Journal of Engineering Geology

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Distribution of static active earth pressure on an inclined retaining wall, with frictional or cohesive-frictional backfill, has been studied in the present research. Based on the limit equilibrium concept, and by implementing the horizontal slices method (HSM), two formulations have been proposed for determination of critical failure wedge. Results obtained from these formulas and results of the suggested equations by other researchers have been compared. Findings of current study show that horizontal slices method is capable of predicting the stress distribution and angle of failure wedge for inclined walls with high degree of accuracy. In addition, this method is applicable for various conditions of soil and wall and is able to consider the slope of backfill, friction between soil and wall, cohesion of soil and the effect of surcharge, simultaneously. Application of achieved formulation from horizontal slices method reveals that active earth pressure on inclined walls is nonlinear for both frictional and cohesive-frictional soils and the center of mass point of the resultant force would be located in an elevation less than one third of the height of wall.

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The shape of slip surface of the wedge creating lateral thrust on rigid retaining walls plays an important role in the magnitude, distribution, and height of point of application of lateral thrust.  Considering the shape of slip surface as linear, circular, logarithmic spiral, or a combination of them has been used in the literature. In the Coulomb lateral earth pressure method, a linear distribution of soil pressure on retaining walls is tentatively assumed and thus the point of application of total thrust is placed at one third of the wall height from the wall bottom. However, some experimental studies have revealed non-linear distribution of lateral earth pressures and that the point of application of resultant thrust is placed upper than one third of the wall height. In the present study, a plasticity equation is used to determine the reaction of the stable soil on cohesionless backfill supported by a retaining wall using an empirical equation derived from experiments performed in the field by others. A new analytical solution for determining the total resultant thrust on the wall is introduced and the distribution of pressures and the point of application of total thrust are computed. The results have been compared with some analytical methods, experimental data, and also with available data reported from field, demonstrating the accuracy and capability of the developed method. The results show that the distribution of the active lateral earth pressure is nonlinear and the point of application of total thrust is located about 0.42H from the wall bottom (H=wall height). In addition, the application point of total thrust is nonlinear function of soil-soil, wall-backfill soil friction angels and the height of the wall

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In this study using finite element procedure was used to simulate the dynamic behavior of reinforced soil walls, to evaluate their dynamic response on all types of deformation modes, different mechanisms of failure detection and identification of parameters in each of the modes and the mechanisms. Detailed numerical modeling, behavioral models and materials were described and Dynamic response of the physical model has been validated experimentally. Parametric study has been of the wall height of 5 meters by the effective parameters such as hardness, length to height ratio, the vertical reinforcement, wall height, and acceleration inputs. Three modes of deformation were observed. The study showed that occur bulging deformation mode while the use of flexible reinforcement and occur overturning deformation mode while the use of stiffness reinforcement. Stiffness reinforcements have the most effective in changing the type of deformation. Length to height ratio of reinforcements has the minimum effective in changing the type of deformation.

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As usage of reinforced soil structures is highly increased in seismic active zones, the analysis of dynamic behavior of these structures begins to be of great significance.  The present paper is an attempt to study the seismic behavior of reinforced soil retaining walls with polymeric strips. The consequences of the most principal parameters counting the length of reinforcement, reinforcement arrangements (zigzag vs. parallel), maximum base input acceleration and wave frequency on the wall displacement have been investigated for sensitivity analyses. The main drawback of numerical methods in dynamic analysis is being very time consuming. Therefore, determination of equivalent coefficients is a suitable, easy and beneficent approach to converge   results of   pseudo-static and dynamic methods. In this case, a relatively accurate design is achieved by using pseudo-static method that takes less time. To this end, an earthquake equivalent horizontal acceleration coefficient is proposed by considering horizontal displacement of the wall as the basis for comparison

