PREFABRICATRED VERTICAL DRAIN IMPROVED SOFT SOIL USING THREE-DIMENSIONAL FINITE ELEMENT

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REKAYASA SIPIL / Volume 15, No.2 – 2021 ISSN 1978 - 5658 150

PREFABRICATRED VERTICAL DRAIN IMPROVED SOFT SOIL USING THREE-DIMENSIONAL FINITE ELEMENT

METHOD

Gilang Ramadan K.

^*1

, Yulvi Zaika

²

, Harimurti

²

1

Student, Magister’s Program, Department of Civil Engineering, Faculty of Engineering, Brawijaya University

2

Lecturer, Department of Civil Engineering, Faculty of Engineering, Brawijaya University

*Correspondence: [email protected]

ABSTRACT

The subgrade layer of freeway construction in East Java contains high compressibility of soft soil with 24.5 m depth and 10.2 m height of the embankment. It is necessary to stabilize using PVD by accelerating the process of consolidation to increase its bearing capacity. In this study, 3D FEM programming is used to analyze the consolidation in pursuing to compare with the analytical results. 3D FEM shows the settlement without PVD is 0.834 m with excess pore water -4 kN/m², while using PVD the settlement 0.819 m with excess pore pressure -8 kN/m². For the analytical results, both variations indicate the settlement 0.787 m. It’s because the FEM discretization analyzed in 3D gives more accurate results.

Keywords: Soft soil, PVD, Degree of Consolidation, 3D FEM

1. INTRODUTION

Cohesive soils such as soft soils mostly consist of slightly grains of loam and silt [1].

The properties of soft soil have low shear strength, high compressibility, low coefficient permeability, and have a low bearing capacity [2]. Cohesive clay is classified as soft soil if it has a carrying capacity of less than 0.5 kg/cm² and a standard penetration test value is less than 4 (N-value<4) [3]. The high compressibility of soft soil causes road and building construction to be damaged. Thus, it requires soil stabilization to prevent structural failure.

One of the improved methods commonly used in Indonesia to stabilize soft soils is by using Prefabricated Vertical Drain (PVD). The functions of PVD as a vertical drain in the soil are an effective method by accelerating the consolidation process of soft soil. Previous research has analyzed the settlement of soft soil on the Gempol-Pasuruan freeway with data of SPT shows the depth of soft soil is 11-13 m [4].

The purpose of this study is to analyze the consolidation of soft soil using 3D FEM. In

saturated soft soils that are stabilized by PVD, the consolidation around the actual soil is 3 dimensional. Therefore, a proper design of an embankment involving discrete vertical drains requires a full 3D analysis [5]. The behavior of 3D embankments on soft soils with a vertical drain will be analyzed using a simple method by Chai et al. (2001). The procedure used an equivalent vertical hydraulic conductivity to represent the drainage by PVDs [5]. The final result of the 3D Finite Element Method program will show of settlement (S) and the degree of consolidation of soft soil, with and without the stabilization of PVD.

2. STUDY LITERATURE

2.1 Time Rate of Consolidation

The primary consolidation settlement occurs due to an increasing effective stress on soil can be calculated by Equation 1.

However, these calculations do not provide any information regarding the time rate of the consolidation process.

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151 REKAYASA SIPIL / Volume 15, No.2 – 2021 ISSN 1978 - 5658

' 0 '

1 log

c o

c

o

C p p

S H

e p

= + 

+ (1)

The equation for the time rate of consolidation giving to Terzaghi’s is:

v 2

v t T H

= C (2)

where, t = time of consolidation (s), Tv = time factor of vertical direction, H = length of drainage path, Cv = coefficient of consolidation in the vertical direction (cm²/s).

The value of time factor (Tv) can be estimated by the following graph below.

Figure 1. Time Factor for Average Degree of Consolidation

The degree of consolidation is evaluated by the ratio between pore pressure that decreases after a period of dissipation to the initial excess pore pressure during the consolidation process. Also known as the percentage of pore water pressure dissipation.

2.2

A Simple Method for Analyzing PVD Improved Soft Soil

Chai (2001) developed an analysis of the degree of consolidation by increasing the mass of hydraulic conductivity, which has different formulas for the vertical and horizontal degree of consolidation. The aim is to make the PVD analysis in the form of axisymmetric equivalent to a plane strain, for further analysis in the finite element method modeling.

Generally, vertical drainage increases the hydraulic conductivity of the subsoil mass in the vertical direction. Therefore, it is logical to try to establish a value of vertical hydraulic conductivity, which approximately represents

both the effect of vertical drainage of natural subsoil and the influence of radial drainage due to the existence of PVD [5].

