Lateral displacement under combined vacuum pressure and

Chai, J. et al. Ge´otechnique [http://dx.doi.org/10.1680/geot.12.P.060]

Lateral displacement under combined vacuum pressure and embankment loading J. C H A I , C . Y. O N G † , J. P. C A RT E R ‡ a n d D. T. B E R G A D O §

Based on examination of existing field results, an empirical equation has been suggested for estimating the likely range of the maximum value of the net lateral displacement (nm ) of ground improved by the installation of prefabricated vertical drains (PVDs) and subjected to the combined effects of vacuum pressure and embankment loading. The effects on lateral displacement of the magnitudes of embankment loading, as well as the vacuum pressure, the loading rate, and the undrained shear strength and consolidation properties of the soil deposit, have been explicitly included in a newly defined parameter, which is given by the ratio of an index pressure to the representative soil shear strength (RLS). The ratio of nm to the surface settlement under the embankment centreline, Sf , is also defined as the normalised maximum (net) lateral displacement (NLD). A direct relationship between RLS and NLD has been proposed, with a prescribed range, based on the results of 18 field case histories from 12 different project sites in five countries. It is suggested that the proposed relationship can be used as a preliminary design tool for preloading projects involving combinations of a vacuum pressure and an embankment pressure as well as PVD improvement. KEYWORDS: case history; displacement; geosynthetics; ground improvement

INTRODUCTION Preloading a soft clayey deposit by embankment loading or vacuum pressure loading, or some combination of both, is commonly used as a soft ground improvement method. Prefabricated vertical drains (PVDs) are usually installed in soil to accelerate the consolidation under these loadings. In most preloading projects, it is an essential design requirement to predict the consolidation settlement and the lateral deformation of the ground. Particularly in urban areas, the lateral displacement of the ground may in fact control the design. Vacuum preloading generally results in inward lateral displacements of the ground, and may in fact cause surface cracks adjacent to the treated area, whereas embankment loading usually results in significant outward lateral displacements of the soil deposit (e.g. Shang et al., 1998; Chu et al., 2000; Chai et al., 2006; Mesri & Khan, 2012). Therefore, conceptually at least, it is possible to minimise the overall lateral displacement by combining an embankment loading with application of a vacuum pressure. Based on the results of laboratory model tests and numerical analysis, Ong & Chai (2011) reported that the lateral displacement occurring under a combination of a vacuum pressure and an embankment loading is influenced mainly by the ratio of the magnitude of the embankment loading to the vacuum pressure, as well as by the rate of application of the embankment loading. However, to date there has been no practical, easy-to-use method for predicting the lateral displacement under this kind of load combination. The aim of this study is to develop a simple method for

estimating the maximum value of the net lateral displacement of a soft clayey deposit under a combination of vacuum pressure and embankment loading. The methodology is discussed first, and then the essential characteristics of ground deformations observed in 18 field case histories located at 12 project sites in Thailand, China, Australia, Japan and Vietnam are analysed. Finally, based on the observed results of these case histories, an empirical equation is proposed for estimating the maximum value of the net lateral displacement of the ground.

APPROACH General considerations A constructed embankment imposes not only consolidation pressures on a soft clayey deposit but also shear stresses. These shear stresses will usually induce immediate outward lateral displacement of the ground beneath the embankment. Normally, the maximum value of lateral displacement due to the embankment loading will occur below a relatively stiff crust layer. By contrast, application of a vacuum pressure will induce inward lateral displacement, which occurs as a result of the consolidation process, and generally under this form of loading the maximum inward movement will be observed at the ground surface. Since the mechanisms of lateral displacement caused by embankment loading and vacuum pressure are different, in general the combination of the two will not necessarily result in zero lateral displacement. Nevertheless, combination of these loading types will generally reduce the overall outward lateral displacements of the soil deposit, and in particular this combination can be used to minimise the maximum value of net lateral soil displacement. The factors influencing lateral displacement induced by embankment loading are

Manuscript received 4 May 2012; revised manuscript accepted 26 November 2012. Discussion on this paper is welcomed by the editor. Department of Civil Engineering and Architecture, Saga University, Japan. † Hacent Consultant, Malaysia. ‡ Faculty of Engineering and Built Environment, The University of Newcastle, Australia. § School of Engineering and Technology, Asian Institute of Technology, Thailand.

