The Effect of Distance between Sheet Pile and Foundation on Bearing Capacity of Foundation

In this study, the presence of a foundation near the sheet pile wall built on sand soil was simulated in the laboratory, similar to the field conditions. For this purpose, laboratory tests of sheet pile wall (SPW) (defo) and bearing capacity (qult) of the foundation were carried out by applying vertical loads to the steel model foundation. Besides, laboratory tests were represented by the MohrCoulomb material model under 3D plane deformation conditions, and numerical analyses were performed. *ese studies were performed by varying the distance among the SPW, the foundation (L), and the penetration depth of SPW (Hp). *e results demonstrated that L had a greater effect on qult and δmax than theHp.When Lwas kept constant andHp was increased, it was seen that qult increased and δmax decreased. Moreover, the raise in L has resulted in an increment in the qult and δmax decreased. In addition, a good agreement between numerical analysis and experimental test was observed.


Introduction
*e increase in urban populations has led to an increase in the need for transportation systems and residential areas. Despite this increase, the useable areas in cities are limited. *erefore, it has become necessary to use existing areas more effectively. New living quarters are often created by deep excavations or by rehabilitating dangerous dip slopes. *is has brought stability and safety problems around dangerous dip slopes and deep excavations. During the construction of foundations or deep excavations in urban areas, slope slips and large settlements may occur [1][2][3][4][5][6][7]. Lateral support systems are used to prevent dangerous deformations around such construction sites. One of the common lateral support systems is SPWs. SPWs are flexible and generally waterproof structures. *ey are also used to limit horizontal displacements of the soil mass as lateral support. *e reasons SPWs are preferred are that they are economical and save time and space.
Safety and economic efficiency are key objectives in the engineering design [8]. In deep excavations, SPWs are designed according to wall displacement to evaluate their safety and economic efficiency. In this evaluation, two extreme conditions are taken into consideration as follows: one of them is very small deformations, which means that SPW is designed uneconomically; the other one is large displacements, which cause safety problems around the excavation area during construction.
As a result of literature research, some of the studies on excavation stability and safety are as follows: in some papers, numerical studies have been carried out using data from case analyses. In other research studies in the literature are investigated excavation width, wall displacements in the corners of the excavations, support geometry on wall and soil movements, the soil and wall interface, and the effects of wall elasticity are effective onwall-soil deformations. Results from theese studies was mostly compared with case studies [9][10][11][12][13][14].
In some papers, only numerical analyses were carried out using typical values of soil strength parameters. *ese studies modeled the construction phase of the diaphragm wall using 3D FEM, generally investigated soil stress distribution mechanisms and soil displacements, stability parameters of 3D rectangular, elastoplastic evaluation of the soil and retaining structure, and wall thickness and wall penetration depth on retaining walls in their analysis [15][16][17][18][19][20][21][22][23][24].
Apart from numerical studies, there are also studies similar to this study. For example, Tan et al. [23] examined the systems for the settlement of buildings adjoining excavations. As a result of their study, it was determined that both the buildings on shallow foundations and those on short piles were sensitive to damage caused by adjoining to deep excavation. *is result is different from the popular opinion in the literature.
In the literature, it was seen that the behavior of retaining walls on cohesive soils was examined in general. Numerous studies have been conducted on the behavior that may occur as a result of excavations on retaining walls built on cohesive soils [25][26][27][28][29][30][31][32][33].
*ere has been a limited number of literature on the behavior of retaining walls built on sand. *ese studies were conducted on sand in which an internal friction an angle below 32°was used and the deformations of SPW were investigated [9,12,[34][35][36] *e effects of the penetration depth and excavation width on the structures around the excavation were examined.