The equivalent of the vertical hydraulic conductivity kve is derived based on the equal average degree of consolidation under 1D conditions. Carrillo's theoretical solution (1942) is used to combine the vertical and radial drainage effects.

1 (1 )(1 )

vr v r

U = − −U −U (3)

where; Uvr = average degree of consolidation of PVD improved subsoil, Ur = average degree of consolidation due to radial drainage, Uv = average degree of consolidation due to vertical drainage. The value of Ur is calculated by Hansbo's solution (1981), which was derived based on equal vertical strain assumption and neglected the natural vertical drainage of natural subsoil.

1 exp 8

r h

U T



 

= − − 

  (4) where; Th = time factor of horizontal direction

=, C t D_h / ², Ch = coefficient of consolidation in horizontal direction, D = diameter of unit cell, and. With value of μ:

22 ln ln( ) 3

4 3

h h

s w

k l k

n s

s k q

= + − + (5)

where; n = D/dw (dw= equivalent diameter of the drain), s = ds/dw (ds = diameter of smear zone), kh and ks= horizontal hydraulic conductivity of natural soil and smear zone, l = drainage length, and qw = discharge capacity of PVD.

To obtain a simple expression for the equivalent vertical hydraulic conductivity kve, an approximation of Terzaghi’s solution for the average degree of vertical consolidation is proposed

1 exp( )

v d v

U = − −C T (6)

where; Cd = constant. Some assumptions were made to determine the value of Cd, the solution for the equivalent vertical hydraulic conductivity by Chai (2001) is:

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2 2

1 2.5 ^h

ve v

v l k

k k

D k



 

 

= + 

 

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where kv = hydraulic conductivity in the vertical direction and other parameters are defined previously.

It needs to be emphasized that the 1D condition is used to obtain the kve value, which does not mean that the proposed method can only be used in 1D analysis. A PVD-improved zone with a vertical hydraulic conductivity of kve and horizontal value of kh can be analyzed in 1D, 2D, or 3D, depending on the requirements [6].

2.3

Utilization of PVD for Stabilization

Soil stabilization using PVD can be accelerating the settlement of the soil due to loads. In the design of PVD, the spacing factor and the coefficient of consolidation use the horizontal direction values. One of the most commonly used methods is Baron's (Baron's Equation) method:

2 1

8 _h ⁿln1 _h

t D F

C U

= − (8)

where; Fn = drainage factor spacing = ln(D/dw)-¾; dw = (a+b)/2; a = width of PVD (m); b = thickness of PVD (m); Uh = degree of consolidation (%).

Generally, PVD installs in a square or triangle pattern. With the area of influence, the equivalent diameter of the quadrilateral D = 1.13S and the triangular pattern D = 1.05S, where S is the spacing or distance between PVDs.

Figure 2. Square and Triangle Pattern of PVD

The theory of consolidation with radial direction drainage assumes that pore water in the soil is drained by vertical drainage with a circular cross-section. The radial consolidation equation considers the vertical drainage diameter (dw). It is the cylinder diameter of the drainage column if the vertical drainage constructs from sand columns.

PVD that is generally a rectangular section, the vertical drainage diameter expressed in terms of the equivalent diameter shows in dw notation. The equivalent diameter of PVD defines as the diameter of the drainage circle that has the same drainage capability as PVD. In many conditions, the equivalent diameter (dw) can be considered independent of soil conditions, soil properties, and the effect of PVD installation, but only on the drainage geometry and configuration.

Figure 3. Equivalent Diameter of PVD In designing, the equivalent diameter determined by the Circumference of the vertical drainage circle = circumference of drainage rectangle, then πdw = 2(a+b). Thus, the equivalent diameter

2( )

w a b

d 

= + (9)

where; a = width section of PVD, b = PVD thickness section.

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3. METHODOLOGY

3.1 Field Data

The required data in this study are obtained on the Gempol – Pasuruan freeway STA 32 ± 000 consist of SPT, and the settlement plate tests.

Figure 4. Research Location of Gempol Pasuruan Freeway STA 32 ± 000 3.2 Analysis Data Method

From the obtained data, the analysis of the degree of consolidation will be calculated based on Equation 3 with the embankment load according to field conditions. The value of kve will assign as input in the numerical programming of the 3D finite element method.

Its use for the stabilization of PVD because of the smear zone during the installation of the mandrel. The distance between PVDs in this study is 1 meter with a triangular pattern [7].

The soil parameters for each layer will be summarized shown in Table 1.

