Introduction

The soft marine Bangkok clay in Thailand covers an area of 80,000 km2 with thicknesses of 10–20 m. The soft soil improvement technique by prefabricated vertical drains (PVD) is widely used because it is cheaper than the other techniques [1,2,3,4,5,6,7,8,9]. PVDs are artificially created vertical paths in the soft clay layer. This technique takes advantage of the higher horizontal permeability in the soft ground deposit. Excess pore water pressures created by preloading leads to preferential horizontal flow towards the PVDs and, along with it, vertically into the permeable layers generated by the hydraulic gradient. Thus, the PVD reduces the drainage path and shortens the time required to complete the consolidation process. However, installing the PVD with a mandrel creates a smear or disturbance in the soft clay surrounding the PVD circumference. This phenomenon causes a lower horizontal permeability in the smear zone [1, 2, 10, 11]. PVDs combined embankment preloading and vacuum pressure (called vacuum-PVD) have been used to accelerate the consolidation rate and reduce the instability of the soft clay. Kjellman [12] first proposed vacuum-PVD in the 1950s, and numerous studies of vacuum-PVD have been subsequently continued up to the present [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38], including clogging effects [14, 39,40,41,42].

Vacuum-PVD consolidation can minimize the pore pressure and keep constant total stress. The effective stress is increased by decreasing pore pressure (less than atmospheric) in the soft clay mass. Low shear strength and high compressibility of soft clay cause instability during construction and considerable consolidation settlement. These are the challenging tasks for geotechnical engineers in solving such problems. Preloading using PVD combined with surcharge and vacuum preloading is popular in the soft ground improvement method that has been applied in many countries. However, crucial inconsistency between field performances and design assumptions has existed, such as residual settlements after construction completion. Furthermore, there are still disagreements in horizontal consolidation coefficient (Ch) and smear effect. Even though soft Bangkok clay has been extensively studied for many decades, the back-calculated Ch values of soft Bangkok clay are significantly different. For example, the Ch value of 0.75 m2/year was reported by Seah et al. [43], while the Ch values of greater than 3 m2/year were derived by Balasubramaniam et al. [44] and Bergado et al. [45] for soft clay improved with PVD at the Second Bangkok International Airport (SBIA) site.

The vacuum pressure causes inward horizontal movements of the surrounding ground into the vacuum-PVD zone, resulting in ground cracks in the vacuum consolidation technique [20, 24, 46]. A certain vacuum pressure combined with embankment preloading can significantly reduce the lateral displacement of the soft clay and relieve the ground crack occurrences [15, 17, 24, 47]. Chai et al. [19] studied the behavior of PVD unit cells under vacuum pressure. After vacuum consolidation, horizontal compression and strain and higher effective stress, and higher shear strength developed near the PVD while horizontal extension occurred far from PVD. Surface settlements were not uniform. The periphery of the unit cell settled more than near the PVD. In the unit cell, non-uniform consolidation was found by Zhou and Chai [48].

Bergado et al. [45] indicated that microstructures of the vacuum-PVD improved soft clay were edge to face orientation and flocculated structure in the vertically dominated smear zone. Moreover, the microstructures of specimens in the horizontally dominated outside of smear zone exhibited mainly face to face orientation and dispersed microstructure and mixed face to face with edge to face orientations. The increasing intensities of edge to face microstructures were successfully correlated with increasing flow parameters and measured shear strengths within the smear zone.

This paper is concerned with the case study of the second improvement of the runway extension site at the Second Bangkok International Airport (SBIA). The vacuum-PVD technique with a combination of field-distributed air–water separation tanks and surcharge embankment preloading was applied. The SBIA is officially named Suvarnabhumi Airport. Thus, the subsoil of this project site is soft to medium stiff clay rather than very soft clay, which was caused by the first improvement. Focused on Zone 3, out of 16 Zones, consisting of an area of 27,544 m2, this paper presents the predictions of settlements and degree of consolidations, and back-calculation of Ch values, and the observations of vertical and horizontal deformations and pore pressures.

Specifications and Discharge Capacity of PVD

Typical specifications of PVD are tabulated in Table 1. These specifications have been used for design by the Thailand Department of Highways, the Vietnam Ministry of Transportation, and the Federal Highway Administration. A discharge capacity is the essential function of PVDs. According to the ASTM standards, routine tests were performed using discharge capacity apparatus [49,50,51,52,53]. The PVD with a solid corrugated core is selected to prevent buckling and maintain the integrity of flow channels. In addition, the filter of the selected PVD is made of strong heat bonded geotextile, satisfying the filter and clogging criteria [54]. The filter surrounding the core allows the pore water entry but restricts the access of fine particles into the core body. At 20% of the corresponding straight condition, the lowest discharge capacity occurred when PVDs surrounded by soft clay particles simulated the actual field conditions under lateral pressures [55]. The lowest discharge capacity at 20% is 500 m3/year when the discharge capacity at 2500 m3/year is considered [53], which meets the minimum requirements as tabulated in Table 1.

Table 1 General specifications of PVD
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Bergado et al. [56] investigated the proposed criteria of the PVD discharge capacity, including reduction factors as a result of creep, deformation and clogging (filtration). The summation of the reduction factors was approximately 10. Thus, the required discharge capacity is 50 m3/year based on the minimum discharge capacity of 500 m3/year, corresponding to the observed value [57]. Summarily, the PVD discharge capacity is not a primary factor because the minimum requirement is simply satisfied.

