# The Settlement Models of Deep Vacuum Dewatering Method

Authors: Feng Huang; Jianguo Lyu; Guihe Wang
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

The deep vacuum dewatering method is effective for groundwater control in projects. By now, although the vacuum consolidation in soft soil foundation treatment has been analyzed much, the settlement of deep vacuum dewatering has not been researched sufficiently. Because of the extra vacuum pressure, the settlement should be analyzed further. In this paper, the settlement models are derived and analyzed based on the 2 vacuum pressure distribution models (plane seepage model and Johnson’s model), Imai and Chai’s vacuum consolidation models, and elastic model of traditional soil mechanics. And then a project case is provided to verify the theoretical models. The results show that the proposed model is suitable to predict the settlement and provide new references for vacuum dewatering engineering.


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## Body

## 1. Introduction

Vacuum consolidation has been extensively applied [1–6] and proved very effective in improving soft ground [7, 8]. Vacuum consolidation usually applies a vacuum pressure into soil and a sealing membrane at the surface of the ground. It is very different from Terzaghi’s consolidation theory for the isotropic additional stress caused by vacuum pressure. Therefore, the settlement of soft soil foundation caused by vacuum pressure has been researched in theoretical, numerical, laboratorial, and practical ways. Chai et al. [9] proposed a method of determining the vacuum-drain consolidation based on unit cell finite element analysis results and proved the method at Tokyo Bay in Japan. Chai et al. [10] also developed a method for the consolidation of dredged mud or clayey soil deposits containing prefabricated horizontal drains (PHDs). Chen and Xiang [11] carried out a theoretical analysis of the settlement of the piles caused by vacuum treatment of the submerged layer, which indicated that the settlement caused by dewatering increased the negative frictional resistance of the pile and increased the settlement. Robinson et al. [12] studied the influence of lateral displacement of soil volumetric strain under vacuum preloading. Then, the lateral displacements of soil under different stress states were analyzed, and the prediction model of volume strain and lateral displacement was proposed, which was validated by 2 projects in China.Rujikiatkamjorn et al. [13] presented numerical analysis of a combined vacuum and surcharge preloading project in China. The simulation analyzed the settlement of the soil by modified Cam-clay model. Indraratna et al. [14] carried out the simulation of vacuum consolidation using finite element. Subsequently, the vertical displacements were predicted by the 2D and 3D numerical multidrain model. Ji et al. [15] analyzed the surface settlement of vacuum preloading of reclamation sludge foundation by using the finite difference method.Saowapakpiboon et al. [16] conducted large-scale consolidation experiments on soil samples with and without vacuum pressure, and then the geotechnical parameters of the soil were analyzed. Kianfar et al. [17] investigated the influences of the duration of application and removal of vacuum pressures on radial consolidation by using excess pore-water pressure, axial strain, and over consolidation ratio. Long et al. [18] conducted trial sections to investigate the soft ground improvement performance using different vacuum consolidation methods. Sun et al. [19] analyzed a site trial of vacuum preloading and vacuum preloading in combination with electro-osmotic. The physical mechanical properties and bearing capacity of soil after treatment were tested, which revealed the consolidation law of vacuum preloading and the combination method.Many results have been obtained and some of them were used in practice. However, the thickness of soil needs to be considered in deep well dewatering project since it is usually larger than in foundation treatment project because the dewatering wells are deep in tunnel excavation. Thus, there is a need to investigate the suitable consolidation model to predict the surface settlement of deep vacuum dewatering method. Because of the capillary force in silty and clay soil, there is still much water that cannot be drained out by the nonvacuum dewatering method. As a result, the deep vacuum dewatering wells are usually applied in tunnel and deep foundation pit excavation. However, there is no specific consolidation model by now to calculate the settlement in the deep vacuum dewatering method. In this paper, 3 methods are proposed based on Imai’s model, Chai’s model, and elastic model. Then, a project case is provided to verify the theoretical models.


