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Numerical modelling of soft ground improvement by vacuum preloading considering the varying coefficient of permeability
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Numerical modelling of soft ground improvement by vacuum preloading considering the varying coefficient of permeability
Increasing the accuracy of numerical prediction of vacuum preloading methods is very urgent to the geotechnical design engineers. This paper describes the application of the finite-element program method incorporating the varying coefficient of permeability with changes in suction (like the variation of permeability in unsaturated soil) to increasing the accuracy of numerical prediction of an axisymmetric single vacuum wellpoint and one case history with prefabricated vertical drains combined with vacuum preloading.
The axisymmetric single vacuum wellpoint was modelled using four numerical models: Model 1 with the hydraulic permeability of saturated soil, Model 2 with a thin layer of unsaturated elements activated at the vacuum well boundary, Mode 3 where hydraulic conductivity function was defined as permeability of unsaturated soil, Model 4 where vacuum pressure value remained a constant along the vacuum well drain. Afterward, the case history was modelled using two numerical models: one was created to verify input parameters, and the other was with the application of the varying coefficient of permeability with changes in suction. The results obtained by comparing all the numerical models data with the measured data indicate that the proposed method improved the accuracy of numerical prediction and using the exact distribution of vacuum pressure value or constant vacuum pressure value along the vacuum wellpoint did not make a significant difference in the numerical prediction in the case of shallow vacuum wellpoint.
Keywords: Soft ground, Vacuum consolidation, Vertical drain, Vacuum wellpoint systems, Finite element method
Introduction
The coastal regions always contain very soft clays that have low bearing capacity, low permeability and high compressibility.
These soft clays are challenges for the geotechnical design engineers. Strengthening the very soft clays is in urgent need of a rapid and effective treatment method because conven- tional methods, such as dynamic compaction and preloading, are unsuitable for these kinds of grounds. A system of vertical drains combined with vacuum preloading is an effective and suitable method to accelerate soft soil consolidation by pro- moting radial flow (Indraratna et al. 2005a). Since the intro- duction of vacuum preloading by Kjellmann (1952), vacuum preloading method has been applying to many soft soils areas all over the world (Bergado et al. 1998; Chai et al. 2010; Chu et al. 2000; Indraratna et al. 2011; Long et al. 2015; Quang and Giao 2014; Shang et al. 1998; Shang and Tang 2000; Yan and
Chu 2005), thus, it is of interest to many scholars in geotech- nical engineering. This method accelerates the consolidation of the soft clay, enhances the shear strength and the bearing capacity of soft ground. Further, the distribution of the vacuum pressure on the ground surface and along the drains reduces the lateral displacements and the surcharge height; therefore, it also enhances the embankment stability.
The development of computer technology makes the FEA method become a useful and efficient tool for modelling the sys- tem of vertical drains combined with vacuum preloading (Chai et al. 2013; Chai et al. 2009; Duong et al. 2012; Ghandeharioon et al. 2011; Indraratna and Redana 2000; Le et al. 2015; Ong et al. 2012; Rujikiatkamjorn et al. 2007; Saowapakpiboon et al. 2011; Tran and Mitachi 2008; Wu and Hu 2013). It can model cases of complex geometries, loadings, material prop- erties where analytical solutions are not easy to obtain. To make the numerical predictions more accurate, material prop- erties, such as soil mechanic models and permeability laws, have been modified for simulating the consolidation process of soil improved by vacuum preloading. Tarefder et al. (2009)
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to successfully predict the field behaviour of a full-scale test embankment constructed. Indraratna et al. (2005b) presented a Darcian-based analytical model with the effects of a varying coefficient of horizontal permeability and coefficient of com- pressibility during the consolidation process. Indraratna et al.
(2013) based on a non-linear relationship between the flow velocity and hydraulic gradient, proposed a radial consolida- tion model incorporating the effects of vacuum preloading.
Toshifumi et al. (2014) presented a numerical analysis using an elasto-plastic finite element program (FEM) for soil–water- coupled problems, incorporating the SYS Cam-clay. Sun et al.
(2015) introduced a plain strain FEM program that was coded with the application of the non-linearity constitutive relation Duncan–Chang’s model and the non-linear permeability law into the Biot’s consolidation theory.
In short, the suitability of using the permeability laws and the varying coefficient of permeability is very impor- tant in increasing the accuracy of numerical predictions.