Flow Parameters and Smear Effect

The soft clay is generally in the NC state during the first PVD improvement. Therefore, the Ch value in NC state is used for estimating the consolidation rate. The Ch value can be determined from laboratory consolidation test, field cone penetration test with pore water pressure measurement, and back analysis of the existing data. However, it is challenging to determine the reliable Ch value in the NC state. The laboratory test results regularly provide underestimating the Cv and Ch values. In contrast, the Ch value derived from the field cone penetration tests is lightly in the OC state, which must be scaled down to the NC state. In design practice, the Ch value is frequently evaluated from the Cv value obtained from the laboratory tests by assuming the Kh/Ks value and utilizing the correlation of Ch = (Kh/Kv)Cv.

The back-analyzed Ch values from the observed settlement data based on the Asaoka method depend on the smear effects, including smear zone diameter, ds, the ratio of Rs = Kh/Ks, and field discharge capacity of the drain, qw. The well resistance can be negligible for the field qw value of greater than 50 m3/year. The ds value is directly related to the equivalent mandrel diameter, dm. The value of ds/dm = 2–3 is typically accepted [10, 58, 59]. However, the value of Kh/Ks is assumed from 1.4 to greater than 10 [10, 43, 60].

For soft Bangkok clay at the Second Bangkok International Airport site (SBIA), based on the measured settlement from three full-scale test embankments, with assumed values of ds/dm = 2 and Kh/Ks = 5, Balasubramaniam et al. [44] and Bergado et al. [3] obtained the minimum Ch value of about 3 m2/year for the weakest soil layer from 4 to 8 m depth. Long et al. [28] reported a back-calculated Ch value of 4 m2/year using similar smear effects combined with the Asaoka method. The flow parameters coupled with the consolidation settlement of 1.50 m correspond to the results from the first PVD improvement. The design of the second improvement used Ch = 4 m2/year.

Settlement Calculations

Primary Settlement

Based on a one-dimensional (1-D) consolidation test, the final primary settlement, Soed, can be derived as follows:

$$ S_{{{\text{oed}}}} = \sum {h\left[ {RR\log \left( {\frac{{\sigma^{\prime}_{{\text{p}}} }}{{\sigma^{\prime}_{{{\text{vo}}}} }}} \right) + CR\log \left( {\frac{{\sigma^{\prime}_{{{\text{vf}}}} }}{{\sigma^{\prime}_{{\text{p}}} }}} \right)} \right]} \,, $$
(1)

where h is the subsoil thickness, CR is the compression ratio, RR is the re-compression ratio, \(\sigma^{\prime}_{{{\text{vo}}}}\) is the existing overburden pressure, \(\sigma^{\prime}_{{\text{p}}}\) is the pre-consolidation pressure, and \(\sigma^{\prime}_{{{\text{vf}}}}\) is the final vertical effective stress.

The total primary settlement of the soft clay layer comprises the primary consolidation settlement induced by an increase in the effective stress, Scf, and immediate settlement induced by undrained deformation, Si. Thus, the following expressions have been used for soft clays:

$$ S_{{{\text{cf}}}} = \mu_{{\text{c}}} S_{{{\text{oed}}}} , \, S_{i} = \, (1 - \mu_{{\text{c}}} ) \, S_{{{\text{oed}}}} \,, $$
(2)

where Soed is the 1-D consolidation settlement, μc value is between 0.8 and 1.0, depending on various factors such as soft clay thickness, embankment width, OCR, and preloading method.

The primary consolidation settlement of soft clay subjected to the embankment loading can be computed applying Eqs. (1) and (2) and the \(\sigma^{\prime}_{{{\text{vf}}}}\) value can be calculated as follows:

$$ \sigma^{\prime}_{{{\text{vf}}}} = \sigma^{\prime}_{{{\text{vo}}}} + \Delta \sigma_{{\text{v}}} { + }\left( {u_{{\text{o}}} {-} \, u_{{\text{f}}} } \right)\,, $$
(3)

where Δσv is an increase in the total vertical induced by the embankment load and permanent loads applying on the ground surface, u0 is the initial pore water pressure before constructing embankment), uf is the final excess pore water pressure. The uf can be smaller than the u0 for the case of pore pressure drawdown caused by the groundwater pumping.

Consolidation with PVD

The degree of consolidation, U, can be estimated using Eq. (4) proposed by Carrillo [61], as follows:

$$ U = \, 1{-}\left( {1 - U_{{\text{h}}} } \right)\left( {1 - U_{{\text{v}}} } \right) \,, $$
(4)

where Uh and Uv are the degree of consolidation in horizontal and vertical directions, respectively. Uv can be neglected for the PVD improved zone because most of the consolidation drainage occurred horizontally. The Uh is zero for the underlying unimproved soil layers (without PVD).

