Effect of surcharge load location on the behavior of cantilever retaining wall
-
Rowida S. Al-khafaji
and
Qutayba N. Al-Saffar
Abstract
In this study, the effect of location of surcharge load on the stability and behavior of the retaining wall under static and dynamic load has been considered. A cantilever retaining wall of 7 m height retained dry sandy soil with 50 kN/m2 surcharge load. Several parameters were taken into account in the numerical analysis, including the horizontal distance (X) from the edge of the wall to the surcharge load expressed as a ratio to the heel width (X/Bh = 0, 0.25, 0.5, 0.75, and 1), as well as the effect of different values of the earthquake's horizontal component (kh = 0.1, 0.2, and 0.3). Lateral earth pressure distribution decreases with increase (X/B h ) in the upper one third of the wall. The effect of surcharge location at the top of the wall disappears at X/B h = 0.25. Under dynamic load, the maximum displacement at the top of the wall is obtained at X/B h = 0.5. It is increased by about 4 times at k h = 0.3. The possibility of sliding increases by about 4.8 times once the k h increases from 0.1 to 0.3. There is a maximum increase in rotation by 2 times at k h = 0.1. In the dynamic case, the differential settlement decreases with increase in X/B h , and increases with the increase in k h .
1 Introduction
Retaining walls are frequently adopted to sustain the necessary difference in ground levels with backfills sited behind the retaining walls or excavations carried out in front of them. In the first case, new buildings could be created next to the retaining wall, while in the second case, where existing buildings are currently behind the wall, the retaining walls have to be protected from any failure due to earthquakes. The wall experienced considerable displacement and rotation as a result of an earthquake [1]. The high displacement can cause damage to the nearby structures [2].
There are many empirical methods that have been developed for calculating the lateral earth pressure, which in turn depend to a large extent on the principles announced by Coulomb, Rankine, Terzaghi, and others [3]. Okabe [4] and Mononobe and Matsuo [5] presented a solution to assess the earth pressure based on the limit-equilibrium method that was developed from the Coulomb sliding wedge theory. Salman et al. [6] examined the effect of the location and magnitude of the surcharge load on the backfill soil near the edge of the retaining wall on distribution of lateral earth pressure in the static case. The results showed that the lateral earth pressure vanished as the position of the surcharge load was relocated away from the wall by around 0.6 height of the wall. Caltabiano et al. [7] investigated the effect of both the location and the value of the surcharge load behind the wall on the critical acceleration of the earthquake using closed-form solution based on a pseudo-static method. It was found that the critical acceleration coefficient increases with an increase in the location of the surcharge load. At a certain distance from the wall, the structure that was found on the backfill did not announce any damage. The structure, near to a specific distance from the wall, remains in a safe state despite the destruction of the wall. Ghanbari et al. [8] stated that the increase in the surcharge is associated with an increase in lateral earth. By using a closed-form solution to analyze a retaining wall subjected to surcharge loading, Srikar and Mittal [9] concluded that the magnitude of the frequency was considerably influenced by the dynamic lateral earth pressure. Woodward and Griffiths [10] studied the effect of the force caused by the earthquake on the retaining walls and calculated the lateral earth pressure by the Mononobe-Okabe method. It was found that the coefficient of lateral earth pressure increases during the earthquake and the displacement of the wall depends on the damping level of the soil. Ghazavi and Yeganeh [11] focused on the non-linear reality of the seismic lateral earth pressure distribution, where the horizontal and vertical components of the earthquake were introduced using the pseudo-dynamic method. Mandal et al. [12] studied the effect of different values of earthquake characteristics by different methods static and dynamic (pseudo-static and pseudo-dynamic). The results indicated that as the horizontal acceleration coefficient (k h ) increases, seismic active earth pressure also increases. Yang et al. [13] examined the seismic reaction of the retaining wall under Wenchuan earthquake by simulating and testing the models of the retaining walls in a large shaken table. The earth pressure under the dynamic load increases with the escalated ground from 0.1 to 0.9g and is a non-linear relationship. Ibrahim [14] found that seismic displacement of the gravity wall is directly proportional to the inclination of the backfill, soil flexibility, and earthquake ground acceleration.