## 2. Vacuum Pressure and Water Level Distribution in Vacuum Dewatering

It is needful to use the vacuum pressure distribution laws in deriving the theoretical settlement model. Therefore, 2 models of air pressure distribution in soil are proposed. One is the plane seepage model [20] and the other one is Johnson’s model [21], which are shown as equations (1) and (2), respectively:(1)p=pe−pwlnre/rwlnrre+pe,(2)p=pw1+1−pa/pw2lnr/rwlnrw/rI1/2,where r = distance from the well, p = air pressure at distance of r, pe = measured air pressure at the known distance of re, rw = the radius of the well, pw = air pressure of the well, pa = absolute ambient pressure, and rI = largest influence distance of vacuum pressure.The water level,hvac (equation (3)), in flow boundary condition has been established by the author [20]:(3)hvac=hphreatic×1+pw1+1−p0/pw2lnr/rw/lnrw/rI−1/21−p0/pw2hw2+H02−hw2lnr/rw/lnR/rwlnR/rw/9806H02−hw2lnrw/rI−1,where hphreatic = water head, R = influence radius of dewatering, p0 = atmosphere pressure, and H0 = thickness of aquifer.The water level distribution law under the vacuum pressure derived by the authors was used to calculate the final draw down of the groundwater in this paper. Then, the water level distribution models were combined to three existing consolidation models to analyze the vacuum settlement.


## 3. Modified Imai’s Method

Imai [22] proposed a method of calculating the final settlement and lateral displacement in vacuum consolidation. It is assumed that the vacuum pressure pvac keeps stable in soil and affects the active earth pressure. The increase of effective stress, Δσvac, is equal to vacuum pressure in both vertical and horizontal directions. At this time, the effective stress in horizontal direction will be reduced to Kaσv0′ (Ka is active earth pressure coefficient) from K0σv0′K0=ν′/1−ν′,ν=poisson’s ratio. The effective stresses in vacuum condition are shown as follows:(4)σv′=σv0′+pvac,(5)σh′=Kaσv0′+pvac,where σv0′ = vertical effective stress without vacuum pressure, σv′ = vertical effective stress in vacuum field, and σh′ = horizontal effective stress in vacuum field.Equations (6) and (7) present the changes of effective stress:(6)Δσv′=pvac,(7)Δσh′=pvac−K0−Kaσv0′.I is defined as the ratio of the change of effective stress in horizontal and vertical direction in the following equation:(8)I=Δσh′Δσv′=1−K0−Kaσv0′pvac.The vertical and horizontal strains in consolidation area are shown in the following equations:(9)εv=−avmvpvac,(10)εh=−ahmvpvac,where, av, ah, and mv are presented in the following equations:(11)av=1+K0−2K0I1+2K01−K0,(12)ah=I−K01+2K01−K0,(13)mv=1−2ν′1+ν′1−ν′1E′,where E = elastic modulus.It is also proposed that the lateral displacement will not happen whenI = K0. Equation (14) can be obtained at the depth where there is no lateral displacement:(14)σv0′pvac=1−K0K0−Ka.If the depth calculated from equation (14) is larger than the well’s depth, I can be changed into the following equation:(15)I=1−1−K0zH,where z = distance from ground surface and H = consolidation depth of vacuum well.Based on the groundwater distribution in flow boundary condition, the thickness of the consolidation (HImai) after draw down will be(16)HImai=H0−hvac=H0−hphreatic×1+pw1+1−p0/pw2lnr/rw/lnrw/rI−1/21−p0/pw2hw2+H02−hw2lnr/rw/lnR/rwlnR/rw/9806H02−hw2lnrw/rI−1.Thus, the vertical displacement of the soil above the water surface in vacuum dewatering method can be derived based on Imai’s method. Imai’s solution is proposed in equations (17) and (18) based on plane seepage model and Johnson’s model, respectively:(17)Δhv=−avmvpvac−planeHImai,(18)Δhv=−avmvpvac−JohnsonHImai,where pvac−plane = vacuum pressure of plane seepage model and pvac−Johnson = vacuum pressure of Johnson’s model.