The solution for calculating the Uh of PVD improved soft ground was given by Hansbo [1] as follows:

$$ U_{{\text{h}}} = 1{-}e \, ^{{\left( {\frac{{ - 8T_{{\text{h}}} }}{F}} \right)}} $$
(5)
$$ T_{{\text{h}}} { = }\frac{{C_{{\text{h}}} t}}{{D_{{\text{e}}}^{{2}} }} $$
(6)
$$ F = F_{{\text{n}}} + F_{{\text{s}}} + F_{{\text{r}}} $$
(7)
$$ F_{{\text{n}}} = \frac{{n^{2} }}{n - 1}\ln n - \frac{{3n^{2} - 1}}{{4n^{2} }} \cong \ln \left( {\frac{{D_{{\text{e}}} }}{{d_{{\text{w}}} }}} \right) - \frac{3}{4} $$
(8)
$$ F_{{\text{s}}} = \left( {\frac{{K_{{\text{h}}} }}{{K_{{\text{s}}} }} - 1} \right)\ln \left( {\frac{{d_{{\text{s}}} }}{{d_{{\text{w}}} }}} \right) $$
(9)
$$ F_{r} = \pi z\left( {2L - z} \right)\frac{{K_{{\text{h}}} }}{{q_{{\text{w}}} }} $$
(10)
$$ d_{{\text{w}}} = \frac{1}{2}\left( {a + b} \right) \,, $$
(11)

where De is the equivalent diameter of a unit PVD influence zone, Ks is the horizontal permeability of soft clay in the smear zone, z is the distance from the drainage end of the drain, L is the length PVD for one-way drainage and is half of PVD length for drainage boundary at both ends of PVD, qw is the in-situ discharge capacity of the PVD, dw is the equivalent diameter of PVD, a and b refer to PVD thickness and PVD width, respectively, ds is the equivalent diameter of the smear zone induced by installing PVD and dm is the equivalent diameter of the mandrel. The correlation of ds and dm was proposed by Hansbo [58] as follows:

$$ d_{{\text{s}}} = 2d_{{\text{m}}} $$
(12)
$$ d_{{\text{m}}} = 2\sqrt {\left( {\frac{wl}{\pi }} \right)} \,, $$
(13)

where w and l correspond to the mandrel width and mandrel thickness, respectively.

In practical cases, the Kh/qw value in Eq. (10) is frequently lower than 0.0001. Thus, the value of Fr is negligible compared with Fn and Fs values, and the Fr has an insiginificant effect for the field qw value of greater than 50 m3/year [3, 44, 57, 61]. Thus, the main factors affecting the calculated consolidation rate consist of the Ch, Rs = Kh/Ks, and ds/dm, which have to be confirmed for the specific project site.

Consolidation Settlement at Time t during Preloading

The consolidation settlement at time t during the preloading stage, Sct, can be calculated based on the corresponding consolidation degree, Ut, and the final consolidation settlement, Scf, under preloading load.

$$ S_{{{\text{ct}}}} = U_{{\text{t}}} S_{{{\text{cf}}}} $$
(14)

The value of Scf is derived using Eqs. (1) and (2).

The σ’vf value for PVD improvement without vacuum pressure is calculated as follows:

$$ \sigma^{\prime}_{{{\text{vf}}}} = \sigma^{\prime}_{{{\text{vo}}}} + \Delta \sigma_{{\text{v}}} \,, $$
(15)

where Δσv refers to the increased vertical stress induced by the embankment stress, pfill, applied on the ground surface.

$$ p_{{{\text{fill}}}} = \sum {\gamma_{{{\text{fill}}}} } h_{{{\text{fill}}}} - \gamma_{{\text{w}}} h_{{\text{w}}} \,, $$
(16)

where γfill refers to the total unit weight of the fill materials, hfill is the fill layer thickness, γw is the water unit weight, and hw is the fill layer thickness located below the groundwater table during the preloading time.

For vacuum PVD using direct tubing system (without airtight membrane):

$$ \sigma^{\prime}_{{{\text{vf}}}} = \sigma^{\prime}_{{{\text{vo}}}} + \Delta \sigma_{{\text{v}}} + p_{{{\text{vac}}}} \,, $$
(17)

where pvac is the effective vacuum pressure.

The \(\sigma^{\prime}_{{{\text{vf}}}} \) can be evaluated by Eq. (17) for the vacuum PVD with an airtight membrane. However, the Δσv should be obtained from \(p_{{{\text{fill}}}} = \sum {\gamma_{{{\text{fill}}}} } h_{{{\text{fill}}}} \) because the pore pressure in the embankment fill under the airtight membrane is negative.

Secondary Compression

The secondary compression is the small magnitude for the improved clay layer after the completion of primary consolidation. From the 1-D consolidation test, the secondary compression settlement, Ss, at time t can be calculated as follows:

$$ S_{s} = hC^{\prime}_{\alpha \varepsilon } \log \left( {\frac{t}{{t_{p} }}} \right)\,, $$
(18)

where C′αε is the secondary compression ratio, and tp is the time at the end of primary consolidation. The secondary compression can be ignored for the soft clay without improvement due to its small magnitude. Moreover, the time to complete the primary consolidation settlement is greater than the project's lifetime. The time to reach 90% of consolidation is approximately one year for the soft ground improved with PVD. Therefore, tp = 1 year is frequently used for estimating the residual compression of soft ground enhanced with PVD. The Cαε value can be taken at NC to OC state, depending on the loading conditions of the underlying soft clay during the operation period.