The previous works show the significant effect of the surcharge load on the stability of the retaining wall under static and dynamic loads. However, few studies considered the effect of the location of the surcharge load from the edge of the wall on its stability, hence, this study considered this factor.
2 Methodology and numerical model
2.1 Model geometry
To select an appropriate model, the dimensions of the wall were examined to achieve the stability against failure based on the methods of analysis that were proposed by Mononobe, Okabe, and Matsuo [3,4,5], and in both static and dynamic cases. Then, depending on the finite element method, PLAXIS 2D package was adopted to analyze the cantilever retaining wall (Figure 1).
Geometry of the model.
2.2 Numerical modeling
Figure 2 shows the 2D-finite element model with domain dimensions of 40 m × 30 m considering the recommendation that was suggested by Al-Rayhani and Naggar [15]. A 15-nodes triangle element was selected to define the soil media. This element offers interpolation for displacements of 4th degree with 12 stress points for numerical integration. The mesh generation of triangulation patterns is generated automatically.
Geometry dimension and mesh generation.
For static analysis, a normally fixed boundary is considered at vertical sides and a fully fixed boundary is used at the bedrock. While a free-field boundary for the earthquake analysis is imposed on the vertical sides. At the bottom boundary, the compliant base has been proposed [16]. The interface element simulated the contact zone between the retaining wall and soil.
2.3 Soil modeling
The type of the soil media considered in the numerical analysis are clayey soil in the foundation under the retaining wall and in passive zone, while sandy soil is used in the backfill behind the retaining wall. The Hardening Soil model with small-strain stiffness (HS-small) was adopted to model the soil. The engineering properties of ground mediums are listed in Table 1. The HS-small strain model meets the requirements of the dynamic problems by considering the stress-dependent stiffness of the soil at small strain that displays an increase in the soil stiffness [17].
Engineering properties of soil media
| Parameter | Symbol | Unit | Backfill soil (sand) | Foundation soil (clay) |
|---|---|---|---|---|
| Material model | Model | — | HS-small | HS-small |
| Type | — | — | Drained | Drained |
| Unsaturated unit weight | γ unsat | kN/m3 | 18 | 19 |
| Saturated unit weight | γ sat | kN/m3 | 18 | 19 |
| Secant stiffness in standard drained triaxial test |
|
kN/m2 | 3.0 × 104 | 8.0 × 103 |
| Tangent stiffness for primary odometer loading |
|
kN/m2 | 3.0 × 104 | 8.0 × 103 |
| Unloading/reloading stiffness |
|
kN/m2 | 9.0 × 104 | 24 × 103 |
| Power of a stress-level dependency of stiffness | m | — | 0.5 | 1.0 |
| Effective cohesion |
|
kN/m2 | 0.2 | 25 |
| Effective angle of internal friction |
|
degree | 30 | 26 |
| Angle of dilatancy | ψ | degree | 0 | 0 |
| Shear strain at which Gs = 0.72G0 | γ 0.7 | — | 2 × 10−4 | 2 × 10−4 |
| Shear modulus at very small strain |
|
kN/m2 | 100 × 103 | 60 × 103 |
| Poisson’s ratio of unloading-reloading |
|
— | 0.2 | 0.2 |
2.4 Retaining wall modeling
The retaining wall was modeled as a reinforced concrete cantilever retaining wall with dimensions shown in Figure 1. The total height of the wall (H) is 7.0 m, The retaining wall has a retained soil height (h) of 6.3 m, and the wall itself penetrated to a depth (d) of 2.0 m. The width of the footing of the wall is 5.9 m. The engineering properties of the cantilever retaining wall are listed in Table 2.