In this paper, the FEM method incorporating the varying coefficient of permeability with changes in suction (like the permeability of unsaturated soil) was proposed to simulate the vacuum consolidation process. An axisymmetric single vacuum wellpoint and one case history of PVD incorporating vacuum preloading were analyzed by using four numeri- cal models and two numerical models, respectively. The proposed method was verified and the relative conclusions would be drawn by comparing the numerical predictions with the measured data.
Proposed method
Most scholars have pointed out that the reason of the field data being smaller than the data of numerical predictions is due to the increase of permeability in smear zone or the clog that occurred in vertical drains or the air leakage, etc. But it can also happen during laboratory test when the testing process can avoid these influences. Indraratna et al. (2004) described the effect of unsaturation at a drain boundary on the behaviour of a single prefabricated vertical drain sub- jected to vacuum preloading based on a two-dimensional plane strain finite-element model, and the results indicate that applying an unsaturated soil layer adjacent to a PVD improved the accuracy of numerical predictions. The unsatu- rated soil layer retarded the pore pressure dissipation and decreased the settlement value.
The thickness of unsaturated soil layer affects the numer- ical model results; however, defining it is very difficult.
Furthermore, unsaturated soil layer at a drain boundary of a single prefabricated vertical drain, which occurred due to man- drel withdrawal, under the surcharge and vacuum preloading might revert to saturated soil again. Therefore, a reasonable way to improve the accuracy of numerical predictions is to assume that the soil hydraulic conductivity under the vacuum preload- ing is similar to the permeability of unsaturated soil. And it is interesting that the negative value of pore water pressure of the soil subjected to the vacuum preloading is very similar to the pore water pressure value of the unsaturated soil. Hence, it makes the proposed method more solid.
Verification of the proposed method via finite-element model
Axisymmetric single vacuum wellpoint
Laboratory testing
The laboratory test was conducted in a vacuum-surcharge consolidation apparatus which was designed and installed at China University of Geosciences (Beijing) (Vu et al. 2016). The schematic illustration of the vacuum-surcharge consolidation apparatus is shown in Fig. 1. The sample tank was made of polymethyl methacrylate with dimensions of 1.0 m in height, 0.44 m in internal diameter and 0.5 m in outer diameter. The top and the bottom pedestal, made of stainless steel with 30 mm thickness, were connected by eight steel rods. The piston loading system consisted of a hollow shaft with 150 mm out- side diameter and a piston with 40 mm thickness. A guide was wrapped around the shaft to enable the piston moving in the straightway without tilting. In order to avoid clogging problems of the loading piston, geotextiles was used at the top of soil specimen. Synthetic rubber ‘O’ rings were useful to seal the small gaps among all parts such as the cylinder cell and the piston, the top pedestal and the shaft, the shaft and the guide.
The ‘O’ rings’ and the internal surface of the chamber were also covered with grease to increase lubrication. A natural rubber membrane was pumped up to create the surcharge pressure on the soil specimen. Vacuum generator was connected to the air pump to generate the vacuum pressure. The vacuum pressure was transmitted to the vacuum wellpoint after it got through a small and special cylindrical tank, which can separate the water and the air. The vacuum wellpoint was a PVC tube, with 25 mm outside diameter and 650mm length, surrounded by very coarse sand. The horizontal displacement of the vacuum well was restricted by wrapping the very coarse sand in the stain- less steel net. Geotextiles were used at the wellpoint filter and the stainless steel net to prevent the influence of the clogging problems during the test. A dial gauge, located at the top of the shaft, was used to measured settlement. The distribution of the vacuum pressure in the vacuum well was investigated by two vacuum gauges. The surcharge loading pressure value was measure by a pressure gauge. Six piezometers were connected to a digital data logger to monitor the pore water pressure at various points in the reconstituted specimen soil during the test. The soil samples were collected from 1.0 to 2.0 m depth at TianJin Province of China, about 120 km southeast of Beijing Capital. At the laboratory, the water content was adjusted to 1.2 times of the clay samples’ saturation limit by mixing soil samples with sufficient amount of water in a mechanical mixer.
A consolidation pressure 10 kPa was applied to preparing the reconstituted specimens. Soil properties of reconstituted clay sample are shown in Table 1. Test loading scheme is listed in Table 2.
