Non-yielding Walls Research Articles

A semi-empirical approach for estimating the lateral earth pressure on rigid retaining walls with EPS inclusions in cohesionless soils

Placing the expanded polystyrene (i.e. EPS) as inclusions between the rigid nonyielding wall and fill enables the lateral displacement of the fill and renders the lateral earth pressure from the at-rest state to the active state. This effectively alleviates the lateral load and facilitates cost-effective designs for rigid retaining walls. This study develops a semi-empirical approach to predict the lateral earth pressure on rigid retaining walls with EPS inclusions in cohesionless soils. This approach is simple and requires only conventional soil and EPS properties for prediction. Its performance is validated by the results of different physical and numerical modeling studies with EPS inclusions of various densities and thicknesses. It is demonstrated that (i) the lateral earth pressure depends on the stiffness of the EPS inclusions (i.e. the ratio of the elastic modulus to the thickness), and (ii) EPS inclusions with a single and proper thickness can fulfill the majority of load reduction purposes. Suggestions for the choices of (i) the EPS materials in terms of density and elastic modulus, (ii) the thickness of EPS inclusions, and (iii) the structure of the EPS inclusions are proposed for the use of EPS inclusions in cohesionless soils.

Active earth pressure on non-yielding retaining walls with geofoam blocks and granular backfills

Geofoam blocks are typically used as buffer layers behind non-yielding retaining walls to reduce the lateral earth pressure. The interaction between the geofoam blocks and the backfills is essential for the determination of the earth pressure and thus the design of the geofoam blocks. In this study, two-dimensional model tests of aluminum rod mass as filling soils were conducted to study the lateral earth pressure acting on a non-yielding wall with geofoam blocks. The following observations were obtained: (i) the compression of the geofoam blocks increases linearly or bi-linearly along the wall height, depending on the stress level; (ii) a clear slip surface can be observed in the aluminum rod mass, which is consistent with the assumptions of the Coulomb’s active earth pressure theory. Considering the deformation of the geofoam blocks and the backfills, a series of equations were proposed for calculating the earth pressure on the non-yielding wall with geofoam blocks and granular backfills. The earth pressure calculated by the proposed equations agrees well with the experimental measurements.

Experimental modeling of strip footing adjacent to non-yielding retaining wall

A series of reduced-scale models were tested to assess the performance of non-yielding basement wall due to strip footing constructed adjacent to it. Construction design parameters such as strip footing width (B), its distance from non-yielding wall back (a), and footing embedment depth below the backfill surface (df) have been considered in this study. This paper presents results of five model tests that isolate effects of non-yielding wall on the strip ultimate footing bearing capacity. The opposite effect of the strip footing distance design parameters on the non-yielding wall responses is also investigated. Experimental results revealed that the strip footing load-carrying capacity increased, and the settlement decreased as its distance from the back of non-yielding wall increased. Furthermore, the vertically loaded strip footing imposed significant vertical and horizontal forces at the back of the non-yielding wall. Results also indicate that distance a > 4B between the footing and the back of the wall enabled the strip footing to mobilize ultimate load-carrying capacity comparable to both control strip footing test and value calculated with Terzaghi’s equation. Comparison of the measured and predicted lateral forces showed that using elastic theory method together with Jacky formula for at-rest lateral earth pressure coefficient led to about 23–35% underestimation of the measured lateral forces. However, including sand overconsolidation ratio, OCR = 2 resulted in an overestimation of the lateral forces by about 20–29% of the measured value. Finally, results of the experimental program are used to identify sources of conservativeness and non-conservativeness in the current design methodologies used to calculate lateral forces imposed on non-yielding walls due to adjacent strip footing and suggested necessary modifications.

Numerical study of earth pressure reduction on rigid walls using EPS geofoam inclusions

This paper presents a numerical study performed to investigate the compressible inclusion function of Expanded Polystyrene (EPS) geofoam panels placed behind a non-yielding rigid wall. EPS geofoam panels placed behind a non-yielding wall can reduce lateral earth pressure acting on the wall by accommodating the lateral movement of the retained soil. Laboratory-scale physical testing was performed to evaluate various combinations of properties and dimensions of an EPS geofoam panel. A numerical model was developed to simulate the laboratory-scale tests. Model outputs were compared against test results to assess the reasonableness of the numerical predictions. A parametric study was performed using the numerical model to evaluate the effects of EPS geofoam panel material type and thickness on the non-yielding wall performance. The results of the parametric study quantify the magnitude of lateral earth pressure when the EPS geofoam panel is selected. Also, a systematic design approach for EPS geofoam panels as compressible inclusions against non-yielding walls is proposed based on the results of this parametric study.