Engineering properties of the cantilever retaining wall
| Parameter | Symbol | Unit | Value |
|---|---|---|---|
| Material model | Model | — | Linear elastic |
| Type | — | — | Non-porous |
| Unit weight | γ | kN/m3 | 24.0 |
| Modulus of elasticity | E | kN/m2 | 35.0 × 106 |
| Poisson’s ratio | υ | — | 0.15 |
| Mass damping coefficient | α | — | 0.2094 |
| Stiffness damping coefficient | β | — | 0.01061 |
2.5 Earthquake motion
The EL-Centro 1940 earthquake has been adopted for dynamic analysis in this study. Its magnitude was 6.9 on the Richter scale. The peak ground acceleration of this earthquake is 0.319g with a maximum frequency of 1.5 Hz from the recorded Fourier amplitude spectrum. The horizontal component of the earthquake was simulated by imposing a prescribed horizontal displacement on the bedrock at a depth of 30 m from the backfill ground [18].
2.6 Parametric study
To inspect the effect of surcharge load and seismic load on lateral earth pressure distribution and the stability of the wall, different horizontal distances of the surcharge load from the edge of the wall were studied. The distances (X) are 0, 2.1, and 4.2 m. The ratio of these distances to the width of the heel (B h ) are considered and referred to as X/B h = 0, 0.25, 0.5, 0.75, and 1, respectively. In addition, different magnitudes of the horizontal component of earthquake (k h ) of 0.1, 0.2, and 0.3 have been considered.
3 Results and discussion
3.1 Lateral earth pressure distribution
The effect of the surcharge load location from the edge of the wall at various distances (X/B h = 0, 0.25, 0.5, 0.75, and 1.0) on the distribution of the lateral earth pressure is shown in Figure 3. It can be shown, generally, that the lateral earth pressure decreases with the distance of the surcharge load in the upper one third of the wall. Then, these lateral earth pressure values begin to fluctuate and converge due to the decrease in the effect of the surcharge load with the height of the wall until it reaches a certain value. Also, note that at the distance (X/B h = 0), the lateral earth pressure at the uppermost part of the wall has a certain value of 12.7 kN/m2. This can be attributed to static and inertial forces created on the wall due to the surcharge. Then, this effect of the surcharge load disappears with the increase in the distance to X/B h = 0.25.
Variation in lateral earth pressure with normalized horizontal distance in case of (a) static; (b) k h = 0.1; (c) k h = 0.2; and (d) k h = 0.3.
The distribution of the lateral earth pressure is sort of linear in the static case; however, a nonlinear state of the lateral earth pressure distribution appears with the increase in the value of the earthquake particularly at 0.3g. At the distance X/B h = 0, in static case, the lateral earth pressure at the uppermost part of the wall of 12.7 kN/m2 increases by 41.2, 24.7, and 11.4% with the magnitude of the earthquake of 0.1, 0.2, and 0.3g, respectively. This increase in lateral earth pressure is probably due to the accumulation of locked-in stresses cycle by cycle and partially due to the increase in soil density resulting from earthquake-induced settlements.
3.2 Stability of the cantilever retaining wall
3.2.1 Maximum horizontal displacement at the top of the wall (u x )
Figure 4 shows the relationship between the maximum horizontal displacement (u x ) at the uppermost part of the wall and the normalized horizontal distance (X/B h ) of the surcharge load at different values of the horizontal component of earthquake. It can be noted that in the static case, the maximum displacement at the uppermost part of the wall is gradually decreased with an increase in the normalized horizontal distance of the surcharge load. When the normalized distance increases from 0 to 0.25, the percentage decrease in the maximum displacement is about 9%. This effect gradually decreases as the surcharge moves away from the edge of the wall and the reduction becomes 4.3% with the increase in the normalized distance from 0.75 to 1.0.
Maximum displacement at the uppermost part of the wall with the normalized horizontal distance of the surcharge load.
In the dynamic case, the peak value of the maximum displacement obtained at normalized distance 0.5 demonstrates a different behavior than in the static case. With the increase in X/B h from 0 to 0.5, the maximum displacement increases to about 6, 9.5, and 6.6% at k h = 0.1, 0.2, and 0.3, respectively.
The magnitude of the earthquake significantly affects the u x at the top of the wall as shown in Figure 4. This effect appears minor at kh = 0.1, but as the magnitude of the earthquake increases to kh = 0.2, the rate of increases in the ux climbs by around 165%, reaching 400% at kh = 0.3.