Research
Significance. *ere are several parameters that affect the bearing capacity of the foundations (q ult ) near the retaining structure and the deformations of the retaining structure. *ese parameters are relative density (D r ), SPW length (H t ), excavation width, the distance between foundation and retaining structure (L), and penetration depth (H p ). It was observed that the effect of only one of these parameters (generally D r or H p ) on q ult was examined in the literature. *e effect of the L parameter on q ult and SPW deformations (δmax) has not been encountered in previous studies. Besides, as can be seen from the literature summary above, some studies were based only on numerical analysis. In some of them, numerical analyses were made using the measurements in the field. *is study was based on the effects of L and H p parameters on q ult and δmax. Except for these two parameters, all other parameters were kept constant. *e soils in the field are generally not homogeneous and consist of different soil layers. *e difficulty of determining the soil strength parameters of all layers and the unknown interaction behavior between the layers complicates the stability problems. In such soils, strength parameters related to the soil layers, which are generally accepted strength parameters or obtained from drilling data, are used. *is study was based on laboratory experiments and numerical analysis. By simulating a homogeneous soil profile in the laboratory, multilayer effects were prevented and model experiments were carried out. *e results obtained were verified by numerical analysis.

Material Properties of the Sand and Sheet Pile Wall Used in Model Experiments
2.1. Properties of the Sand. *e sand is a dark color river soil and has an angular shape, as shown in Figure 1. Internal friction angles (ϕ) of this material are determined by using a direct shear test, ranging from 42°to 52°, which means the sand has high friction. *e material properties of the sand were determined according to ASTM standards [37]; ASTM (D422 -63 [38]e2, 2007). *e granulometry of the soil used in the tests was shown in Figure 2.
Since SPW is driven into the soil with vibration, it cannot be applied on extremely stiff soils. *erefore, in order to provide similarity between field conditions and laboratory model, 16% relative density sand, which is quite loose, was used in the tests. Another objective here was to clearly see the effect of changes in dimensions without changing the properties of the soil. *e relative density of the sand was determined according to the ASTM standard [39]. *e shear box test on sand was performed according to the ASTM standard [40] and the internal friction angle value was obtained. *e material properties obtained are given in Table 1.
*e angle of repose of normal loose sand and sand-gravel mixtures is 25-32° [41]. Experiments were carried out to determine the angle of repose of the sand. As a result of this experiment, it was determined that the angle of repose was 35°, as shown in Figure 3. Since the structure of the grains of this sand is angular and basaltic origin, it has a higher internal friction angle than other sands.

Properties of the SPW.
Plexiglass was used as SPW in the tests. *e reasons for the use of this material are that its strength and physical properties are standard, and its technical properties are well known. Another reason for using plexiglass as SPW material is that it is easily cut into the desired dimensions, light, and has the capacity to provide the desired deformation in the test. It is known that vinyl material with properties similar to the plexiglass is used in field applications. *e material properties of the plexiglass used in the tests can be seen in Table 2.

Test Setup.
Due to the stress-dependent soil properties, it is important to accurately model the prototype stress conditions in small-scale modeling experiments. One of the common ways to apply gravity (g)in model experiments is to re-establish the full-size stress levels. Details of the rules and modeling practice used in laboratory modeling can be found in [42]. Information about the scaling laws used in this study is given in Table 3. Figure 4 and 5 show the plan and cross-sectional view of the modeling test system.İn this study, the in-plane strain condition of the test system is assumed. *e conditions and dimensions of the test system are similar in all experiments with the exception of the SPW restraint conditions. Since the experimental system is symmetrical, only half of the system is modeled. While the deep of excavation was 100, 150, 200 mm (*e equivalent in the prototype was 10, 15, and 20 m), respectively, the thickness of the sand layer was constant and 950 mm (*e equivalent in the prototype was 95 m). *e width of the system was 750 mm (*e equivalent in the prototype was 75 m). According to the scaling law given in Table 3, experiment-making procedures were explained and results obtained from the experiments were given. All abbreviations used in the study are given in Table 4.

Model SPW and
Properties. *e model SPW was made of 3 mm thick plexiglass sheet and consisted of a single piece. In terms of bending stiffness, the model wall is considered nearly equivalent to a prototype-scale reinforced concrete sheet pile wall. *e Young's modulus of these materials, respectively, for plexiglass and concrete is 3.3 GPa and 25 GPa. *e ratio of SPW penetration depth to excavation depth is commonly 0.5-2 in engineering application [12,43,44]; (100, 150, 200 and 10, 15, 20 m are the model and the prototype dimensions, respectively).

