Study on the depth of cantilever sheet pile wall based on the type of soil where sheet pile embedded

The northern part of Semarang is known as a region having a thick depth of soft clay. In the construction of sheet pile wall for Terboyo Retention Pond dike Semarang must take into account stability aspect and financial aspect. The characteristic of granular soil is different from that of cohesive soil, and the stability aspect relies on the type of soil. This study aims to investigate the influence of the type of soils where sheet pile embedded to the theoretical depth of cantilever sheet pile wall. This research used the soil data from Terboyo Retention Pond of Semarang. Modelling of wall was differentiated based on the type of soil where sheet pile embedded whereas the type of soil above the dredge line was the same. Two type of soils where sheet pile embedded, clay and sand were modelled. The variation of soil parameters of both soils was also modelled. Safety factor for clay soil was taken 1.5. The result shows that different soil in which wall embedded give significant difference of length of sheet pile. Based on N-SPT, with the same N-SPT value theoretical depth of cantilever sheet pile wall in sand soil is deeper than that of in clay soil.


Background
For years, flooding has been a huge problem in Semarang especially in the region of Kaligawe and Genuk.One of solutions to overcome flooding has been used in Semarang is a polder system.This system includes drainage, retention pond, and water pump.The retention pond that functions to collect water is enclosed by embankment (barrier) known as dike.The type of dike used for the retention pond can vary, for instance gravity wall and sheet pile wall.The Terboyo Retention Pond dike is made from sheet pile wall and the type of sheet pile wall used is cantilever sheet pile wall.
The stability of the sheet pile wall depends on the length of wall embedded in soil and the force of anchor.The wall can be long or not depend on surcharge on the soil behind the wall, the type and the density of soil behind the wall, and the type of soil where the wall embedded.Cohesive soil and cohesionless soil have different characteristic that can effect on the different length of sheet pile wall even if surcharge, the density and the type of soil behind the wall is the same condition.
From the result of SPT soil test, the soil of Terboyo Retention Pond can be classified as soft clay to medium clay with N-SPT ranges from 2 to 8. In some cases, failure of building resting on soft clay owe to its low bearing capacity such as settlement of the approaching bridge [1].This case was due to the problem of imperfect soil consolidation process.According to TA, Ooi, and Chan CB [2], many piled bridge abutments lying on soft clay experienced failures during earth embankment construction.
Several studies on the stability of sheet pile wall on cohesive soil or cohesionless soil have been conducted such as Mahdi and Ebid [3], Akan [4], Arifin [5], and Chalid and Lubis [6].These studies analyzed the stability of sheet pile wall solely on one type of soil.However, this study aims to compare the embedment of cantilever sheet pile wall in cohesive soil and granular soil.

Research method
This study was conducted by taking a case in Terboyo Retention Pond located in the region of Kaligawe, Gayamsari Subdistrict Semarang, as shown in Figure 1.The total area of Terboyo Retention Pond is 225 hectares and all the area is enclosed with dike.Soil data used for this research was soil data from the Terboyo Retention Pond.The cross section of Terboyo Retention Pond can be seen in Figure 2. From Figure 2 it can be seen in the sheet pile wall next to the embankment (this study case) that the total length of sheet pile wall is 18 m and about 16 m wall is embedded in clay soil.Taking into account safety factor 1.60 for clay soil gives the theoretical depth of sheet pile wall embedded in clay soil equals to 10 m.Table 1 presents soil parameters of Terboyo Retention Pond which is located in Gayamsari Subdistrict.As seen in Table 1 N-SPT value for the soil depth 0 m -24 m ranges from 2 to 8, and the soil is classified as clay soil and can be described as follows: medium clay (depth from 0 to 4 m), soft clay (from 4 m to 14 m), medium clay (from 14 m to 24 m), and stiff clay (from 24 m to 50 m) According to N-SPT value, ground soil of Terboyo Retention Pond contains soft clay reaching 10 m from the depth 4 m to 14 m.However, the end of sheet pile wall stands in medium clay soil with average N-SPT value less than 8.This soil data is in line with the study conducted by Rochim and Fitriyana [8] that site class of region in Gayamsari Subdistrict is soft soil.
Several methods are used to design the depth of wall embedded in soil such as Coduto [9], Das [10], among others.Analysis of sheet pile wall was based on the diagrams of soil pressure working on the wall for clay soil and sand soil as displayed in Figure 3.As seen in Figure 3 soil pressure diagram above the dredge line is the same for sand soil whereas soil pressure diagram under the dredge line is different for sand soil (left side) and clay soil (right side).This difference leads to a question which soil will give longer sheet pile wall embedded in soil.As exact surcharge value and cohesion value to obtain 16 m deep sheet pile wall are not known so that a back analysis was carried out.The back analysis was conducted by choosing the right value of surcharge and shear strength parameters c and  in order to fit the total length of sheet pile 18 m.In this study, the calculation for soil clay above the dredge line does not take into account cohesion value but only internal friction angle (IFA) value in order to obtain greater soil pressure.It means that soil above the dredge line is modeled as cohesionless soil (sand soil).The cohesion value of soil under the dredge line for back analysis was calculated based on N-SPT value according to Terzaghi's theory [13].Afterward these values from the back analysis were used as an input for modeling to find the length of sheet pile wall when it is embedded in various soils (Figure 4).The soil where sheet pile wall was embedded was modeled as clay soil and sand soil.However, soil above the dredge line was modeled as cohesionless soil (sand soil) and the surcharge applied on the soil was also the same condition.Cantilever sheet pile wall model and soil parameter for analysis are presented in Figure 4 and Table 2 respectively.With this scope of problem then the length of sheet pile wall was compared.4. From back analysis, surcharge and cohesion value of soil 2 were obtained.Afterward using variation of cohesion value in soil 2 from 12 kPa to 50 kPa is conducted in order to do regression by plotting cohesion value versus the depth of wall in clay soil.With the same method for soil 3, using variation of internal friction angle (IFA) from 10 degrees to 50 degrees is conducted in order to do regression by plotting IFA value versus the embedment depth of wall in sand soil.