Table 1. Soil Properties Data

Parameter Name Unit Value

Material Model Model -

Material Type Type -

Density ϒunsat kN/m³

ϒsat kN/m³

Permeability kx m/day

ky m/day Modulus Young (constant) Eref kN/m²

Poisson’s Ratio v -

Cohesion (constant) cref kN/m²

Shear Strength ø ^o

Compression Index Cc ^-

Swelling Index Cs ^-

Earth Pressure Coefficient K0 -

Lambda λ ^-

Kappa κ ^-

4. RESULT AND DISCUSSION

Obtained data based on the final report of the Gempol-Pasuruan freeway site plan [8]

shows that the depth of soil from the SPT data is 24.5 m. The depth of PVD is 13 m through 3 layers of soil which is clayey silt with a little sand, sandy silt with gravel, and sandy clayey silt with gravel. The geometry of the embankment at the research site shows in Figure 5. The data on the settlement plate at the research location is 1.398 m.

Figure 5. Embankment and Soil Layer Geometry

4.1 Input Data Parameter

Soil parameters obtained from secondary data [7] is used as input for soil parameters according to the geometry of Figure 5.

The simplified method by Chai et al.

(2001) will apply in the analysis by using the value of kve from Equation 7 as the input for the PVD improved zone parameter value in 3D FEM on soft soil. From the calculation of soft soil with stabilization of PVD, it can be determined the value of µ = 1.9784; kh = 0.000978 m/day; kv = 0.000078 m/day; ks = 0.0001958 m/day; De = 1.05 m; dw = 0.0661 m; dmandrel = 0.00812 m. Thus, the value of kve is 0.04748 m/day that will be applied as input parameters in the PVD improved zone.

Mandrel causes diameter if smear (ds) and smear permeability coefficient (ks) to appear.

The greater the smear zone that occurs around soft soil during the inclusion of PVD by the mandrel, the smaller the permeability coefficient of a smear.

4.2 Degree of Consolidation Analysis The calculation of the degree of consolidation is applied to determine the time for consolidation settlement. From Equation 3, the average degree of consolidation (Uv) with and without PVD and using PVD presented in Figure 6.

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Figure 6. Analytical Degree of Consolidation With and Without Using PVD

Analytical result shows the 90% degree of consolidation on soft soil without the stabilization of PVD sustains a consolidation process for 10065 days (± 28 years) with a settlement of 0.787 m. Meanwhile, with improvements using PVD, there is a very significant acceleration of the consolidation time from its original condition. It took 40 days (1.3 months) to achieve a settlement of 0.787 m.

It means that a 90% degree of consolidation has been reached on the 40 day with the same settlement as the original soil conditions.

Characteristics of soft soils that easily bind water and are difficult to release cause a long time for soft soils to become compressed.

Stabilization with PVD provides a faster time with the same amount of reduction from the original condition. Due to the way PVD works, which absorb pore water radially due to the load on the embankment. Then it will be continued vertically, making it easier for the soil grains to compress quickly with each other.

4.3 Finite Element Method Analysis

The geometry to be used is following Figure 5 with the parameters used based on Table 2. Chai et al. (2001) assume PVD as the zone of influence in his analysis so that in the programming analysis it does not require PVD as a vertical drain otherwise kve as the value of the PVD improved zone on soil and already including the effect of smear that cause by the mandrel.

The meshing in finite element method programming uses numerical simulation shown in Figure 7. Because the geometry is symmetrical, only half of the embankment will show in the meshing of finite element method programming. The boundary geometry used in the finite element analysis in the horizontal direction is 100 m and 24.5 m in the vertical directions.

Referred to the Table 2 and embankment geometry (Figure 5), it will be analyzed using the 3D finite element method programming.

The numerical results obtained are not much different from the analytical results, where the difference is in the settlement and time. Based on calculation the soil needs 10265 days (28.5 years) to reach 90% consolidation without PVD and 45 days by using PVD and settlements are 0.834m and 0.819m respectively.

Table 2. Soil layer parameter

Parameter Depth (m)