## 4. Modified Chai’s Method

Chai and Carter [22] believed that when the vacuum pressure is larger than the stress needed to keep K0 status, the lateral displacement will happen and the vertical displacement will be less than that without vacuum. Otherwise, there is no lateral displacement and the settlement will not be affected. The vertical strain of vacuum consolidation model is shown as follows:(19)εv=αλ1+eln1+Δσvacσv0′,where λ = compression index, e = porosity ratio, and p = consolidation stress. α = αmin at the ground surface and α = 1 when z≥zl (zl is the depth where there is no lateral displacement) or Δσvac≤k0σv0′−σav′/1−k0. However, if(20)Δσvac≥k0σv0′−σav′1−k0,α=αmin+1−αminΔσvack0σv0′−σav′1−K0,where k0=1−sinϕOCRsinϕ, ϕ = effective friction angle, OCR = over consolidation ratio, and αmin = αmin−T or αmin = αmin−P in triaxial stress condition and plane strain condition. αmin−T = 0.8 and αmin−P=1+αmin−T/2 proposed by experimental results.


## 5. Elastic Method

Soil is assumed elastic in the elastic method. When the air extraction is performed in the dewatering well, the air pressure in the pores of the soil will be reduced. At this time, the pressure difference between the atmospheric pressure at the ground surface and the pressure in the soil leads to a compression, resulting in settlement. The soil above the original phreatic water surface can be considered as a sealing layer. Boussinesq [23] used the elastic theory to derive the analytical solution of the stress at any point M (shown in Figure 1) when the vertical concentrated force (P) acts on the surface of the semi-infinite space elastomer.Figure 1
Diagram of Boussinesq’s model.The stress and strain of Boussinesq’s method are presented in the following equations:(21)σz=3P2π⋅z3R5=3P2πR2⋅cos3β,(22)σx=3P2π⋅x2zR5+1−2ν31RR+z−2R+zx2R+z2R3−zR3,(23)σy=3P2π⋅y2zR5+1−2ν31RR+z−2R+zy2R+z2R3−zR3,(24)τxy=3P2π⋅xyzR5−1−2ν3⋅2R+zxyR+z2R3,(25)τzy=3P2π⋅yz2R5,(26)τzx=3P2π⋅z2xR5,(27)u¯=P4πGxzR3−1−2ν′xRR+z,(28)v¯=P4πGyzR3−1−2ν′yRR+z,(29)w¯=P4πGz2R3−21−ν′1R,where σx, σy, and σz are the stresses and u¯, v¯, and w¯ are displacements in x, y, and z directions, respectively; τxy, τzy, and τzx are shear stresses; G=E′/2/1+ν′; and R=x2+y2+z2.The vacuum pressure iny direction shown in equations (30) and (31) is obtained from equations (1) and (2):(30)pv=p0−pe−pwlnre/rwlnyre−pe,(31)pv=p0−pw1+1−pa/pw2lny/rwlnrw/rI1/2.The stress atM caused by Pvdy is presented in the following equation:(32)dσz=3pvz32πR5dy.It is assumed that the dewatering well is located at pointo. Then, the vertical stresses in the plane seepage model and Johnson’s model can be expressed in equations (33) and (34), respectively:(33)σz=∫0rI3Pvz3dy2πy2+z25/2=∫0rI3pw−pe/lnre/rwlny/rez32πy2+z25/2dy,(34)σz=∫0rI3Pvz3dy2πy2+z25/2=∫0rI3p0−pw1+1−pa/pw2lny/rw/lnrw/rI1/2z32πy2+z25/2dy.Then, the settlement can be calculated with the following equation:(35)S=∑i=1nσziEsi⋅Hi,where Hi = soil layer thickness. The calculation depth is where the ratio of vacuum pressure and soil gravity stress is 0.2.