Procedure of Model Tests.
To investigate the behavior of SPWs on sand, model tests were conducted in the laboratory. *e first group of test was performed by keeping H p constant and changing L. *e second test group was carried out by   1 Figure 4: View of the test system.    [45]; El Sawwaf and Nazir [46]; Sadrekarimi and Abbasnejad [47], the tank and foundation dimensions were determined by considering that the boundary effects of the tank should be minimal. *us, in semi-infinite environment conditions, the fundamental rule of model experiments were provided. *e test tank was filled with raining method from a height of 20 cm before placing SPW on the test set. After the filling process was completed, the front part of SPW was excavated until the desired penetration depth was achieved, and loading was started after the model base was placed, as shown in Figure 6 and7. *e model foundation was loaded at a speed of about 2.00 mm/min in the tests. *e condition of the model foundation and SPW after loading is shown in Figure 8 in order to determine δmax, δmax was taken from point A Figures 4 and 5).

First Group Test Results.
In the experiments, model foundations were loaded with a speed continuous of 1.0 mm/ min until a settlement value of 0.1 B consisted. *e bearing capacity of the foundation is determined when the deformation reaches 10% of the foundation width, which is 15 mm. *e load corresponding to this foundation settlement was determined from the graph, and the bearing capacity of the foundation was determined in this way. *is method of determining the q ult has usually been used in model experiments [48,49]. As a result of the loading tests, the loadsettlement graphs for the foundation are obtained in Figure 9.
For H p � 20, 25, 30 cm, the δmax versus L graph is shown in Figure 10. For cases of Hp � 20, 25, 30 cm, SPW had minimum deformations when L was equal to 4 B/3. *is δmax was chosen as a reference, and all results were compared with L � 4 B/3 to see the effect of L.
In the case of Hp � 20 cm, the decrease of L from 4 B/3 to B, it is caused at δmax an increase of 85.74%. *e decrease of L from 4 B/3 to 2 B/3 is caused at δmax an increase of 141.30%. In case of Hp � 25 cm, the decrease of L from 4 B/3 to B is caused at δmax an increase of 84.69%. *e decreasing of L from 4 B/3 to 2 B/3 it is caused at δmax by an increase of 124.72%. In case of Hp � 30 cm, the decrease of L from 4 B/3 to B is caused at δmax by an increase of 61.13%. *e decrease of L from 4 B/3 to 2 B/3 is caused at δmax by an increase of 97.23%. As seen in the results, δmax decreases with increasing L. When the Hp increases; however, the effect of the change of L on δmax decreases.
As a result of the tests performed, the effect of the foundation load and the change of L value on δmax was measured as in Figure 11, for H p � 20.
As a result of the tests performed, the effect of changing in L on q ult was measured as shown in Figure 12, for Hp � 20, 25, 30 cm. At these 3 penetration depths, in the case of L � 4 B/3, the SPW had the minimum deformation and the foundation carried the maximum load. However, when L decreased, δmax increased, and the load carried by the foundation decreased. Due to q ult is minimum at L � 2 B/3, this q ult value was chosen as a reference, and the other q ult values have been compared with this value to see the effect of L. In the case of        *e effect of load and the change of Hp value on δmax can be seen in Figure 14 for the L � 2 B/3.
As a result of the tests performed, the effect of the change of Hp value on qult was measured as in Figure 15, for Hp values where L � 2 B/3, B, 4 B/3. At these L values, in the case of Hp � 30 cm, the SPW had been the minimum deformation and the foundation carried the maximum load. When Hp decreased, δmax increased, and q ult decreased.
Due to q ult is minimum at H p � 20 cm, this q ult was chosen as reference and the other q ult values have been compared with this value to see the effect of H p . In case of L � 2 B/3, the increase of H p from 20 cm to 25 cm is caused at in q ult an increase of 20.42%. *e increase of H p from 20 cm to 30 cm is caused at in q ult an increase of 51.76%. In case of L � B, the increase of H p from 20 cm to 25 cm is caused at in q ult an increase of 17.82%. *e increase of H p from 20 cm to 30 cm is caused at in q ult an increase of 36.31%. In case of L � 4 B/3, the increase of H p from 20 cm to 25 cm is caused at in q ult an increase of 6.78%. *e increase of H p from 20 cm to 30 cm is caused at in q ult an increase of 24.47%. As seen in the results, q ult increases with the increase in H p . However, when L increases, the effect of the change in H p on q ult decreases.