Settlement Control

Asaoka’s method [63] is commonly used for estimating the settlement versus time using the actual observed settlement data. The 1-D consolidation equation is expressed in a first-order estimation as follows:

$$ S_{{\text{t}}} { } = S_{{\text{f}}} \left( {1 - e^{\lambda t} } \right)\,, $$
(19)

where St refers to consolidation settlement at time t, Sf is the primary consolidation settlement, and λ is a constant value. Equation 19 was derived by Asaoka [63], expressed as a solution of the following differential equation:

$$ \frac{dS}{{dt}} - \lambda S{ } = f\,, $$
(20)

where f is an unknown constant.

Based on Eq. (20), the time is equally divided into the interval of Δt. The following equations are obtained:

$$ S_{{\text{n}}} = \beta_{0} + \beta_{1} S_{{{\text{n}} - 1}} $$
(21)
$$ \beta_{1} = \frac{1}{1 - \lambda \Delta t} $$
(22)
$$ \beta_{0} = f\beta_{1} \,, $$
(23)

where Sk and Sk−1 are the settlements at time t = tk and time t = tk − Δt, respectively.

β0 and β1 from Eq. 21 can be derived from the intercept and the slope of the best fitted straight line of (Sk ~ Sk−1) plot, respectively. As time approaches infinity, Sk = Sk−1 = Sf; then

$$ S_{{\text{f}}} = \frac{{\beta_{0} }}{{1 - \beta_{1} }} $$
(24)

Based on Eqs. (5), (19), and (22), the following equation can be obtained to derive the Ch value, which is often used for its back analysis based on the monitored settlement data. From Eqs. (5), (19), and (22), the following equation can be derived to obtain the coefficient of horizontal consolidation (Ch), which is frequently employed for the back analysis based on the observed settlement data.

$$ C_{{\text{h}}} = \frac{{\left( {1 - \beta_{1} } \right)d_{{\text{e}}}^{{2}} F}}{{8\beta_{1} \Delta t}} $$
(25)

As indicated in Eq. 25, the Ch value depends on the time interval Δt. Asaoka [63] recommended a larger time interval for more accurate results, and thus, the time interval Δt of 21 days was used.

Project Description

Site Conditions and Soil Properties Before and After First PVD Improvement

The site is located approximately 30 km southeast of Bangkok at the SBIA land in the Central Plain of Thailand with an area of 8 by 4 km (Fig. 1). As part of the SBIA expansion plan, the runway extension and the locations of boreholes and field vane tests are shown in Figs. 2a and b, respectively. The project site is subdivided into 16 different zones, which have been partially improved by PVD in the previous project. This paper is focused on Zone 3 (see Figs. 2a and b) since this zone was performed first. As shown in Fig. 3, the soil profile consists of approximately 2–4 m thick sand and rockfill overlying soft to medium clay of approximately 12 m thickness followed by a stiff clay layer around 8–10 m thickness, which is in turn underlain dense to very dense sand. The dummy pore pressures were obtained at the unloaded part of the site located away from the improvement area. The dummy piezometer readings (Fig. 4) represent the initial pore pressures conditions before Preloading. Figure 4 demonstrates the pore pressure drawdown due to excessive withdrawal of groundwater from underlying aquifers that caused ground subsidence. Thus, the PVDs should be limited in length to be installed only above the pore pressure drawdown area.

Fig. 1
figure 1

Location of runway extension test site

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Fig. 2
figure 2

Locations of a boreholes and b field vane shear tests at the runway extension site

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Fig. 3
figure 3

Variation in the soil profiles of at the runway extension site

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Fig. 4
figure 4

Soil properties after the first improvement

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The index and engineering properties of the underlying clay before and after the first improvement are shown in Tables 1 and 2, respectively. Before the first improvement, the underlying soil layers consisted of very soft to soft clay with average liquid limit values and water content of more than 100%t. After the first improvement, the average liquid limit values and water content were reduced to 100 and 80%, respectively. Moreover, the undrained shear strengths obtained from corrected field vane tests increased from 8–12 kPa to 20–27 kPa, and the maximum past pressures rose from 40–60 kPa to 78–118 kPa. As expected, the compression and recompression ratios did not change much, but the void ratios decreased while the overconsolidation ratios (OCR) increased. The water contents, liquid limits, plastic limits, unit weights, undrained shear strengths, and maximum past pressures after the first PVD improvement are also plotted in Fig. 4.

Table 2 Index properties of underlying clay layers (Before and after 1st improvement)
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Second Vacuum-PVD Improvement Procedures and Monitoring Instrumentations

After the first improvement with PVD, the underlying clay layers were pre-compressed by as much as 1.50 m. Then, the surcharge embankment was excavated and moved to an adjacent site. The site conditions and soil properties were mentioned earlier in the previous section. It can be seen that the average undrained shear strength increased up to 27 kPa and the average maximum past pressure increased from 40 to 80 kPa together with the reductions of water contents and void ratios. As part of the runway extension project, there is a need to increase the maximum past pressure to more than 100 kPa. Subsequently, the second improvement works were implemented consisting of vacuum PVD with airtight membranes (VCM-MH). The PVD elements were connected to the horizontal drains in the sand blanket at the ground surface to accelerate the consolidation. The configuration of PVD installations is indicated in Fig. 5.