## 6. Case Studies

Andinglu-Beitucheng range of line 10, Beijing subway, is taken as an in situ example. According to the geological survey, the geotechnical parameters before dewatering are proposed in Table1, the stratigraphy of the test site is shown in Figure 2, and the layout of the monitor points is shown in Figure 3.Table 1
Geotechnical parameters of the soil.
Layer
Depth (m)
ρ (g/cm3)
w (%)
e
0
λ
0.183
e
0
−
0.0021
e
0
2 [24]
Silt
3.0
1.83
21.3
0.776
0.141
Silt
4.5
1.86
23.7
0.748
0.135
Clay
7.5
1.89
24.8
0.706
0.128
Clay
10.5
1.93
20.0
0.615
0.112
Silt
12.0
1.86
17.5
0.652
0.118
Clay
15.0
1.86
18.3
0.613
0.111
Clay
16.5
1.85
20.2
0.722
0.131
Silt
18.0
1.87
18.1
0.727
0.132
Layer
Depth (m)
E
s (MPa)
φ (°)
c (kPa)
Silt
3.0
16.95
22.60
45.7
Silt
4.5
6.22
24.35
11.2
Clay
7.5
5.22
15.93
13.1
Clay
10.5
8.16
29.50
47.8
Silt
12.0
11.46
27.36
35.1
Clay
15.0
9.14
29.86
36.2
Clay
16.5
13.74
31.05
23.8
Silt
18.0
8.22
30.50
30.8Figure 2
Stratigraphy of the test site.Figure 3
Layout of monitor points. z1–z7: vacuum pressure monitor points; D: settlement monitor point.The pore pressure is kept stable after a long period of dewatering according to the monitoring work, which means the moisture content is in dynamic equilibrium status. At the same time, it is rarely possible to keep a stable water head boundary condition in a limited area. Therefore, the flow boundary condition is considered in this case. In order to analyze the settlement, the vacuum dewatering is operated for more than 5 months. The settlement measured was 5.8 mm. The vacuum pressure measured in dewatering well was 13.5 kPa. The water depth is 10.75 m and 18.13 m, respectively. The thickness,H0, of the 1st phreatic aquifer was 4.25 m while the 2nd was 4.37 m.In the field tests, the sensors were put into the drilled hole and buried. And then the gauges were connected to the sensors’ wires. The settlement measuring instrument was fixed on the ground, and the settlements were recorded by electronic total station (ETS). A fixed point was marked firstly and then the changes in distance between the fixed point and the measuring point were measured over time.The settlement versus time is shown in Figure4.Figure 4
Surface settlement versus time.The measured and calculated settlement results are shown in Tables2–6 and Figure 5.Table 2
Settlement of modified Imai’s model (mm).
Measurement
Plane seepage model
Johnson’s model
5.80
8.20
8.40Table 3
Settlement of modified Chai’s model (mm).
Measurement
Plane seepage model
Johnson’s model
5.80
3.70
3.68Table 4
Settlement of the elastic model (mm).
Measurement
Plane seepage model
Johnson’s model
5.80
5.322
5.321Table 5
Settlement of the plane seepage model (mm).
Measurement
Imai’s model
Chai’s model
Elastic model
5.80
8.20
3.70
5.322Table 6
Settlement of Johnson’s model (mm).
Measurement
Imai’s model
Chai’s model
Elastic model
5.80
8.40
3.68
5.321Figure 5
Results of theoretical analysis.It can be seen from Table2 that the results of Imai’s model are larger than the measured value. It is believed that it is safe for the real project because the theoretical results are larger than the measured one, which shows that the modified Imai’s model is suitable to predict the settlement of vacuum dewatering. In Chai’s model, the theoretical results are smaller than the measured ones because the model considers the lateral displacement which restricts the vertical displacement. The results of elastic model in Table 4 show that the difference between theoretical and measured values is much smaller than the other two methods, which illustrates that the soil can be assumed as elastic medium in calculating settlement. The settlements caused by vacuum pressure from equations (33) and (34) are 0.112 mm and 0.111 mm, respectively. It can be seen from the results that the extra displacement by vacuum pressure is small enough to be neglected in real projects according to the elastic model. Thus, the main settlement of the soil is caused by the final drawing down of the water. However, the result of theoretical method is a little smaller than the measured value, so it is safe for the real project to modify the theoretical result with a coefficient larger than 1 according to experience.


## 7. Conclusion

This paper proposed 3 methods to predict the settlement of vacuum dewatering, which provide optional references for engineering.Modified Imai’s model is suggested to predict the settlement of vacuum dewatering project because of the adequate safety reserve. Modified Chai’s model is suitable for the soft soil consolidation because the soft soil is sensitive to the vacuum pressure in horizontal direction, which will restrict the vertical consolidation ratio. When the soil is assumed to elastic, the elastic model is suggested. The elastic model provided the best prediction at this site but the other models may perform better in different ground conditions, which will require checking with further analysis.



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*Source: 5329795-2019-03-14.xml*