3.2.2 Sliding the wall
From the sliding values shown in Table 3, it can be seen that the location of the surcharge load is ineffective on sliding the wall in both static and dynamic cases. This behavior is due to that the sliding of the wall does not depend on the location of the surcharge load, but rather depends on the ratio between the forces that resist failure to the forces that cause failure. Whatever the location of the surcharge load, the sliding is roughly 28 mm in the static case, increasing to 33.3, 84, and 159 mm under dynamic load at kh = 0.1, 0.2, and 0.3, respectively.
Sliding of the wall in different locations of the surcharge load
| X/B h | Sliding of the wall (mm) | |||
|---|---|---|---|---|
| Static case | Dynamic case | |||
| k h = 0.1 | k h = 0.2 | k h = 0.3 | ||
| 0 | 27.5 | 33.3 | 83.8 | 159 |
| 0.25 | 28.6 | 33.2 | 84 | 160 |
| 0.5 | 29 | 33.3 | 84.8 | 158 |
| 0.75 | 29 | 33.3 | 83.9 | 158 |
| 1 | 28.6 | 33.4 | 83 | 160 |
Sliding is greatly affected by the magnitude of the earthquake, as displayed in Table 3. The sliding increases by about 150% with the increase in k h from 0.1 to 0.2. Also, the ratio is 90% with an increase in k h from 0.2 to 0.3.
3.2.3 Overturning the wall
If the driving moments acting on the retaining wall are larger than the resisting moments, the retaining wall will tip over. Figure 5 shows the relationship between the rotation angle of the wall obtained at different surcharge locations and different magnitude of the earthquake. Note that the effect of the surcharge location is clear in the static case since it gets a rotation of about 0.15° at normalized distance of X/B h = 0. This value decreases to 0.009° with the increase in the distance to X/B h = 0.75, beyond which the rotation remains unchanged. In the dynamic case when kh = 0.1, the surcharge location has a slight effect on the wall rotation. Then, the angle of rotation fluctuates when k h = 0.2 and the maximum rotation of 0.212° is obtained at X/B h = 0.5. At k h = 0.3 the value of the angle of rotation decreases with the increase in the location of the surcharge load.
Rotation of the wall with the normalized horizontal distance of the surcharge load.
Because of the existence of surcharge load on the surface of the backfill, the angle of rotation increases dramatically as the magnitude of the earthquake increases. As shown in Figure 5, the average angle of rotation in the static case is 0.066°, while in the dynamic case, it is 0.05, 0.19, and 0.27° at k h = 0.1, 0.2, and 0.3, respectively.
3.2.4 Differential settlement under the footing of the wall
Note that in Table 4, the differential settlement under the base of the retaining wall in case of static is 8.4 mm at X/B h = 0 which decreases to 1.6 mm at X/B h = 0.5. Thereafter, with the increase in the normalized distance, the differential settlement becomes negative, which means the retaining wall settles at the active side more than that in the passive side. While in the dynamic case, the differential settlement decreases with the increase in the normalized distance of the surcharge in general.
Differential settlement under the footing of the wall
| X/B h | Differential settlement of the wall base (mm) | |||
|---|---|---|---|---|
| Static case | Dynamic case | |||
| k h = 0.1 | k h = 0.2 | k h = 0.3 | ||
| 0 | 8.4 | 5.6 | 20.7 | 29.5 |
| 0.25 | 5.3 | 5.27 | 19.5 | 28.3 |
| 0.5 | 1.6 | 5.1 | 20 | 26.6 |
| 0.75 | −3 | 4.6 | 17.6 | 23.8 |
| 1 | −6.9 | 3.6 | 14.7 | 20.7 |
Moreover, the differential settlement values increase with the increase in the magnitude of the earthquake as illustrated in Table 4. The average values are about 4.2, 18.5, and 25.7 mm at k h equal to 0.1, 0.2, and 0.3, respectively. Accordingly, with an increased magnitude of the earthquake from 0.1 to 0.2g, the differential settlement increases by about 340%, and with an increased magnitude of the earthquake from 0.2 to 0.3g, the differential settlement increases by about 39%. This increase is because the soil begins to collapse under the wall.
