reinforcement and the volume of failing mass considering the feasible length of potential failure, a series of design charts are presented. These charts can also be useful in forensic studies when back-calculating the in-situ mobilized strength of the geosynthetic for 3D failures. The impact of seismicity and the assumed function of forces distributed amongst the reinforcement layers were investigated to highlight their importance. To keep this study focused on 3D end effects, this study is limited to a simple 3D GRES problem; however, extending the present framework to deal with complex homogenous problems is straightforward.

Discussion of “Load-Carrying Capacity and Required Reinforcement Strength of Closely Spaced Soil-Geosynthetic Composites” by Jonathan T. H. Wu and Thang Q. Pham

Discussion of “Load-Carrying Capacity and Required Reinforcement Strength of Closely Spaced Soil-Geosynthetic Composites” by Jonathan T. H. Wu and Thang Q. Pham

Discussion of “Load-Carrying Capacity and Required Reinforcement Strength of Closely Spaced Soil-Geosynthetic Composites” by Jonathan T. H. Wu and Thang Q. Pham

This discusser belonged to a university class that was exposed to the contents of this paper in 2011. Seeing the W factor [Eq. (14) of the original paper] and its application [Eq. (24)], students were absolutely mystified. Outside of class, most people share this reaction. The strangeness of this exponential function, which seems unlike anything seen elsewhere in civil engineering, causes its validity to be questioned. This discussion provides three alternative views intended to demystify the equations and promote insight.

Performance of an 11 m high block-faced geogrid wall designed using the K-stiffness method

An 11 m high dry-stacked masonry concrete block wall reinforced with a high-density polyethylene (HDPE) geogrid was designed, instrumented, and monitored for a period of 2 years as part of a highway-widening project southeast of Seattle, Washington, in the USA. An extensive materials-testing program was conducted to characterize the geogrid and backfill soil properties. The empirical-based K-stiffness method was used to design the wall, and this approach resulted in a 35% reduction in total required reinforcement strength compared with the American Association of State Highway and Transportation Officials / Federal Highway Administration (AASHTO/FHWA) simplified method. The cost savings more than compensated for the cost of the instrumentation program. Geogrid strains were measured using strain gauges and extensometers, and the walls were surveyed to monitor facing deformations. The stiffness of the geogrid materials was computed from the results of laboratory in-isolation constant-load (creep) tests. The time- and strain-dependent stiffness values, in combination with measured strains, were used to compute measured reinforcement loads at the reinforcement connections and at locations within the reinforced soil backfill. The measured loads were compared with class A, B, and C1 predictions using the AASHTO/FHWA simplified and K-stiffness methods. These comparisons demonstrate that the simplified method significantly overestimated reinforcement loads, whereas the K-stiffness method provided estimates that were judged to be in better agreement with the measured results. The paper also quantifies the influence of construction procedures on reinforcement strains and load, shows that long-term creep of the reinforcement after 2 years after construction is negligible, and identifies lessons learned.

Load-Carrying Capacity and Required Reinforcement Strength of Closely Spaced Soil-Geosynthetic Composites

AbstractIn current design methods for reinforced soil walls, it has been tacitly assumed that reinforcement strength and reinforcement spacing play an equal role. This fundamental design assumption has led to the use of larger reinforcement spacing (0.3–1.0 m) in conjunction with stronger reinforcement to reduce construction time. Recent studies, however, have clearly indicated that the role of reinforcement spacing is much more significant than that of reinforcement strength. With closely spaced (reinforcement spacing ≤0.3 m) reinforcement, the beneficial effects of geosynthetic inclusion is significantly enhanced, and the load-deformation behavior can be characterized as that of a composite material. A reinforced soil mass with closely spaced geosynthetic reinforcement is referred to as geosynthetic-reinforced soil (GRS). In this study, an analytical model is developed for predicting the ultimate load-carrying capacity and required reinforcement strength of a GRS mass. The model was developed based on a...

An analytical model for calculating lateral movement of a geosynthetic-reinforced soil (GRS) wall with modular block facing

Current design methods for Geosynthetic-Reinforced Soil (GRS) walls consider only the stresses and forces in the wall system. A GRS wall with modular block facing is inherently a fairly "flexible" wall system; hence it can be of critical importance to include the lateral movement of the wall in design. This paper presents an analytical model for estimating the lateral movement of a GRS wall with modular block facing. Derivation of the analytical model is given in this paper. In addition, an equation for determining the connection forces in the reinforcement immediately behind the facing is provided. The equation for the lateral movement can be readily used in design of a GRS wall, whereby the required reinforcement strength can be determined for a prescribed value of maximum allowable lateral movement. The analytical model was verified through comparisons with Jewell-Milligan method for GRS walls constructed with negligible facing rigidity. Comparisons were also made with a full-scale experiment of GRS wall with modular block facing. It is shown that the analytical model offers a simple and improved tool for estimating lateral movement of a GRS wall with modular block facing.

Use of ‘Limited Life Geotextiles’ (LLGs) for basal reinforcement of embankments built on soft clay

Polymeric technical fabrics have long working lives and are sometimes used in practical situations where a geosynthetic is only needed to be fully functional for a relatively short period of time, e.g. a separator layer beneath a temporary access road. This article concerns the use of ‘Limited Life Geotextiles’ (LLGs), i.e. high specification geotextiles, which are designed on the basis of having a limited working life, as basal reinforcement for an embankment built on soft clay. A method is given for defining the allowable progressive loss of tensile strength of the foregoing basal LLG as a result of improvement of the shear strength of the foundation soil due to consolidation. It is shown that the derived relation between required reinforcement strength and consolidation time (the Time-Strength-Envelope) can be represented by a simple exponential equation. Vegetable fibres are natural candidates for use in the manufacture of LLGs since they are a renewable resource and their degradation with time is accounted for in the design of the LLG. Combinations of vegetable fibres growing in tropical regions which are capable of satisfying the Time-Strength-Envelopes for several embankment slopes are presented.