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Soil nailing is a prevalent method for temporary or permanent stabilization of excavations which, if it is used for permanent purposes, the seismic study of these structures is important. There are a few physical models, with limited information available, for the study of behavior of soil nailed walls under earthquake loading. Numerical methods may be used for the study of effects of various parameters on the performance of soil nailed walls, and this technique has been used in the current paper. In this research, the effects of various parameters such as the spacing, configuration, and lengths of nails, and the height of wall on seismic displacement of soil nailed walls under the various earthquake excitations were studied. To investigate the effects of the configuration and the lengths of nails on the performance of these structures, two configurations of uniform and variable lengths of nails have been used. To study the effects of the spacing between nails and the height of the wall the spacings of 2 and 1.5 meters and the heights of 14, 20, and 26 meters have been considered. The seismic analysis has been carried out using the finite element software Plaxis 2D. To analyze the lengths' of nails, it was assumed that the safety factors of stability of different models are constant, and the limit equilibrium software GeoSlope was used. After specification of the lengths of nails based on constant safety factor of stability, the deformations of the models under several earthquakes records were analyzed, and recommendations were made on minimizing the deformations of soil nailed walls under seismic loading.

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Evaluation of the excavation-induced ground movements is an important design aspect of supporting system in urban areas. This evaluation process is more critical to the old buildings or sensitive structures which exist in the excavation-affected zone. Frame distortion and crack generation are predictor, of building damage resulted from excavation-induced ground movements, which pose challenges to projects involving deep excavations. Geological and geotechnical conditions of excavation area have significant effects on excavation-induced ground movements and the related damages. In some cases, excavation area may be located in the jointed or weathered rocks. Under such conditions, the geological properties of supported ground become more noticeable due to the discontinuities and anisotropic effects. This paper is aimed to study the performance of excavation walls supported by nails in jointed rocks medium. The performance of nailed wall is investigated based on evaluating the excavation-induced ground movements and damage levels of structures in the excavation-affected zone. For this purpose, a set of calibrated 2D finite element models are developed by taking into account the nail-rock-structure interactions, the anisotropic properties of jointed rock, and the staged construction process using ABAQUS software. The results highlight the effects of different parameters such as joint inclinations, anisotropy of rocks and nail inclinations on deformation parameters of excavation wall supported by nails, and induced damage in the structures adjacent to the excavation area. The results also show the relationship between excavation-induced deformation and the level of damage in the adjacent structure.

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In the narrow geosynthetic-reinforced retaining walls a stable rear wall exists in a short distance and so there is no enough space to extend appropriate length of reinforcements. In this case, the probability of overturning of retaining wall increases especially when subjected to earthquake loading. To increase the stability of the wall, reinforcements may be connected to the stable rear surface. Alternative solution is the utilization of full-height cast in-place concrete facing in order to resist the earth pressure by combined actions of reinforcements pullout capacity and facing flexural rigidity. One of the main questions about this type of walls is the portion of earth pressure resisted by the facing. In this study, the seismic earth pressure of narrow geosynthetic-reinforced backfill on rigid facing was evaluated using limit equilibrium approach and horizontal slices method. The critical failure surface was assumed to extend linearly from the wall toe to the rear surface and then moves along the interface of the backfill and rear surface up to the backfill surface. The effects of various parameters such as wall aspect ratio have been investigated. The obtained results show that the applied soil pressure on wall facing will be increased with depth in the upper part of the wall according to the Mononobe-Okabe equation, but its pattern is inversed in the lower part of the wall and it decreases until it reaches to zero at the wall toe. The results of analyses indicate that the attracted soil thrust by the facing increases with lessening of backfill width.