3.7.
Outcome of the Model Tests. *e load-deformation data of SPW and the settlement-load data of the foundation were given according to different Hp and L. *e effects of different Hp and L on δmax and q ult were analyzed by comparing the data obtained from the first and second group tests. *e δmax corresponding to the maximum q ult obtained in the tests is given in Table 5. *e results of q ult are given in Table 6.

Numerical Analysis
In numerical study, the effect of H p and L on the behavior of SPW and q ult was investigated by using FEM. *e data obtained were compared to those obtained from the model test. *e Plaxis 3D Foundation program was used for numerical simulations performed in this study [50]. In Figure 16, it can be seen that a typical 3D mesh for which a numerical model was created. For 3D analyses, a horizontal midsize mesh and a vertical midsize mesh were used to achieve a balance between the processing time and accuracy. Similar to the previous studies, the Mohr-Coulomb material model was used in the modeling of the sand [51][52][53][54][55][56][57][58][59]. In all cases, the cohesion was assumed to be 0.01 kN/m 2 . *e modulus of elasticity of the soil was taken as E � 21000 kN/m 2 .
In the 3D FEM, the sand was modeled with 10-node tetrahedral elements. 10-node tetrahedral elements provide a second-order interpolation of displacement. *e SPW was modeled with 6-node triangular surface element with three translation degrees of freedom per node (U x , U y , and U z ). *e shear modulus (G) and bulk modulus (K) were obtained using the equations (1) and (2), respectively. *e ] in the formulas is the Poisson's ratio.
*e properties of sand, SPW, and foundation used in the numerical analysis are shown in Table 7-9, respectively.
In Section1 of the numerical modeling, sand was placed in the soil test tank. *en SPW was driven into sand. *e      Advances in Civil Engineering excavation was carried out according to H p in Section 2. In Section 3, the foundation was placed, the load was applied, and the analyses were performed. Finite element models of the wall and foundation were created by using the foundation modeling module and wall modeling modules in Plaxis 3D. After that finite element analyses were made. In the model tests, δmax was taken from point A (mentioned in section 3.1) of SPW. It is clearly seen in Figure 17 that numerical solutions also support this situation. Numerical analyses were performed by creating the same conditions as the model tests. *e maximum load values    Table 10. *e results obtained from the numerical analyses for δmax values were compared with the results obtained from the model tests, and the comparison can be seen in Figures 19 and 20.

Conclusions
In this research, SPW deformations (δmax) and the bearing capacity of the foundations (q ult ) close to SPW were investigated by laboratory experiments and numerical analysis.
(i) When penetration depth (Hp) increases, δmax decreases on average by 81% and q ult increases on average by 27%. (ii) When penetration depth (Hp) decreases, δmax increases on average by 44%, and q ult decreases on average by 38%. (iii) As the distance between the foundation and the retaining structure (L) increases, δmax decreases by approximately 121% and q ult increases by approximately 16%. (iv) As the distance (L) between the foundation and the retaining structure decreases, δmax increases by an average of 55%, and q ult decreases by an average of 19%. In the present study, the maximum value of L was taken as 4 B/3 due to the geometric conditions of the test system. It is recommended that the effect of L on δmax and q ult can be determined in more detail when different L values are tried in future studies.

Data Availability
*e data used to support the findings of this study are included within the article.