Rational and practical method for determination of seismic-induced earth pressure on non-yielding walls

Okabe and Mononobe proposed a pseudo-static method in late 1920s, the so-called Mononobe–Okabe (M–O) method, to determine the seismic-induced earth pressure (SIEP) on a wall. Because of its simplification and ease of use, this method has been widely used since its introduction. Since the M–O method is intended for yielding or flexible walls, it is questionable to extend it to non-yielding or massive walls such as bridge abutments. Due to the lack of a better method, engineers have the tendency to keep using the familiar M–O method, raising the concern on wall design safety. In the modern era, some authorities arbitrarily specified an unjustified constant SIEP value for designing a rigid/massive wall. Others advocated a fairly complex equation or numerical approach to handle the issue. This paper closely examines the suitability of the M–O method first, followed by the proposal of a rational and practical method for determining SIEP. The proposal method is verified by the finite element method. Effects of superstructure and various system parameters on SIEP are also discussed. The proposed method is particularly suitable for non-yielding walls with the rear face sloping downward away from the backfill.

Earth pressure distribution behind rigid non-yielding walls under the effect of repeated loading on backfill

One of the most important factors in optimized design of non-yielding retaining walls like basement walls and bridge abutments is to determine the exact variation of earth pressure acting on such walls. In this paper, the distribution of at rest earth pressure behind a laboratory model of a fixed and rigid retaining wall with a cohesionless dry backfill is measured under the effect of static and repeated loads. The same conditions of the experimental model are then simulated numerically with a two-dimensional finite-difference analysis computer code. For the purpose of model verification, the results of numerical model are compared to the results of the experimental model, which is similar in geometrical and geomechanical properties. Cyclic surcharges with different amplitudes and frequencies are applied in different distances from the wall, and the earth pressure distribution, the resultant force, and its point of application are investigated. The effect of soil and loading parameters on the at rest earth pressure is also evaluated, and a parametric study has been carried out. The results of model show a significant increase in the earth pressure due to cyclic loading compared to static loading, especially in the initial cycles of loading. It indicates that the effect of cycling nature of loading should be essentially taken into account in the design of retaining walls.

Use of EPS geofoam compressible inclusions for reducing the earthquake effects on yielding earth retaining structures

The effectiveness of EPS geofoam compressible inclusions in reducing both the seismic earth pressure and displacement increment (i.e., horizontal translation and rotation) of yielding, gravity type, earth retaining walls, was investigated by parametric numerical analyses. The 2-D finite element code PLAXIS was used for analyzing the seismic response of two gravity-type retaining walls (with heights equal to 4m and 7.5m) under harmonic excitation at the wall base of varying amplitude (0.1g to 0.7g) and frequency (0.3Hz to 20Hz). The isolation efficiency of the inclusions (defined as the ratio of displacement or pressure reduction, due to inclusion, to the corresponding values for a non-isolated wall) was studied as a function of the normalized – with respect to wall height – thickness of the inclusion and shaking intensity. The results of the analyses indicate that – as in the case of non-yielding walls – the isolation efficiency, in general, increases with increasing inclusion thickness and also depends on shaking intensity, wall height and excitation frequency. However, in contrast to the case of non-yielding walls, the isolation efficiency of yielding walls increases with inclusion thickness only up to a limiting value which cannot be exceeded with a further increase of inclusion thickness. For the case of EPS 100 (i.e., ρEPS=20kg/m3) a compressible inclusion with a relative thickness of 15% to 20%, can reduce the seismic pressure by up to 20%, and the seismic displacement increment of a wall by up to 50%, depending on shaking intensity and height of wall. Finally, it was shown that the excitation frequency as well as its relative value, with respect to the natural frequency of the wall-backfill system, is an important parameter which affects the seismic isolation efficiency of EPS and its dependence on shaking intensity, and particularly the isolation against wall rotation. It is concluded that EPS compressible inclusions can provide an effective means for reducing the permanent seismic displacement and lateral thrust increments for new or existing seismically retrofitted yielding earth retaining structures.

Simple Wave Solution for Seismic Earth Pressures on Nonyielding Walls

AbstractDesign of retaining walls for earthquake action is traditionally performed by limit analysis procedures—notably the classical solution of Mononobe-Okabe and its variants. Fundamental assumptions of these methods are (1) the static nature of seismic excitation, (2) the compliance in sliding and/or rocking of the base of the wall, (3) the shear failure of the backfill and the soil-wall interface, and (4) the prespecified point of application of soil thrust. Given the restrictive nature of these assumptions, alternative solutions based on wave-propagation theory have been developed that do not require failure of the backfill and thereby are applicable to nonyielding walls. Because of the complex mathematics involved, the use of these solutions in practice appears to be limited. A special integration technique inspired from the seminal work of Vlasov and Leontiev is presented, which simplifies the analysis by providing closed-form solutions suitable for practical use.

Reduction of Lateral Earth Forces Acting on Rigid Nonyielding Retaining Walls by EPS Geofoam Inclusions

Expanded polystyrene (EPS) geofoam panels of low stiffness installed vertically against the rigid nonyielding retaining structure provide additional deformations in the backfill. This behavior will lead to the mobilization of a greater portion of the soil strength, thus decreasing the lateral earth thrust acting on the rigid retaining wall. This study addresses the effect of geofoam compressible inclusion on lateral earth thrust acting on a rigid nonyielding retaining wall by small-scale model tests and numerical analyses. The finite-element code used in the numerical modeling is validated against the stress measurements on a 0.7-m-high wall model. Significant reduction is observed in the lateral earth pressures attributable to deformations concentrated at the lower half of retained soil mass. The effects of compressible inclusion thickness, relative stiffness of the EPS geofoam, and strength parameters of the backfill on lateral earth thrust acting on rigid nonyielding walls are investigated by a series ...