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Introduction
Retaining walls are geotechnical structures built to resist the driving and resistant lateral pressure. In terms of serviceability life, these walls are divided into two groups including short-term structures (temporary), such as urban excavation project, and long-term (permanent) structures, such as Mechanically Stabilized Earth Walls (MSE Walls). Retaining walls are implemented by two main methods including Top-down and Bottom-up. Among the reinforcements applied in the Bottom-up walls, one can name geocells, geogrids, metal strips, and plate anchors. On the other hand, the common reinforcements applied in the Top-down walls are grouted soil nails and anchors and helical (screw) soil nails and anchors.
Plate anchors are burial mechanical reinforcements that have one or multiple bearing plates with a bar or cable to transfer the load to an area with stable soil. Among different types of plate anchor applied in onshore and offshore projects, one can name simple horizontal, inclined, and vertical plate anchors, deadman anchors, multi-plate anchors, cross-plate anchors, expanding pole key anchors, helical anchors, drag embedment anchors, vertically loaded anchors (VLAs), suction-embedded plate anchors (SEPLAs), dynamically-embedded plate anchors (DEPLAs) like Omni-max and torpedo anchors, and duckbill, manta ray and stingray anchors.
The present research reports the results from physical modeling of plate anchor retaining walls under static loading. The evaluation parameters in this work include the geometry, dimension, and reinforcement configuration of plate anchors on wall stability. PIV technique was employed to observe critical slip surface. It is worth mentioning that PIV is an image processing technique firstly used in the field of fluid mechanics to observe the flow path of gas and fluid particles. This method was used in geotechnical modeling by White et al. (2003) and few reports are already available about its application to observe wedge failure of mechanically stabilized retaining walls.
Material and methods
To carry out tests at a laboratory scale, a dimensionality reduction ratio of 1/10 was applied. Thus, all dimensions of the designed retaining wall were divided by 10. As a result, a retaining wall with a height and length of 3000 mm was reduced to a wall with 300×300 mm² dimensions. To build a retaining wall, a chamber was designed with a length, width, and depth of 1000 mm, 300 mm, and 600 mm, respectively.
The soil used in all tests was the sandy soil supplied from Sufian (in Eastern Azerbaijan, Iran). According to the Unified Soil Classification System (USCS), the soil is classified as poorly graded sand with letter symbol ‘SP’.
To create a perfect planar strain condition and prevent any friction between the footing and the lateral sides of the test box, the footing length was selected 1 mm smaller than the 300 mm width of the test chamber. Therefore, the length, width, and thickness of footing were selected as 299, 70, and 30 mm, respectively.
The length and diameter of applied tie rods were respectively 300 mm and 4 mm, which are the smaller scales of 3000 mm length and 40 mm diameter tie rod. The two sides of the tie rods were threaded to plate anchors and wall facing. Four polished square and circular anchor plates with two different areas were used. The area of small and medium circulars are respectively equivalent to the area of small and medium square plates.
Because no post-tensioning occurs in these plate anchors, the horizontal and vertical distances were both selected as 1500 mm. By applying a dimensionality reduction coefficient of 1/10, a 150 mm center-to-center distance was obtained for reinforcements in the wall. Accordingly, three applied reinforcement configurations including 5-anchor, diamond, and square configurations were used.
To construct permanent retaining wall facing, prefabricated or precast concrete blocks with a thickness of 300 mm were used. Wood (2003) conducted a dimensional analysis and introduced four types of material with different thicknesses for a 300 mm concrete facing in laboratory modeling. Accordingly, a 0.9 mm thick aluminum plate was used in the experiments performed in the present work.
Results and discussion
With an increase in dimensions of anchor plates, an increase in bearing capacity of footing and a decrease in horizontal displacement of the wall are noticed. By comparing the 24 mm footing settlement in three configurations, with changing dimension of the plates from C1 to C2 and S1 to S2 respectively, 63% increases are observed in bearing capacity of the wall.
An increase in anchor plate dimensions results in a significant decrease in wall displacement. Therefore, changing the plates from C1 to C2, S1 to S2 leads to 24% and 28% declination in wall displacement.
By changing reinforcement configuration from square to diamond, diamond to 5-anchore, and square to 5-anchor, respectively, 27%, 31%, and 67.5% increases in bearing capacity for small plates, 9.2%, 27%, and 38% for medium plates are achieved using a comparison of the final loading steps in experiments. An analogy of percentages shows that a decrease in the effect of changing the reinforcement configurations on the bearing capacity of the wall with an increase in plate anchors dimensions is reached. 
Conclusion
In the present research, a set of laboratory experiments were carried out to evaluate the stability of mechanical retaining walls reinforced with plate anchors with different geometries (square and circular), sizes (small and medium), and configurations (diamond, square, and 5-anchor). The main results of the present work can be outlined as follows:
• The maximum bearing capacity is for the 5-anchor configuration since it has one more reinforcement. After 5-anchor configuration, the diamond configuration results in a higher bearing capacity compared to the square configuration.
• Circular anchor plates compared to square anchor plates provide a higher wall stability and in the most of the experiments lead to higher bearing and lower displacement in the wall.
• Wall displacement in a diamond configuration with one less reinforcement shows a little difference with 5-anchor configuration. The maximum wall displacement occurs in a square configuration and more wall swelling is observed in the wall middle height due to inefficient anchors configuration in the wall.
./files/site1/files/132/2Extended_Abstracts.pdf