Fig. 5
figure 5

Details of PVD installation

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The 10 m-long PVDs with 1.0 m spacing in the square pattern were installed from the 0.5 m-thick sand drainage blanket (equivalent to 10 kPa surcharge), through 1.5 m existing fill, to − 10 m elevation. The third layer of nonwoven geotextiles in Fig. 5 was used for separation and protection. As previously mentioned, the horizontal drainage at the sand blanket was provided by horizontal band drains. An additional 1.0 m-thick surcharge fill equivalent to 20 kPa was added on top of the sand blanket. Moreover, at the end of vacuum PVD loading, an additional 30 kPa fill with the pavement will be added. The PVD installation commenced on 3 January 2021, and the vacuum preloading was started on 29 April 2021 with a full surcharge a month later.

The PVD utilized in this case study has a cross-section of 100 × 4 mm and has a filter permeability of greater than 1 × 10–4 m/s. The general PVD properties are presented in Table 3. The typical cross-section of the new vacuum-PVD system is shown in Fig. 6a, together with the relevant photographs. The connection between PVDs and the horizontal strip drains is within the 0.5 m-thick sand blanket (Fig. 6b). The vacuum pressures were consistently generated by vacuum pumps and efficiently assisted by the field-distributed air–water separation tank (Fig. 6c). The geomembrane layer (sealing layer) was placed on top of the sand blanket layer. Three layers of geotextiles were also installed below and above the geomembrane as protection against puncture (Fig. 6d). The horizontal strip drains were connected to the perforated pipes and the vacuum pump (Fig. 6e), and pore water discharges can be observed (Fig. 6f).

Table 3 Engineering properties of underlying clay layers (Before and after 1st improvement)
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Fig. 6
figure 6

The modified air–water separation system used in this project

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Figure 7 illustrates the layout of the monitoring instruments consisting of surface settlement plates, pushed-in and bored piezometers, and inclinometers. The surface settlement plate was made of a 16 mm-diameter riser steel rod welded to a square-base steel plate with a size of 0.4 × 0.4 m and thickness of 3 mm. Optical leveling measurements to the top of the riser provide a record of plate elevations. A collimation error should be smaller than the allowable one of 1/20,000. Two types of GEOCON piezometers were utilized to monitor pore water pressure induced by the vacuum pressures, including pushed-in and bored piezometers. Both types have similar specifications, such as a standard range of − 100 kPa, resolution of 0.025% full-scale range, and an accuracy ± 0.1% full-scale range. The model 4500DP pushed-in piezometer has the transducer located inside a housing with a drill rod thread and removable pointed nose cone. This model is ideally suited for use in peat and soft clays. The model 4500 bored standard piezometer is designed to measure fluid pressures such as groundwater elevations and pore pressures when installed inside boreholes and observation wells. The pushed-in and bored piezometers monitored the pore water pressure at − 5 m and − 10 m elevations.

Fig. 7
figure 7

Location of monitoring instrumentations for Zone 3 of runway extension site

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The GEOCON digital inclinometer system was used to motor the lateral displacement profiles of the improved ground during the vacuum preloading. The system includes a model 6100D digital inclinometer probe, a reel-mounted cable, and a readout data logger. The inclinometer casing used in this project was a 65 mm-diameter plastic pipe. The probe has a standard range of ± 30°, resolution of 0.0013°, and accuracy of ± 3 mm/30 m. The inclinometer casings were installed up to the stiff clay layer at a depth of 19 m, which is sufficient to obtain a zero reading at this depth based on the practical work. The piezometers and settlement plates were installed at locations RA-01, TA01, and RB-02. Two inclinometers were installed at locations RA-01 and TA-01.

Loading Stage by Surcharge Load and Vacuum Pressure

In Zone 3, the 30-kPa surcharge load and 80 to 90 kPa vacuum pressure with time are presented in Fig. 8a. The 30-kPa surcharge load induced by the 0.5 m-thick sand blanket and 1.0 m-thick fill layer were added to the 90-kPa vacuum pressure. The field-distributed air–water separators were very efficient in consistently generating the vacuum pressures underneath the sealing geomembranes. However, variations in vacuum pressures at the initial stage during the saturation process of embankment fill above the water table were observed, and problems related to preliminary salt clogging for the pump filter were also detected. After the blockage problem was successfully solved, the vacuum pump consistently and efficiently maintained the vacuum pressure aided by the field-distributed air–water separation devices, as mentioned previously.

Fig. 8
figure 8

a Vacuum pressure and surcharge, b surface settlement, c excess pore water pressurat -5.0 m depth, d excess pore water pressure at − 7.5 m depth, and e excess pore water pressure at − 10.0 m depth (Note: solid line = pushed in type; dashed line = bored type)

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Data Analyses

Measured Surface Settlements

The surface settlement versus time and settlement rate versus time curves are presented in Fig. 8b and c, respectively. The surface settlements and settlement rates increased rapidly and subsequently decreased with time during the preloading period. The surface settlements and settlement rates were currently measured at around 600 mm and 4 mm/day, respectively. Negligible amounts of rebound can be further observed later up to one month after stopping the vacuum pressures.