Numerical modelling
In many past studies, vacuum pressure application has been simulated by simply fixing the negative pore pressure along the drains boundary (Indraratna et al. 2004), thus, in this study,
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the vacuum pressure distribution was simulated by fixing the negative pore pressure at the vacuum wells boundary. The data of the laboratory test, which was conducted by Vu et al. (2016),
kPa) was at wellpoint filter and the minimum value of the vac- uum pressure (45 kPa) was at the top of the vacuum well. Four models were examined:
Model 1 – The minimum value of the negative pore water pressure (45 kPa) was at the top of the vacuum well. Because the vacuum pressure value varied linearly along the vacuum well so the maximum value of the negative pore water pressure (50 kPa) was at the wellpoint filter (see Fig. 2). The hydrau- lic conductivity function was defined as the permeability of saturated soil (khi = 5.06E-07 cm/s). However, the effect of a varying coefficient of horizontal permeability due to the chang- ing of void ratio was taken into consideration. Figure 3 shows the horizontal permeability–void ratio relationship which was evaluated according to the formulas by Tavenas et al. (1983).
The soft clay behaviour was governed by the elastic–plastic properties (see Table 1).
Model 2 – The vacuum pressure condition and the horizontal permeability –void ratio relationship were identical to those of Model 1. Initially, soil was fully saturated. When loading the Elevation view
Plan view
1 Schematic of vacuum-surcharge consolidation apparatus and sampling locations (unit: mm) (Vu et al. 2016)
Table 1 Soil properties of reconstituted clay sample (Vu et al. 2016)
Soil properties Reconstituted clay
Water content, w (%) 35
Unit weight, γ, (g/cm3) 1.881
Initial void ratio, e0 0.952
Particle density, Gs (g/cm3) 2.710
Liquid limit, LL (%) 35
Plastic limit, PL (%) 22
Initial horizontal permeability, khi (cm/s) 5.06E-07 Initial vertical permeability, kvi (cm/s) 2.07E-07
Cohesion, c, (kPa) 15.6
Friction angle, φ,(0) 7.0
Modulus, E_recompression (kN/m2) 1000
Modulus, E_compression (kN/m
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Model 4 – Conditions were identical to those of Model 3 except for the distribution of vacuum pressure values. In this case, vacuum pressure value remained a constant along the vacuum well drain (see Fig. 2).
Use GeoStudio 2007 software, a FEM with Biot consol- idation theory, to simulate four models. A two-dimensional axisymmetric mesh was used. After defining the global element size (0.026 m) and the finite-element mesh pattern (triangles), the software automatically generated a finite-element mesh inside the regions: 278 Nodes, 480 Elements for Model 1, 3, 4 and 277 Nodes, 480 Elements for Model 2. The axisymmetric finite-element mesh of four models is shown in Fig. 2. The surcharge load of 25 kPa was applied at the top. At the bottom edge, the displacements were restricted in horizontal and ver- tical directions. On both the right and the left sides, only the horizontal component of displacements was fixed. Assign an impervious boundary condition to all the boundaries, but along at the vacuum well boundary. The thickness of unsaturated layer
did not change with time. The assumed suction – unsaturated permeability relationship represented in Fig. 3, and the soil behaviour was still governed by the elastic–plastic properties.
Model 3 – Conditions were identical to those of Model 1, but the hydraulic conductivity function was defined as perme- ability of unsaturated soil: the hydraulic conductivity varied with changes in suction. The assumed suction – unsaturated permeability relationship was shown in Fig. 3.
Table 2 Summary of the loading for the laboratory test (Vu et al. 2016)
Time (h) 0–8 9–19 20–55
Surcharge pressure 25 25 25
Vacuum pressure 50 0 50
2 Axisymmetric finite-element mesh
Horizontal permeability–void ratio (Vu et al. 2016)
Assumed suction – unsaturated permeability
3 Variation of soil permeability
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the pore water pressure. Model 2 and Model 3, however, had more accuracy of numerical predictions. The hydraulic con- ductivity of unsaturated soil was a main reason to retard the dissipation of pore water pressure.
Although the numerical prediction data of two models, Model 2 and Model 3, agreed with the measured data, however, it is a big challenge to determine the thickness of unsaturated layer. In addition, according to Indraratna et al. (2004): ‘unsatu- ration of soil adjacent to the drain can occur due to mandrel withdrawal’ but the vacuum wellpoint was not installed by using a mandrel and hoist, thus, the assumption that was used in Model 3 is more reasonable in this case.