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One of the effective parameters in the dynamic behavior of reinforced soil walls is the fundamental vibration frequency. In this paper, analytical expressions for the first three natural frequencies of a geosynthetic reinforced soil wall are obtained in the 3D domain, using plate vibration theory and the energy method. The interaction between reinforced soil and the wall is also considered by modeling the soil and the reinforcement as axial springs. The in-depth transverse vibration mode-shapes, which were impossible to analyze via 2D modeling, are also analyzed by employing plate vibration theory. Different behaviors of soil and reinforcements in tension and compression are also considered for the first time in a 3D analytical investigation to achieve a more realistic result. The effect of different parameters on the natural frequencies of geosynthetic reinforced soil walls are investigated, including the soil to reinforcement stiffness ratio, reinforcement to wall stiffness ratio, reinforcement length, backfill width and length to height ratio of the wall, using the proposed analytical expressions. Finally, the results obtained from the analytical expressions proposed are compared with results from the finite element software Abaqus and other researchers’ results, showing that the proposed method has high accuracy. The proposed method will be a beginning of the 3D analytical modeling of reinforced soil walls.
 

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In recent years, with the growing use of the nailing method for stabilizing excavation walls, there has been a need for a comprehensive investigation of the behavior of this method. In the  previous studies, the behavior of nailed walls has been investigated in static and dynamic states and under different conditions. However, due to the different feature of near-field ground motions, it is  necessary to study the effect of these motions on the behavior of the nailed walls. Near-fault ground motion is significantly affected by the earthquake record direction and the rupture mechanism. So, in this study, to compare the effects of near-field and far-field ground motions, a two-dimensional (2D) soil- nailed wall was considered. PLAXIS 2D was used for the modeling of the soil-nailed wall system. An excavation with a dimension of 10 meters in height was taken into the account. In this study, 10 records (Five fault-normal near-field ground motion records and five far-field ground motion records), were recorded  on the rock and  applied to the model. These ground motion records were derived from the near-fault ground motion record set used by Baker. These records were scaled to the Peak Ground Acceleration (PGA) of 0.35g and then applied to the bottom of the finite element models. Mohr-Coulomb model was then used to describe the soil behavior, and Elasto-plastic model was employed for the nails. A damping ratio of 0.05 was considered at the fundamental periods of the soil layer. The results showed that the  generated values of bending moment, shear force and axial force in nails under the effect of the near-fault ground motions were  more than those in the far-ault ground motions. These values were  almost equal to 23% for the maximum bending moment, 30% for the  shear force,  and 22% for the axial force. The created displacement under the effect of near-fault ground motions was  more than that in the far-fault since a higher energy was  applied to the model in the near-field ground motions during a short time (pulse-like ground motions). In contrast, in the far-fault ground motions, due to the more uniform distribution of energy during the record, such pulse-like displacements were not observed in the system response. Increasing in nail length and soil densification, decreases the displacement of the soil-nailed wall but does not change the general behavior of the soil under the effect of near-field ground motions. Based on the obtained results, for a constant PGA, there were  positive correlations between the values of the  maximum displacement on the top of the wall and  the PGV values of near-fault ground motion records. However, the mentioned correlations were  not observed in the case of far-fault ground motions.

