Journal of Engineering Geology

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Tunneling in complex geological and geotechnical conditions is often inevitable, especially in urban areas. The stability analysis and the assessment of ground surface settlement of a shield tunneling are of major importance in real shield tunneling projects. The objective of this research is to determine the collapse pressure of a shallow circular tunnel driven by a Tunnel Boring Machine (TBM) of the Earth Pressure Balance (EPB) type.  In this study, analytical methods and three-dimensional numerical modeling with ABAQUS software were implemented to examine the effect of face pressure on the behavior of the tunnel. The parameters were calculated using data from Karaj subway-line 2 as a case study. The analytical method used in this study is Leca-Dormiex which is based on limit analysis theory.  The method is based on a translational multiblock failure mechanism.  Also, elastic and Mohr-Coulomb constitutive model have been used for soil behavior. The results of analytical method and numerical modeling were then compared. Based on the obtained results, face pressure assessed from the analytical method of Leca-Dormiex (upper bound) is the minimum pressure that can be implemented on the face tunnel. It also indicates that with implementation of suggested pressure of analytical method, Karaj subway face tunnel is stable and consequently execution of pre-consolidation methods in this section of the tunnel does not seem to be necessary

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In tunnelling in soil mass, in groundwater existing mode, liquefaction, elastic displacements and settlement in soils upon the tunnel, are the risks may attack the excavated underground space stability. In this case study that were performed on second line of Mashhad city subway route, information catched from Standard Penetration Test, in situ and laboratorial tests, were used to optimum numerical values search for soil engineering parameters that could optimize the TBM stationing level. In order to this goal attaining, intelligent, numerical and probabilistic methods were used and the reliability of intelligent and numerical methods with the Safety Factors of tunnel stability, investigated simultaneously. The results were denoting the accordance of intelligent models such as Genetic Algorithm (GA) and Multi objective Genetic Algorithm with Finite Element model's output. So these models could be complement of each others in planning and designing of tunnels and using of them advised in tunneling and excavations.

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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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Earth-fill dams stability in steady state seepage condition is very important, especially during earthquakes. Numerical software analyses require accurate and realistic modeling of construction stages. Since earth-fill dams are constructed in different layers, so these conditions should be considered in software modeling to achieve a reasonable design. In this study, an earth-fill dam is modeled in PLAXIS software and the effects of the number and shape of layers are studied in dry and steady-state conditions. Obtained results in static and pseudo-static analyses show that modeling of earth-fill dams with different layers has significant effects on shear stresses and horizontal displacements. For example, horizontal displacements and shear stresses, increase at least 50% and 17% respectively, in comparison with single layer models. According to the obtained results, it can be mentioned that modeling of an earth-fill dam in the layered model and rather in inclined layers are more reasonable

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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.
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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.

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