3.2.5 Pressure distribution under the footing of the wall
Figure 6 shows the effective stresses measured at the toe and the heel of the wall to describe the pattern of the pressure distribution under the footing of the wall. Note that in the static case, the increase in the surcharge location resulted in a reduction in the pressure at a toe, while the pressure at a heel increased because of the increased stresses acting at that point. In addition, the pressure decreases as the surcharge moves away from the wall. At X/B h = 0, the pressure at toe (Q toe) is 476 kN/m2, this value decreases to 325 kN/m2 at X/B h = 1. In contrast, at heel, the pressure (Q heel) is 152 kN/m2 when X/B h = 0, and this value increases to 173 kN/m2 at X/B h = 1.
Pressure distribution at toe and heel of the wall.
In the dynamic case, the effect of the surcharge location seems clear at the toe and higher than that at the heel. The difference is about 3.1 and 1.9 times for distance X/B h = 0 and 1, respectively. A minor effect of the intensity of the earthquake displayed the pressure under the wall footing.
In general, with the increase in the magnitude of the earthquake, the average pressure at toe increases, but the average pressure at heel decreases. The increase ratio of the average pressure is 2.8% at the toe, and the decrease ratio is about 5–12% at the heel.
4 Conclusion
From the results obtained from this study, the following conclusions can be stated:
The presence of the surcharge load at the backfill soil has a direct impact on the lateral earth pressure distribution and stability of the wall.
Lateral earth pressure distribution decreases with the increase in X/B h in the upper one third of the wall while its effect disappears on the top of the wall at X/B h = 0.25.
A nonlinear behavior of the lateral earth pressure distribution is caused by the earthquake acceleration. At the top of the wall when X/B h = 0, the lateral earth pressure increases by about 41.2, 24.7, and 11.4% under k h = 0.1, 0.2, and 0.3, respectively.
Stability of the wall, in general, is influenced by both surcharge location and magnitude of the earthquake because of increasing the stresses acting on the wall.
At the uppermost part of the wall, the maximum horizontal displacement gradually decreases with the increase in X/B h in the static case, while in the dynamic case, the peak value obtained at X/B h = 0.5. The maximum displacement is greatly affected by k h and increased by about 400% at k h = 0.3.
The sliding of the wall is unaffected by the location of the surcharge but is greatly affected by the severity of the earthquake, with an increasing sliding ratio of (90–150)%.
Increasing X/B h leads to decreased rotation of the wall in the static case, but in the dynamic case, there is some fluctuation in rotation of the wall. Increasing k h leads to increased rotation of the wall, since the average angle of rotation is 0.05, 0.19, and 0.27° under k h = 0.1, 0.2, and 0.3, respectively.
In the static case, the differential settlement translated from passive to active with the increase in X/B h . In the dynamic case, the differential settlement decreased with the increase in X/B h , and increased with the increase in k h .
Increasing X/B h leads to decreasing the pressure at toe and increasing it at the heel in the static case. In the dynamic case, there is some fluctuation in the pressure at the heel. Increasing (k h ) leads to an increase in the average pressure at the toe, but the average pressure at the heel decreases. The increased ratio of the average pressure is 2.8% at the toe, and the decreased ratio is about 12–5% at the heel.
-
Funding information: The authors state no funding involved.
-
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
-
Conflict of interest: The authors state no conflict of interest.