Observed Porewater Pressures with Time

As plotted in Fig. 8a, the loading at the sand blanket below the airtight membranes consisted of 80–90 kPa vacuum pressures and 30 kPa surcharge pressure. The generated porewater pressures in the underlying clay layer at − 5 m and − 10 m elevations, as presented in Fig. 8d and e, respectively, consisted of − 50 to − 60 kPa and − 40 to − 50 kPa. These piezometers were installed in between the PVD locations with a spacing of 1.0 m in a square pattern. The measured pore pressures at − 10 m elevation were slightly lower than the corresponding observed values at − 5 m elevation. The pore pressures were expected to reduce with depth slightly.

In Zone 3, the generation of pore pressures with time at different depths is illustrated in Fig. 9, which were measured from bored type piezometers at locations RA-01, RB-02, and TA-01. Because of the loading vacuum pressures of 80–90 kPa and embankment surcharge of 30 kPa, pore pressure values of − 50 to − 60 kPa were created at − 5 m elevation and slightly decreased from − 40 to − 50 kPa at − 10 m elevation. These piezometer readings were similar to the previous illustrations with time in Fig. 8d and e. Logically, the pore water pressures reduced slightly with depth.

Fig. 9
figure 9

Excess pore water pressures with time and depth in Zone 3 measured from bored type piezometers

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Lateral Displacements and Ground Cracks

The lateral movement profiles of subsoils in Fig. 10 for locations RA-01 and TA-01 moved inward perpendicular to the embankments. The maximum lateral movement of 180 mm was observed at the current preloading stage because of the higher vacuum pressures than the embankment surcharge stresses [47]. Chu et al. [20] reported the maximum lateral displacement of 500 mm for the vacuum-PVD improvement project with similar magnitudes of vacuum and surcharge pressures. Similar investigations were also conducted in many projects [5, 8, 25, 40, 65].

Fig. 10
figure 10

Lateral movement profiles in Zone 3

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Ground cracks were detected at a distance of about 6 m from the trench edge of the sealing membrane area, as shown in Fig. 11. The ground cracks specified larger vacuum pressure than the horizontal soil pressures, causing inward lateral displacement. The ground crack depth (zc) can be derived utilizing the active soil pressure, soil strength parameter and groundwater level, according to Chai et al. [47], as follows:

$$ \begin{gathered} z_{{\text{c}}} = \frac{2c^{\prime}}{{\gamma_{{\text{t}}} \sqrt {k_{{\text{a}}} } }}\,,\,\,{\text{for}}\,\,z_{{\text{c}}} < z_{{\text{w}}} \hfill \\ z_{{\text{c}}} = \frac{1}{{(\gamma_{{\text{t}}} - \gamma_{{\text{w}}} )}}\left[ {\frac{2c^{\prime}}{{\sqrt {k_{{\text{a}}} } }} - \gamma_{{\text{w}}} z_{{\text{w}}} } \right]\,,\,\,{\text{for}}\,\,z_{{\text{c}}} > z_{{\text{w}}} \hfill \\ \end{gathered} $$
(26)

where zw = groundwater level below the ground surface, γt = total unit weight of soil, γw = unit weight of pore water,c′ and ϕ′ = effective cohesion and friction angle of soil, respectively, and ka = active earth pressure coefficient = tan2(45-ϕ′/2). Assuming c′ = 5 kPa and ϕ ′ = 23ο, γt = 15.8 kN/m3, and zw = 0.5 m, Eq. (26) predicts zc = 4.36 m from the existing ground surface. The crack depths could correspond to the observed lateral displacement profiles, as shown in Fig. 10. The maximum lateral displacement could amount to 10% of the settlement observed by other investigators [5, 8, 25, 35, 64].

Fig. 11
figure 11

Photographs of the ground cracks in Zone 3

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Prediction of Ultimate Settlements, Consolidation Degree, and Back-Calculation of Ch Values

For Zone 3, the Asaoka plots [58] are shown in Fig. 12 to derive the ultimate settlement. The predicted ultimate settlement of 0.81 m based on the Asaoka method [63] generally agreed with the corresponding 1-D consolidation settlement prediction of 0.79 m with 100 kPa vacuum pressure and surcharge load as tabulated in Table 4. With increased vacuum and surcharge load to 110 kPa and the designer’s parameters, the 1-D consolidation settlement prediction of 0.81 m is tabulated in Table 5.

Fig. 12
figure 12

Asaoka plot for TA-01 with time interval ∆t = 21 days to obtain the ultimate settlement

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Table 4 Predicted settlements with 100 kPa surcharge during vac-PVD improvement
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Table 5 Predicted settlements with 110 kPa surcharge during Vac-PVD improvement using designer’s parameters
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The degree of consolidation (DOC) of soil under vacuum preloading can also be calculated, based on the excess pore water pressure data, as follows [65]:

$$ \begin{gathered} U = 1 - \frac{{\int\limits_{0}^{{h_{{{\text{dr}}}} }} {\left[ {u_{{\text{t}}} (z) - u_{{\text{s}}} (z)} \right]dz} }}{{\int\limits_{0}^{{h_{{{\text{dr}}}} }} {\left[ {u_{0} (z) - u_{{\text{s}}} (z)} \right]dz} }}\, \hfill \\ u_{{\text{s}}} (z) = \gamma_{{\text{w}}} z - u_{{\text{s}}} \,, \hfill \\ \end{gathered} $$
(27)

where u0(z) = initial pore water pressure at depth z, ut(z) = pore water pressure at depth z and time t, us(z) = vacuum pressure at depth z, us = vacuum pressure applied (typically 80 kPa); hdr = drainage path. If us = 0, the above equations can be used for fill preloading. Since the vacuum-PVD Preloading is still going on, the DOC predictions from the Asaoka method and 1-D consolidation are compared in Table 6 using the current values of observed settlements. The DOC estimated by the Asaoka method also agreed with the corresponding values calculated by the 1-D consolidation method and the excess pore water pressure data.