The numerical prediction data of pore water pressure at piezometers No2, 6 of Model 3, 4 are shown in Fig. 5, the results indicated that using the exact distribution of vacuum pressure value or constant vacuum pressure value along the vacuum wellpoint did not make a significant difference in the numerical prediction in the cases of shallow vacuum wellpoint.
The variation of the settlement was the same as that of the pore water pressure. Model 1 overestimated the settlement value while Model 2 and Model 3 increased the accuracy of the settlement predictions (see Fig. 6).
the drain boundary (vacuum well) the negative pore pressure was applied.
Figure 4 shows the measured and predicted curves of pore water pressure at various points in the reconstituted specimen.
Model 1, the conventional saturated soil model, overestimated
4 The measured and predicted curves of pore water pressure at the piezometer No1, 2, 3, 4, 5, 6
5 Predicted curves of pore water pressure at the
piezometers No2, 6 of Model 3, 4
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was also built up in stages (see Fig. 8). The variation of vacuum pressure with time and depth is shown in Fig. 9. The equivalent vertical band drain radius rw = 0.026 m, the radius of the smear zone was 0.120 m (Indraratna et al. 2004). The equivalent plane strain permeability coefficients for the disturbed (smear) and undisturbed zones were the same as those in study of Indraratna et al. (2004).They are listed in Table 3.
Numerical modelling
GeoStudio 2007 software was also employed in this case.
Model 1 – The conditions were identical to those of Model 4 by Indraratna et al. (2004): the model only had sur- charge load, no unsaturated elements along the PVD and the soil behaviour was governed by modified Cam-Clay model.
In this Model, PVDs were modelled using Interface elements with elastic properties (E = 1 MPA, ν = 0.25). Well discharge capacity qw = 50m3/year (Indraratna et al. 2004), thus, an equivalent plane strain permeability kw = 1.585E-5m/s can be obtained from the method by Hird et al. (1992). The pore water pressure value in Fig. 11 confirmed that the initial pore water pressure value was 5 kPa (the groundwater level was at 2.5 m depth).
Figure 10 shows the finite-element mesh for embankment.
Due to the symmetry, only one half of embankment was exam- ined. The mesh consisted of elements with four integration points (four – node quadrilateral). The global element size was specified as 0.5 m; however, the thickness of interface elements and the smear zone elements was defined as a radius of equivalent vertical band drain (0.026 m) and a radius of the Case history of PVD incorporating vacuum
preloading
Case description
The Second Bangkok International Airport, located in Samutprakan Province – Thailand, was used to examine in this case. Ground treatment at this site was previously studied by Indraratna and Redana (2000). The subsoil profile of this site was divided into five layers (see Figure 7). The embankment 6 The measured and predicted curves of settlement
7 Cross section of an embankment with the subsoil profile (Indraratna et al. 2004)
8 Loading history for embankment TV1, second Bangkok International Airport, Thailand (Indraratna et al. 2004)
9 Variation of suction with depth and time for embankment TV1 (Indraratna et al. 2004)
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smear zone (0.120 m), respectively. At the bottom edge, the displacements were restricted in horizontal and vertical direc- tions; on the right and the left sides, they were only fixed in the horizontal direction. Impervious boundaries were applied to the ground surface, two sides and at the bottom edge. However, at the sand blanket, full drainage was allowed by assigning the drainage blanket boundary zero pore pressure.
To examine the accuracy of simulating the lateral displace- ment of Model 1, two models were set up. One had no PVD ele- ments, and the other had PVD elements (E = 1 MPA, ν = 0.25).
The lateral displacement profiles of two such models and those of models which were studied by Indraratna et al. (2004) are all shown in Fig. 12.
Model 2 – The conditions were identical to those of Model 1, however, the vacuum pressure changed with depth and time – the same as those of Model 3 which was proposed by Indraratna (see Fig. 9). The interface elements were not used to simulate the PVDs. The hydraulic conductivity functions were defined as the permeability of unsaturated soil. The initial groundwa- ter level was at 0.5 m depth, after 20 days (drain installed &
vacuum pressure stage) the groundwater level decreased to 2 m depth.