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The increasing rate of construction activities in urban areas is accompanied by excavation in the vicinity of existing structures and urban utilities. This issue has highlighted the importance of constructing protecting structures in order to control displacements and prevent damage to structures and their neighboring area. Among the important widely used wall stabilization techniques, one can name nailing and grouted anchors. However, these methods suffer some drawbacks such as annoying noise and vibration during the drilling, implementation difficulties below the water table, grouting problem, installation of strands and bars in the borehole in porous and collapse soils, and long curing time for the grout of post-tension anchors. Since the helical anchor method lacks many of the mentioned problems, it is now widely used in many applications.
In the present work, a laboratory model of helical anchor stabilized wall is presented and evaluated. For this purpose, four types of anchors at 20° back slope are designed in a sandy soil and the effect of helix configuration (in term of its diameter and number of blades) is investigated. Considering the laboratory scale of the designed model, the results obtained using helical anchor were compared with numerical results of soil nailing wall by applying the particle image velocimetry (PIV) analyses.
Material and methods
The test box designed in this work is made of a metal plate with a thickness, length, width, and depth of 1.5 mm, 100 cm, 60 cm, and 30 cm, respectively, and a Plexiglas in its opposing side with a thickness of 50 mm. The soil used in the experiments was the dry sand of Soufian region in east Azerbaijan province of Iran. The soil is classified as SP according to USCS classification. The helical anchors were fabricated by welding the helical pitches to a metal shaft. The end part of the shafts is screw threaded such that to fasten a bolt to them.
To start the experiment, the empty box was completely cleaned using the detergents to remove any pollution or soil on the Plexiglas and metal surface. Afterward, the sandy soil was poured on the wall floor and the facing was placed inside the box vertically. Again, the sandy soil was poured from both sides of the facing up to the installation height of the helices. Helices were installed in the assigned holes and their angle was adjusted through the pre-fabricated stencils. The soil height was increased up to the next row assigned for helices installation. These steps were repeated until reach the wall crest. After preparation of the physical model, its behavior during the preparation must be modeled. We first filled both sides of the model and then modeled the stability behavior of the helical anchor wall through excavating its facing opposed side. Overall, the wall was built through eight excavation steps.
Results and discussion
The maximum displacement is related to the anchor type 1, which does not have enough bearing capacity under surcharge conditions. By changing the anchor type and increasing the number of helices, shear strains and their expansion in the wall back decline. The decrease in displacement rate by changing the anchor from type 1 to type 2 is 18%, which is due to the low bearing capacity of type 2 anchor compared to the type 1 anchor. Increasing the number of pitches from one to two (changing the type 1 anchor to type 3 anchor) showed a considerable decrease (i.e., 43%) in displacement rate. Increasing the number of pitches from 1 to 3 (changing the anchor from type 1 to type 3) resulted in a 62% decrease in wall crest displacement. This displacement decrease rate seems to decline with an increase in the number of helixes.
The displacement rate for all four anchors is almost similar in two excavation steps, which probably is because of the need for displacement for activation of the anchors. One strategy to deal this issue in the sensitive projects and control the displacement is to apply post-tension helical anchors. Then, in stages 4 to 6, the displacement was almost constant due to four main reasons including wall rigidity, the presence of reinforcements, formation of pre-step displacement-induced tension force, and enough capacity of anchors to face with more displacement. In stages 6 to 8, type 1 and 2 anchors showed growing displacements due to the reduction and ending the wall rigidity and lower bearing capacity. In type 3 and 4 anchors, the maximum displacement was related to 4 initial stages. In type 1 and 2 anchors, which have two helical plates, almost a similar behavior was observed until stage 6 of excavation, but eventually type 3 anchors showed better performance because of higher bearing capacity to overall displacement.
Conclusion
In the present study, a physical model was designed to investigate the effect of helical anchors’ geometry on displacement rate of helical anchor wall and compare it with a nail wall. Overall, comparing the results obtained by conducting these experiments on a helical anchor stabilized wall and a nail wall revealed that:
- Wall crest displacement is affected by the diameter and number of helices and decreases by an increase in bearing capacity.
- The increase in the number of pitches from one to two (single-pitch to double-pitch anchor) has a higher effect on displacement control compared to the case of changing the double-pitch to triple-pitch anchor. So, it can be stated that a further increase in the number of anchor pitches results in a declined performance of the anchors.
- All anchors need a slight displacement for activation. This issue cannot be resolved by changing the type of helical anchors. Hence, when the displacement required for activation of the anchors exceeds the allowable wall crest displacement, use of post-tensioned helical anchors is recommended.
- A comparison between nailing and helical anchor results revealed that the relative density of the wall stabilized with the helical anchor is less than that of the nail wall; and wall crest displacement in the helical anchor wall was very lower than that of nail wall. Thus, the helical anchor wall stabilization is preferred when other economic and technical requirements are met.