Table 6 Comparisons of observed and predicted final settlements and calculated consolidation degrees obtained from the Asaoka method, 1-D consolidation procedure, and pore water pressure data
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Following the Asaoka method [63], the Ch values were back-analyzed and plotted in Fig. 13 for Zone 3 [63]. In Fig. 13, along the line of ds/dm = 2, the DOC are predicted using Hansbo method as tabulated in Table 7 corresponding to three pairs of flow parameters, namely the following: Kh/Ks = 3 with Ch = 4.1, Kh/Ks = 4 with Ch = 5.1, and Kh/Ks = 5 with Ch = 6.2. Interestingly, the plots of DOC with time coincide in one line, as illustrated in Fig. 14. It can be seen that the predicted time to 90% DOC at a spacing of 1.0 m in the square pattern is about 5.3 months (0.44 years) which satisfied the design requirements of approximately 90 percent DOC (U ≥ 90%) in 5.3 months (0.44 years).

Fig. 13
figure 13

Back-calculated Ch values with Rs = Kh/Ks for TA-01 at ∆t = 21 days using the Asaoka method

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Table 7 Prediction of the degree of consolidation using the Hansbo method at the time, t = 5.3 months (0.44 years)
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Fig. 14
figure 14

Degree of consolidation (DOC) with time using Hansbo method

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During the first ground improvement using conventional PVD with ds/dm = 2 and Kh/Ks = 5, the average back-calculated Ch values of 2 to 4 m2/year were derived. Bergado et al. [8, 57] also reported a similar Ch value of 3 m2/year obtained from the adjacent SBIA project utilizing a traditional PVD improvement method. However, the Ks value for vacuum-PVD technic can slightly increase. Thus, the ratio, Kh/Ks, can also slightly decrease. Based on the back-calculations of settlement rates obtained from soft clay improved with vacuum-PVD, Artidteang et al. [66], Lam et al. [26], Long et al. [30], Saowapakpiboon et al. [32,33,34], and Bergado et al. [67] obtained a slight reduction of Kh/Ks because of the increased Ks within the smear zone and a slight increase in Kh (outside the smear zone). Bergado et al. [45] derived flocculated microstructures with a high degree of edge to face orientation within the smear zone and a low degree outside the smear zone. The flocculated microstructure is related to the increased Ks with consequent slight reduction of Kh/Ks and the associated increase in Ch values. Thus, using the Asaoka method with Kh/Ks = 3 and ds/dm = 2, the back-calculated value of Ch = 4 m2/year is obtained in Fig. 13 and plotted in Fig. 14 for the second improvement using Vacuum-PVD in the runway extension project.

Secondary Settlements

For OC clays, the secondary compression ratio, \(C^{\prime}_{{\upalpha }}\) = 0.04 (Cr/(1 + e0)) = 0.04 (RR) where RR is the recompression ratio. If RR = 0.05, then \(C^{\prime}_{{\upalpha }}\) = 0.002. Since ts = 10 tp, then log ts/tp = 1. The simplified soil profile and PVD zone of the Vacuum-PVD runway extension project are shown in Fig. 15. The groundwater table is located at a − 0.5 m elevation. The PVDs were installed through a 1.5 m-thick old fill from the first improvement project to -10 m elevation within the soft to medium clay layer. Below the PVD installation lies the unimproved 5 m-thick medium stiff clay layer followed by a stiff clay layer. In Fig. 15, the thickness of the clay layer, h = 13.5 m, then the Ss in 10 years is given as: Ss = \(C^{\prime}_{{\upalpha }}\)(h) = 0.002 (13.5 m) (1000) = 27 mm or 0.027 m.

Fig. 15
figure 15

Simplified soil profile and PVD zone of the vacuum-PVD improvement

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Prediction of Settlements with Time

Using the current average settlements at locations RA-01, RB-02, and TA-01, the settlement with time can be predicted using the Asaoka and 1-D consolidation methods as plotted in Fig. 16. The corresponding degrees of consolidation (DOC) are tabulated in Table 6 with an average value of 74%. Using the predicted degree of consolidation (DOC) by Hansbo method as indicated in Table 7 and the 1-D consolidation settlement assuming 100 kPa surcharge load as tabulated in Table 4, the predicted settlement with time can be plotted as shown in Fig. 17. The 100 kPa surcharge load is the sum of 70 kPa vacuum pressure and embankment surcharge of 30 kPa. The flow parameters used in Table 7 consist of Kh/Ks = 3 and Ch = 4.05 m2/year. After the second vacuum-PVD improvement, when the vacuum pressure stopped and only 60 kPa surcharge load remained, the 1-D consolidation settlement of the improved clay layer up to 15 m thickness was obtained as 0.265 m, as shown in Table 8. The predicted compression from − 1.5 to − 10 m depths as tabulated in Table 8 amounted to 0.06 m which constitutes the compression after the second vacuum-PVD improvement.