Results and discussion
This section firstly explains back analysis to obtain surcharge value and cohesion value in soil 2. Then in the second section using variation of cohesion values for soil 2 and internal friction angle (IFA) values for soil 3, the comparison of the theoretical embedment depth of cantilever wall in clay soil and sand soil is conducted.

Back Analysis
From back analysis, to fit the theoretical embedment depth of wall in clay soil equal to 10 m, it is found that surcharge value 19.8 kPa and cohesion value 13.33 kPa (it is taken from average N-SPT 2).The surcharge value was determined by calculating the embankment height (1.2 m) multiply by the soil unit weight (16.5 kN/m 3 ) (see Figure 2).The surcharge and cohesion values were then used as input in model of cantilever wall.The soil parameter from back analysis can be seen in Table 3. Figure 5 shows plot of the embedment depth in clay soil versus cohesion value.The relation between the embedment depth of wall and cohesion creates two slopes, the first slope created from cohesion value 10 kPa to 20 kPa whereas the second slope from cohesion 20 kPa to 50 kPa.It can be seen that a higher cohesion value gives to lower depth of wall.In the first slope with small difference of cohesion value gives significant difference in depth of wall.However, in the second slope shows that difference in depth of wall is not significant for high cohesion value.It means that there will be a minimum value of cohesion which the increase of cohesion value will not give any difference.It can be noticed from the second slope that cohesion value 45 kPa and 50 kPa do not give difference in depth of wall.The linear regression line for the two slopes is displayed in Figure 6.The R-squared value of both slopes are 0.827 and 0.878 that it is categorized as a high level of correlation.According to Chin [13], a R-squared value above 0.67 is seen as showing a strong correlation.The equation derived from the linear regression is y = 1.7787x -35,284 for cohesion value below 20 kPa and y = 0.0743x -5 for cohesion value above 20 kPa.The choice of cohesion value of 20 kPa here is because slope change occurs around cohesion 20 kPa.