0,0 – 9,0 9,0 – 11,0 11,0 - 15,5 15,5 - 20 20 – 22 22 – 24.5 - -

Layer 1 2 3 4 5 6 - -

Soil Type Clayey silt with a little sand

Sandy silt with gravel

Sandy clayey silt with gravel

Silty clay sandstone

Sand with gravel

Sandstone Embankment Sand Layer Model Material Soft Soil Hardening

Soil

Hardening Soil

Soft Soil Hardening Soil

Hardening Soil

Mohr Coulomb

Type Undrained Drained Drained Undrained Drained Drained Drained Drained

γsat (kN/m³) 15.016 17.272 19.523 15.068 20.062 17.269 16.67 21.2

γdry (kN/m³) 8.421 11.729 14.318 8.257 16.269 11.366 16 16.269

Cohesion (kN/m²) 29.883 19.61 26.48 33.34 29.42 15.69 25 29.42

Friction Angle (˚) 8.522 22 17 13 14 25 20 14

E (kN/m²) -

E50 =

2343.75 E50 = 2000 -

E50 = 35000 E50 = 35000

30000 40000

Eoed = 1875 Eoed = 2500 Eoed = 35000 Eoed = 35000 Eur = 10000 Eur = 6000 Eur = 105000 Eur = 105000

kx (m/day) 0.000978 1 1 0.2497 1.063 7.128 0.0864 8.64

ky (m/day) 0.000078 1 1 0.2497 1.063 7.128 0.0864 8.64

Cc 0.0345 0.184 0.138 0.1725 0.0099 0.0099 - -

Cs 0.0043 0.031 0.052 0.0173 0.003 0.003 - -

K0 0.85 0.5 0.7 0.775 0.758 0.577 - -

λ 0.01 - - 0.050 - - - -

κ 0.0025 - - 0.01 - - - -

Poisson Ratio (ν) 0.15 0.2 0.2 0.15 0.2 0.2 0.2 0.2

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(a) Without PVD

(b) With PVD

Figure 7. Mesh Without and By Using PVD on The Soil

Figure 8. Excess Pore Water With and Without PVD Using 3D FEM Figure 8 shows that excess pore water in stabilization with PVD is higher in value than soil without using PVD. Dissimilar with the results of the settlement of soft soils that have almost the same issue, excess pore water shows a different value and time. The output from 3D FEM shows a sizable difference between the two of -4 kN/m². It proves that the material of PVD can absorb water laterally around the soft soil due to the load and then flow vertically.

(a) Without PVD

(b) With PVD

Figure 9. Total Deformation of Embankment

Figure 10 shows the comparison results of the settlement in analytical and numerical methods with a 90% degree of consolidation on soft soil for conditions with and without stabilization of PVD.

The comparison results show that using the 3D finite element method programming, without using PVD shows that a more dominant magnitude of settlement with the difference of time is 200 days. The same is the case with using PVD with a time difference of 5 days.

Figure 10. Comparison of Settlement with and Without PVD on Soft Soils

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5. CONCLUSION

The function of PVD as a vertical drain in improving soft clay soils is an efficient alternative. It proves that after stabilization, the soil has consolidated at early time.

Also, the 3D finite element method program showed approximately the same settlement results compared to the analytical method (difference in values ± 0.04 m).

Based on a simple method for PVD modeling in soil improvement by Chai et al.

(2001), the analysis in 3D finite element method programming will be more efficient.

Because by assuming the value of kve as the zone of influence of PVD without needing to describe it in the analysis geometry for 3D modeling. It can speed up the calculation process due to the reduction of elements and nodes in the meshing geometry of the soft soil layers.

The analyzed FE in 3D or 2D will evaluated in the same result if equivalent permeability used in x and y direction.

6. REFERENCES

[1] V.O.Iskandar, Priadi E, Aswandi. 2013.

Perilaku Pengembang Tanah Lempung Akibat Pengurangan Beban di Bangunan Benua Idah Pontianak. Universitas Tanjungpura.

[2] Siska, H. N., & Yakin, Y. A. (2016).

Karakterisasi Sifat Fisis dan Mekanis Tanah Lunak di Gedebage (Hal. 44-55). RekaRacana:

Jurnal Teknil Sipil, 2(4), 44.

[3] Terzaghi, K., Peck, R. B., & Mesri, G. (1967).

Soil Mechanics in Engineering Practice, John Wiley & Sons. Inc., New York.

[4] Zaika, Y., & Rachmansyah, A. (2019, October).

Geotechnical behaviour of soft soil in East Java, Indonesia. In IOP Conference Series: Materials Science and Engineering (Vol. 615, No. 1, p.

012043). IOP Publishing.

[5] Yildiz, A., & Karstunen, M. (2009).

Three-dimensional analyses of PVD-improved soft soils. Geotechnics of soft soils: focus on ground improvement, 197-203.

[6] Chai, J. C., Shen, S. L., Miura, N., & Bergado, D. T. (2001). Simple method of modeling PVD-improved subsoil. Journal of Geotechnical and Geoenvironmental Engineering, 127(11), 965-972.

[7] Laporan Akhir (2017). Konsultan Teknik &

Advis Penanganan Tanah Lunak pada Jalan Tol Gempol-Pasuruan STA.28+000 sampai dengan 34+000.