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© 2023 the author(s), published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
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- Mechanical properties and durability of ultra-high-performance concrete with calcined diatomaceous earth as cement replacement
- Characterization of rutting resistance of warm-modified asphalt mixtures tested in a dynamic shear rheometer
- Microstructural characteristics and mechanical properties of rotary friction-welded dissimilar AISI 431 steel/AISI 1018 steel joints
- Wear performance analysis of B4C and graphene particles reinforced Al–Cu alloy based composites using Taguchi method
- Connective and magnetic effects in a curved wavy channel with nanoparticles under different waveforms
- Development of AHP-embedded Deng’s hybrid MCDM model in micro-EDM using carbon-coated electrode
- Characterization of wear and fatigue behavior of aluminum piston alloy using alumina nanoparticles
- Evaluation of mechanical properties of fiber-reinforced syntactic foam thermoset composites: A robust artificial intelligence modeling approach for improved accuracy with little datasets
- Assessment of the beam configuration effects on designed beam–column connection structures using FE methodology based on experimental benchmarking
- Influence of graphene coating in electrical discharge machining with an aluminum electrode
- A novel fiberglass-reinforced polyurethane elastomer as the core sandwich material of the ship–plate system
- Seismic monitoring of strength in stabilized foundations by P-wave reflection and downhole geophysical logging for drill borehole core
- Blood flow analysis in narrow channel with activation energy and nonlinear thermal radiation
- Investigation of machining characterization of solar material on WEDM process through response surface methodology
- High-temperature oxidation and hot corrosion behavior of the Inconel 738LC coating with and without Al2O3-CNTs
- Influence of flexoelectric effect on the bending rigidity of a Timoshenko graphene-reinforced nanorod
- An analysis of longitudinal residual stresses in EN AW-5083 alloy strips as a function of cold-rolling process parameters
- Assessment of the OTEC cold water pipe design under bending loading: A benchmarking and parametric study using finite element approach
- A theoretical study of mechanical source in a hygrothermoelastic medium with an overlying non-viscous fluid
- An atomistic study on the strain rate and temperature dependences of the plastic deformation Cu–Au core–shell nanowires: On the role of dislocations
- Effect of lightweight expanded clay aggregate as partial replacement of coarse aggregate on the mechanical properties of fire-exposed concrete
- Utilization of nanoparticles and waste materials in cement mortars
- Investigation of the ability of steel plate shear walls against designed cyclic loadings: Benchmarking and parametric study
- Effect of truck and train loading on permanent deformation and fatigue cracking behavior of asphalt concrete in flexible pavement highway and asphaltic overlayment track
- The impact of zirconia nanoparticles on the mechanical characteristics of 7075 aluminum alloy
- Investigation of the performance of integrated intelligent models to predict the roughness of Ti6Al4V end-milled surface with uncoated cutting tool
- Low-temperature relaxation of various samarium phosphate glasses
- Disposal of demolished waste as partial fine aggregate replacement in roller-compacted concrete
- Review Articles
- Assessment of eggshell-based material as a green-composite filler: Project milestones and future potential as an engineering material
- Effect of post-processing treatments on mechanical performance of cold spray coating – an overview
- Internal curing of ultra-high-performance concrete: A comprehensive overview
- Special Issue: Sustainability and Development in Civil Engineering - Part II
- Behavior of circular skirted footing on gypseous soil subjected to water infiltration
- Numerical analysis of slopes treated by nano-materials
- Soil–water characteristic curve of unsaturated collapsible soils
- A new sand raining technique to reconstitute large sand specimens
- Groundwater flow modeling and hydraulic assessment of Al-Ruhbah region, Iraq
- Proposing an inflatable rubber dam on the Tidal Shatt Al-Arab River, Southern Iraq
- Sustainable high-strength lightweight concrete with pumice stone and sugar molasses
- Transient response and performance of prestressed concrete deep T-beams with large web openings under impact loading
- Shear transfer strength estimation of concrete elements using generalized artificial neural network models
- Simulation and assessment of water supply network for specified districts at Najaf Governorate
- Comparison between cement and chemically improved sandy soil by column models using low-pressure injection laboratory setup
- Alteration of physicochemical properties of tap water passing through different intensities of magnetic field
- Numerical analysis of reinforced concrete beams subjected to impact loads
- The peristaltic flow for Carreau fluid through an elastic channel
- Efficiency of CFRP torsional strengthening technique for L-shaped spandrel reinforced concrete beams
- Numerical modeling of connected piled raft foundation under seismic loading in layered soils
- Predicting the performance of retaining structure under seismic loads by PLAXIS software
- Effect of surcharge load location on the behavior of cantilever retaining wall
- Shear strength behavior of organic soils treated with fly ash and fly ash-based geopolymer
- Dynamic response of a two-story steel structure subjected to earthquake excitation by using deterministic and nondeterministic approaches
- Nonlinear-finite-element analysis of reactive powder concrete columns subjected to eccentric compressive load
- An experimental study of the effect of lateral static load on cyclic response of pile group in sandy soil