Figure 6. Linear regression line of clay soil
Figure 7 shows plot of the embedment depth of wall in sand soil versus IFA value.The relation between the depth of wall and IFA value creates two slopes, the first slope created from IFA value 10 degree to 25 degree whereas the second slope from IFA 25 degree to 50 degree.It can be seen that a higher IFA value gives to lower depth of wall.In the first slope, small IFA value with increment 5 degrees gives significant difference in depth of wall.However, in the second slope with the same increment 5 degrees does not gives significant difference in sheet pile wall depth.It means that there is a minimum IFA value which the increase of that will not give difference, that is 45 degree.
The linear regression line for the two slopes is presented in Figure 8.The R-squared value of both slopes above 0.90 that it is seen as showing a high level correlation.The equation derived from the linear regression is y = 0.8668x -28,009 for IFA value below 25 degrees and y = 0.1854x -12.875 for IFA value above 25 degree.6 and Table 7 present correlation between N-SPT value and the theoretical depth of sheet pile embedded in clay soil and sand soil respectively.N-SPT value in clay soil is calculated according to the formula of Terzaghi and Peck [13], whereas N-SPT value in sand soil is calculated according to Uchida and Hatanaka [15].In Table 6 can be seen that small range of N-SPT value from 2 to 8 gives big range of the depth of sheet pile wall embedded in clay soil.However in Table 7 big range of N-SPT value from 2 to 8 gives small range of the depth of wall embedded in sand soil.As comparison from the two soils, N-SPT value from 2 to 8 gives 15.3 m difference in depth in clay soil and 1.4 m in sand soil.Moreover in sand soil, great range of N-SPT value from 2 to 64 only gives 4.7 m difference in depth.There is a minimum IFA value (45 degree) in which the increase of that will not give significance in depth difference.Table 6.N-SPT versus the depth of sheet pile wall embedded in clay soil (D) N-SPT is calculated according to Terzaghi and Peck [13] Table 7. N-SPT versus the depth of sheet pile wall embedded in sand soil (D) N-SPT is calculated according to Uchida and Hatanaka [15] Comparison of sheet pile wall depth in clay and sand soil based on N-SPT is displayed in Table 8.The graph of plotting between the depth of wall embedded in soil versus N-SPT value of clay and sand soil is presented in Figure 9.It is noticed from Figure 9 that with the same N-SPT value sand soil gives deeper sheet pile wall than clay soil.It can be summarized that the theoretical depth of wall embedded in cohesionless soil (sand soil) is deeper than that of in cohesive soil (clay soil).However, the stability of sheet pile depends on the soil where the wall embedded in.According to Chalid and Lubis [6], Powrie [16], the theoretical depth of cantilever sheet pile wall is multiplied by a factor of safety (FoS) of 1.2 (for cohesionless soil), and a FoS of 1.6 (for cohesive soil) in order to accommodate a stability.If it is noticed from Table 1, Table 6 and Table 7 the theoretical depth of wall is embedded in soft clay (for cohesive soil) and very loose sand (for cohesionless soil).Multiplying the theoretical depth by FoS of 1.2 (for cohesionless soil) and 1.6 (for cohesive soil), it is obtained that the actual depth of the walls is rested in medium soil.To reach medium soil, the embedment depth of wall in sand soil only needs a little deeper whereas that of in clay soil needs much more deeper.From this finding, even though the cantilever embedment depth of wall in cohesionless soil is deeper but its actual embedment depth of wall can be lower.

Conclusions
Higher shear strength parameters both cohesion and IFA values give lower depth of cantilever sheet pile wall.From comparison the theoretical depth of cantilever sheet pile wall according to N-SPT value, the depth of cantilever sheet pile wall embedded in cohesive soil (clay soil) is lower than that of in granular soil (sand soil).

Figure 3 .
Figure 3. Diagram of soil pressure for sand soil (left) and clay soil (right)[12]

Figure 4 .
Figure 4. Cantilever sheet pile wall model for analysis

Figure 5 .
Figure 5. Theoretical depth of wall based on cohesion value

Figure 9 .
Figure 9. Theoretical depth of sheet pile wall embedded in soil based on N-SPT value of clay and sand soil

Table 2 .
Soil parameter for sheet pile wall model Table2presents soil parameters for sheet pile wall model as seen in Figure

Table 4 .
Table 4summarizes the embedment depth of sheet pile wall in clay soil (D) based on cohesion value (c) whereas Table5summarizes the embedment depth of sheet pile wall in sand soil (D) based on IFA value ().From the two tables, there is a similarity that a lower cohesion value and IFA value give a deeper sheet pile wall embedded in soil.It is noticed from Table4and Table5that to reach the same sheet pile wall around 10 m in both clay soil and sand soil, it needs cohesion value 13.33 kPa and IFA value 21.4 degrees respectively.If it refers to soil consistency / packing, there is difference in soil consistency for the cohesion 13.33 kPa and the IFA 21.4 degrees that is soft clay and very loose sand respectively.However, in term of N-SPT value, the cohesion 13.33 kPa and the IFA 21.4 degrees have the same N-SPT value < 4. Variation of cohesion (c) versus the embedment depth of wall in clay soil (D)

Table 5 .
Variation of internal friction angle () versus the embedment depth of wall in sand soil (D)

Table 8 .
N-SPT versus the depth of sheet pile wall embedded in clay and sand soil (D)