The application of vacuum pressure has been simulated by fixing the negative pore pressure along drains boundary (the edge of PVD and sand blanket). If the PVD was modelled using Table 3 Soil parameters used in the analysis (Indraratna et al. 2004)
Deep, (m) e0 λ κ ν M γ, (kN/m3) khp, (m/s) k′hp, (m/s)
0–2.0 1.8 0.3 0.03 0.3 1.2 16.0 8.98E-09 5.86E-10
2.0–8.5 2.8 0.73 0.08 0.3 1.0 14.5 3.80E-09 2.48E-10
8.5–10.5 2.4 0.5 0.05 0.25 1.2 15.0 1.80E-09 1.17E-10
10.5–13.0 1.8 0.3 0.03 0.25 1.4 16.0 7.06E-10 4.96E-111
13.0–18.0 1.2 0.1 0.01 0.25 1.4 18.0 4.15E-11 2.71E-12
10 The finite elements mesh for embankment
11 Pore-water pressure at 3 m depth below ground level, 0.5
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Vu and Yang Numerical modelling of soft ground improvement
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finite-element mesh for embankment of Model 2 was basi- cally the same as that of Model 1, but there were no interface elements.
By analysing the variation of surface settlement of Model 1, 2, 4 by Indraratna et al. (2004), a conclusion can be made that there was no vacuum preloading in the first 20 days; the surface settlement was derived from the effect of the loading surcharge and the decrease of groundwater. The initial groundwater level was at 0.5 m depth (Indraratna et al. 2004) and after 20 days it was at 2 m depth.
The variation of settlement and pore water pressure of Model 1 was agreed with those of Model 4 by Indraratna (see Figs. 11 and 13). But in Fig. 12, none of lateral displacement profiles were agreed with those of Model 4 by Indraratna. It would be a validation that the means of PVD modelling play a major role in creating the numerical models to predict the lateral displacement. Because the prediction of lateral displacement was affected by many factors, the lateral displacement was not examined in this paper.
The pore-water pressure, the settlement predicted from all the models and the field data are plotted in Figs. 11 and 13. The pore-water pressure and the settlement of Model 2 – Proposed and those of Model 3 – Indraratna were all agreed with the field data. So it confirms that the proposed model (Model 3) and its assumptions are acceptable.
Conclusion
In this paper, four numerical models were used to examine the laboratory test of an axisymmetric single vacuum wellpoint and two numerical models were created to examine one case history of PVD incorporating vacuum preloading. Based on the accuracy of numerical prediction, the following conclusions can be drawn.
• The model with thin layer of unsaturated elements at the vacuum well boundary and the mode with hydraulic per- meability of unsaturated soil improve accuracy more than the model with the permeability properties of saturated soil. However, it is very difficult to determine the thick- ness of unsaturated layer. Besides, the vacuum wellpoint was not installed by using a mandrel and hoist, so it did not cause the unsaturation of soil adjacent to the drain.
Thus, the proposed method that soil hydraulic conduc- tivity under the vacuum preloading was similar to the permeability of unsaturated soil is reasonable.
• The proposed method not only improves the accuracy of numerical model but also helps to create a numerical model without difficulty. The hydraulic conductivity of unsaturated soil retarded the dissipation of pore water pressure, and thus, it caused the pore water pressure value and the settlement value to agree with the field data.
Besides, it is interesting to find out that the negative value of pore water pressure of the soil subjected to the vacuum preloading is very similar to the pore water pressure value of the unsaturated soil. And it makes the proposed method more solid.
• The similarity in the results of prediction between the model that used the exact distribution of vacuum pressure value along the vacuum wellpoint and the model that used the constant value of vacuum pressure along the vacuum interface elements were very thin. Therefore, the PVD were
not modelled using the interface elements in Model 2. The 12 Lateral displacement profiles at the end of construction
(after 150 days) through the toe of embankment (‘Laboratory testing’)
13 Surface settlement for embankment (Point B)
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wellpoint indicates that we can simply use the constant value of vacuum pressure along the vacuum wellpoint to create numerical models in the cases of shallow vacuum wellpoint. The accuracy of numerical predictions of such models is the same as that of the models which used the exact distribution of vacuum pressure value along the vacuum wellpoint.
Conflict of interest
No potential conflict of interest was reported by the authors.
Funding
This work was supported by the Research Fund for the Doctoral Program of Higher Education [project number 20120022120003]; National Natural Science Foundation of China [project number 41202220], [project number 41472278];
Fundamental Research Funds for the Central Universities [pro- ject number 2652012065].
ORCID
Van-tuan Vu http://orcid.org/0000-0001-9605-5046
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