Journal of Engineering Geology

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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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Introduction
Geofoames are used as a light weight fill material in those places which soil borrows is not cost effective for engineering or economic purposes. In general, geofoames are highly capable of improving some of geotechnical properties of soils such as inflation creation, reduction of density, and etc., due to their light weight, no change of volume against water, low permeability, and relatively proper strength. Using mixture of geofoam beads and soil has been recently taken into consideration by researchers. The mixture causes tangible reduction of soil density and severe drop of active pressure of retaining walls. Also, using the mixture in seismic zones is of special importance. In the paper, effect of mixing geofoam (4 different percent) and three types of poorly graded sandy soils have been dealt with. The research innovation has been compared to previous ones is using poorly graded sandy soil, separating geofoam beads based on their diameter, and reviewing the effect of adding various percentage of geofoam on improvement of poorly graded sandy soil’s properties.
Materials and Test Method
Tests have been performed in direct shear box (10 ^cm x10 ^cm) under three stress levels of 50, 100, and 150kPa. First type of soil has been Firoozkooh sand (#161) with specific gravity of 2.65, as uniformly graded sand (SP). Second type of soil has been mixture of uniformly graded sand and 10% silt (SM-SP); and, third type of soil has been mixture of Firoozkooh sand and 20% silt (SM). The three above types of soils have been named as soil 1, soil 2, and soil 3, respectively.
Geofoam beads have been all fine grained, passing through sieve No. 10; and, their added weighted values have been 0, 0.2, 0.4, and 0.6% of weighted percentage of soil. All of tests have been performed with optimum moisture content of geofoam and soil mixture. Due to diversity of soil types and ratio of geofoam-soil mixtures, soil compaction test has been performed on each direct shear test’s sample to specify optimum moisture content of various types of mixtures; because there have been various types of soils used, and also various ratios of soil and geofoam mixtures.
Results
According to the results, using geofoam beads leads to considerable reduction of soil density. Decrease made in density will be more tangible when higher percentages of geofoam are added to the soil. Also, as far as geofoam absorbs water, optimum level of moisture will be increased through increase of geofoam percentage in soil-geofoam mixture.
Since geofoam beads are less rigid compared to grains of sand, sand and geofoam interlocking and friction level is lower than sand interlocked to sand; and shear strength has been decreased through increase of geofoam percentage in soil. The point to be remembered is that, reduction level of shear strength in soils containing various percentages of geofoam is not so tangible compared to the soil itself. In its worst case, the reduction would be about 12%.
Adding geofoam beads to all of the three types of soil has led to their increase of apparent cohesion. Moreover, through increase of mixture percentages, more increase has been made in apparent cohesion of mixture. The results are indicative of significant effect of mixing geofoam and soil 1 in increase of soil cohesion up to 9 times. The cohesion increase has been about 4 and 2 times for soils type 2 and 3 respectively. So, it could be concluded that the lower the soil cohesion, the higher would be effect on cohesion increase of soil, through increase of geofoam percentage.
In figure 1, chart of internal friction angle is shown based on mixture percentage of geofoam for those types of soils being tested. Considering decrease of internal friction angle through increase of geofoam percentage, the important point is slope drop observed when geofoam percentage added has been 0.4%. Therefore, reduction speed of internal friction angle has become slower, after this level. Considering the figure, internal friction angles of soils type 1, 2, and 3 have shown respectively 15, 16, and 18% of reduction, through highest percentage of geofoam added (0.6%).
Figure 1- Internal friction angle based on geofoam percentage mixed with different soils
Comparing the results from present and previous researches, it could be concluded that adding higher percentages of geofoam results in cohesion increase of sandy soils; however, the increase level is different for various types of soils. The lower the initial cohesion of sandy soils and the more uniform their gradation, the more the effect of adding geofoam on increase of cohesion coefficient of soil. Also, downward trend of internal friction angle for well graded and poorly grades sandy soils is almost similar.
Using the results from present research and considering acceptable level of reduction made in internal friction angle of the soil mixed with geofoam against cohesion increase and reduction of soil density; mixture of geofoam beads and soil could be used in construction of embankments, retaining walls and other earth structures, appropriately.
 

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Expansive soils contain clay minerals such as compacted kaolin which are widespread in nature. Displacements of this type of soils are associated with matric suction and degree of saturation. To determine the in-situ characteristics, necessary measures may be required to deal with the possible failure related to this type of soil. Different constitutive models of unsaturated soils have been considered the subject of many recent researchers (Sheng et al. 2004; Wheeler et al. 2003; Nuth and Laloui 2008; Zhang and Lytton 2009 a, b 2012). However, those constitutive models are generally complicated that are not properly implemented in computer programs for practical applications. The Barcelona Basic Model (BBM) is one of the geomechanical constitutive models to capture the elastoplastic behavior of unsaturated soils../files/site1/files/152/%D8%B5%D8%A7%D8%AF%D9%82_%D8%A2%D8%A8%D8%A7%D8%AF%DB%8C.pdf