Earth Pressure due to Vibratory Compaction

This paper presents experimental data on the variation of lateral earth pressure against a nonyielding retaining wall due to soil filling and vibratory compaction. Air-dry Ottawa sand was placed in five lifts and each lift was compacted to achieve a relative density of 75%. Each compacted lift was 0.3 m thick. The instrumented nonyielding wall facility at National Chiao Tung University in Taiwan was used to investigate the effects of vibratory compaction on the change of stresses at the soil-wall interface. Based on the experimental data it has been found that, for a compacted backfill, the vertical overburden pressure can also be properly estimated with the traditional equation v=z. The effects of vibratory compaction on the vertical pressure in the backfill were insignificant. On the vertical nonyielding wall, extra horizontal earth pressure was induced by vibratory compaction. After compaction, the lateral earth pressure measured near the top of the wall was almost identical to the passive Rankine pressure. It is concluded that as the cyclic compacting stress applied on the surface of the backfill exceeded the ultimate bearing capacity of the foundation soil, a shear failure zone would develop in the uppermost layer of the backfill. For a soil element under lateral compression, the vertical overburden pressure remained unchanged, and the horizontal stress increased to the Rankine passive pressure. It was also found that the compaction-influenced zone rose with the rising compaction surface. The horizontal earth pressure measured below the compaction-influenced zone converged to the Jaky state of stress.

Numerical study of parameters influencing the response of flexible retaining walls: Discussion

The author has provided a useful, significant contribution to the important need of developing relatively simple yet accurate models for analyzing the load-deformation behavior of earthretaining structures in practice. The discusser would like to make two comments that may contribute to and expand the utility of the author’s work. First, the author stated “No exact formulae exist to characterize arching ...” There are actually a few papers on this subject that the author may find of use (Handy 1985; Harrop-Williams 1989a, 1989b). In particular, the discusser has found the approximate solutions in Harrop-Williams (1989b) of use in engineering analysis. Second, one of the most rapidly growing technologies involving earth-retaining structures is the use of a “compressible inclusion” to allow ground (both soil and rock) deformation adjacent to rigid and (or) non-yielding walls and other below-ground structures (e.g., tunnels, navigational locks). The compressible-inclusion material of choice is expanded polystyrene (EPS) geofoam. A complete discussion of geofoams can be found in Horvath (1995), with an overview of compressible-inclusion applications using EPS in Horvath (1996). The relevance of EPS geofoam and compressible inclusions to this discussion is that models such as the author’s, which were developed for use with relatively flexible walls, can be easily extended toproblemsinvolvingrigid–non-yieldingwallswithcompressible inclusions. In such cases, the load-deformation characteristics of the wall are replaced by the load-deformation properties of the EPS-geofoam compressible inclusion, which are determined by the engineer. An example of applying this concept that involves applying a solution developed originally for rigid gravity walls under seismic loading can be found in Horvath (1997).

Dynamic Lateral Pressures Due to Saturated Backfills on Rigid Walls

One‐directional (horizontal) shaking‐table experiments were conducted on one sandy and two cohesive saturated backfills to investigate the dynamic water and total lateral pressures against rigid nonyielding walls during earthquakes. It was found that the dynamic water pressure against the wall is generated due to two different sources. The first source is Westergaard‐type, which is due to the flow of free water in nondeformable backfill soil skeleton and the second is due to the deformability of backfill soil skeleton under undrained conditions. For highly permeable backfill soils, the first source dominates in the generation of pore pressure and the second source dominates for cohesive backfills. The magnitude of the first type of dynamic water pressure is expressed as a function of the parameter 2πn;γwH2w/EwkT, where n is the porosity of soil, γw is the unit weight of water, Hw is the depth of water table to the impermeable base in the backfill, Ew is the coefficient of compressibility of water, k is the coefficient of permeability of backfill soil, and T the period of vibration. The water pressure distribution is a shape of the Westergaard solution. The distribution of the second type is different from the Westergaard‐type with a peak value at an upper section of the backfill depth and zero at the bottom. The dynamic water pressure resultants of this type for cohesive backfills are nearly as much as the value of Westergaard's but is applied at approximately 0.6H from the bottom of the backfill. The dynamic total pressure resultants for cohesive backfills are nearly twice Westergaard's dynamic water pressure resultant and also applied 0.6H from the bottom of the backfill.

Coefficients of active and ‘at rest’ earth pressures behind rotating and non-yielding walls : Sherif, M A; Fang, Y S; Sherif, R I J Geotech Engng Div ASCEV110, NGT1, Jan 1984, P41–56

Coefficients of active and ‘at rest’ earth pressures behind rotating and non-yielding walls : Sherif, M A; Fang, Y S; Sherif, R I J Geotech Engng Div ASCEV110, NGT1, Jan 1984, P41–56