Fig. 16
figure 16

Prediction of settlement with time using Asaoka method 1-D consolidation method

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Fig. 17
figure 17

Simplified prediction of 1-D consolidation settlement during vacuum-PVD improvement, including the calculated compressions during 10 years of post-improvement operation

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Table 8 Predicted settlements with 60 kPa surcharge after vac-PVD improvement
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Moreover, as shown in Table 8, the predicted compression in the underlying and unimproved medium stiff clay layer from 10 to 15 m depth (Fig. 17) amounted to 0.20 m. Using Cv = 2 m2/year, and assuming 1-D vertical drainage, the predicted settlement with time, after the vacuum was stopped, is also plotted in Fig. 17, where the end of consolidation was indicated after 10 years. If the secondary compression of 0.027 m together with the compression of 0.06 m from − 1.5 to − 10 m elevations in the improved overconsolidated layer is added together (see bottom of Fig. 17), the total compression at 10 years after the second vacuum-PVD improvement amounted to 0.29 m < 0.30 m which is within the design specifications. Furthermore, the 1-D consolidation settlement with 110 kPa loading (80 kPa vacuum pressure and 30 kPa surcharge) amounted to 0.81 m as tabulated in Table 5, which corresponds to the predicted settlement with time plot by the design as shown in Fig. 18 within the design specifications.

Fig. 18
figure 18

Predicted settlements during ground improvement and 30 years’ operation by the design consultant of the runway extension project

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Conclusions

The previous first improvement using PVD combined with embankment surcharge pre-compressed the underlying compressible clay layer by 1.5 m and transformed from very soft to soft clay into soft to medium stiff clay layer with maximum past pressure of 80–83 kPa. There is a need to increase the maximum past pressure to more than 100 kPa for the runway extension project. Thus, the second vacuum-PVD improvement was implemented to accelerate the consolidation. The second soft ground improvement performance, including settlement predictions, flow parameter calculations, and comparisons of soil properties after and before improvement, has been reported. Based on the field and analysis results, the main conclusions can be drawn, as follows:

  1. 1.

    This presentation is focused on Zone 3 of the test site with an area of 27,544 m2 which is part of the runway extension project. The runway extension project was divided into 16 Zones. The groundwater table was located at a − 0.5 m elevation below the original ground surface. The 10 m-long PVDs were installed to a depth of − 10 m with a spacing of 1.0 m in a square pattern.

  2. 2.

    The vacuum pumps efficiently combined with embankment surcharge and assisted by the field-distributed air–water separation tanks generated and maintained 80–90 kPa vacuum pressures at the sand blanket below the airtight membranes. The build-up pore pressures of − 50 to − 60 kPa were generated at -5 m elevation and slightly decreased with the depth ranging from − 40 to − 50 kPa at -10 m elevation.

  3. 3.

    The predicted ultimate consolidation settlements with 100 kPa vacuum pressure and surcharge load obtained from the Asaoka method (0.81 m) were slightly higher than the corresponding values derived by the 1-D consolidation method (0.79 m). The consolidation degrees from the 1-D consolidation method were marginally higher than the Asaoka method's corresponding values. The consolidation degree values from the pore pressures were lower than the Asaoka method.

  4. 4.

    After the first improvement, the average liquid limit values and water content were reduced to 100 and 80%, respectively. Moreover, the undrained shear strengths obtained from corrected field vane tests increased from 8–12 kPa to 20–27 kPa, and the maximum past pressures rose from 40–60 kPa to 78–118 kPa. By the current progress of the works, it is predicted that soft to medium stiff clay will be changed to medium stiff clay after the second improvement. The unit weights, undrained shear strengths, overconsolidation ratios, and maximum past pressures will be increased. However, water contents, void ratios, and compression indices will be further reduced. Notably, the maximum past pressures should exceed 100 kPa.

  5. 5.

    From the Asaoka method, the back-calculated Ch value of 4 m2/year using ds/dm = 2, and Kh/Ks = 3 were obtained from the vacuum-PVD second improvement method. The Kh/Ks is slightly reduced due to the slight increase in Ks at the smear zone. Consequently, the Ch is also slightly increased. The corresponding values from the first improvement using PVD consisted of ds/dm = 2, Kh/Ks = 5, and Ch = 3 m2/year, similar to the previous project involving the adjacent runways at the Second Bangkok International Airport (SBIA). Thus, the Kh/Ks slightly decreased and Ch slightly increased

  6. 6.

    From inclinometer readings, maximum inward lateral displacements of 180 mm can be observed because of higher vacuum pressure than the embankment surcharge pressure. Ground cracks were located 6 m from the sealing membrane trench. The ground cracks illustrated that the vacuum pressure was more significant than the horizontal soil pressure, resulting in inward movement.

  7. 7.

    The vacuum-PVD second improvement with efficient field-distributed air–water separation system and airtight membranes with a connection of PVDs, horizontal prefabricated drains, and perforated pipes have been successfully applied in the runway extension project.