(a) the magnitude and loading rate of the embankment (b) the undrained shear strength (su ) of the subsoil (c) the consolidation and deformation characteristics of the soft subsoil. 1

CHAI, ONG, CARTER AND BERGADO

2

The factors influencing lateral displacement induced by vacuum pressure loading are (d ) the magnitude of the vacuum pressure (e) the consolidation and deformation characteristics of the soft subsoil. In order to estimate the lateral deformations induced by a combination of an embankment pressure and a vacuum pressure, all these factors need to be considered, either directly or indirectly. Method With the combination of an embankment pressure and a vacuum pressure, there are three possible lateral displacement patterns. These are (a) generally outward displacement (away from the embankment) (b) generally inward displacement (c) inward displacement near the ground surface, and outward displacement at greater depth. Obviously, considering only the maximum value of the net outward or inward lateral displacement cannot give a clear picture in situation (c). Hence a parameter is introduced that identifies the maximum value of net lateral displacement (nm ), defined as the maximum value of the net outward lateral displacement (mo ) reduced by the maximum value of the net inward lateral displacement (mi ). That is, nm ¼ mo jmi j

(1)

If the loading conditions are the same, in general the larger the settlement, the larger will be the magnitude of nm : A dimensionless parameter, the normalised maximum value of net lateral displacement (NLD), is introduced, which can be expressed as NLD ¼

nm Sf

(2)

where Sf is the ground surface settlement under the centre of the embankment. Ideally, values of Sf and nm at the end of primary consolidation are desirable for substitution in this equation. However, in many projects, vacuum pumping is stopped at an earlier time – that is, prior to the attainment of the maximum displacements. Since the aim of this study is to develop an empirical method based on observable field data, it is proposed to use the value of embankment settlement (Sf ) at the end of the vacuum pressure application in the definition presented in equation (2). As for the most appropriate value of nm to be adopted in this definition, there are field cases that indicate that the magnitude of the lateral displacement increased after embankment construction was completed – that is, during the subsequent consolidation process in the underlying soil. There are also cases that indicate that the magnitude of the lateral displacement actually reduced after the embankment construction period (Loganathan et al., 1993). However, in general, for an embankment with a sufficiently large factor of safety (FS) against bearing capacity failure, the value of mn will not change much after the embankment construction period. For consistency in the empirical approach it is proposed to use the value of nm corresponding to the end of embankment construction in the definition provided by equation (2). It is emphasised that there are two displacements to be substituted into equation (2), which are determined at potentially different points in time: nm at the end of embankment construction, and Sf at the end of the period of application of the vacuum pressure.

The proposed approach also requires the definition of a parameter that captures the main factors influencing the lateral displacement of a soil deposit under the combined embankment and vacuum pressure loading. It is generally accepted that the magnitude of the outward lateral displacement in the soil deposit induced by embankment loading is influenced by the value of the FS of the embankment system against bearing capacity failure (Tavenas & Leroueil, 1980; Japan Road Association, 1986). In computing a representative value of FS, the magnitude of loading and the undrained shear strength (su ) of the deposit are included. Under embankment loading, the minimum value of FS normally corresponds to the end of embankment construction. For an embankment constructed on a soft clayey deposit, the ratio of embankment pressure (pem ) applied to the underlying soil to the representative value of the undrained shear strength of that subsoil (su ) is approximately inversely proportional to FS, provided the contribution of the shear strength from the embankment fill material to the overall FS is relatively small. For a deposit improved by the installation of PVDs, partial drainage (consolidation) of the subsoil will occur during the period of embankment construction. Partial drainage will increase the effective stresses as well as the strength of the subsoil, and therefore will reduce that component of the lateral displacement induced by the application of shear stresses arising from the embankment loading. Therefore, the effect of partial drainage needs to be considered when estimating lateral displacements. Those parts of the overall embankment pressure and the applied vacuum pressure that have notionally already caused some consolidation of the subsoil by the end of the embankment construction period are denoted as the ‘partial consolidation embankment pressure’ and the ‘partial consolidation vacuum pressure’ respectively. An index pressure (pn ), corresponding to the end of the embankment construction period, is introduced. It is defined as the embankment pressure (pem ) reduced by the magnitudes of the partial consolidation embankment pressure and the partial consolidation vacuum pressure. This index pressure, pn , is therefore expressed as pn ¼ pem ðjpvac j þ pem ÞU

(3)

where pvac is the vacuum pressure applied to the deposit; and U is the average degree of consolidation of the PVDimproved zone at the end of the embankment construction period. In cases where a vacuum pressure is applied to the soil, there may be situations where the value of pn is negative at the end of embankment construction. The ratio of pn to su for the deposit is designated as the ratio of the index pressure to the representative shear strength (RLS): that is p RLS ¼ n (4) su where su is the representative undrained shear strength of the subsoil. Normally, PVDs are installed in the zone of soil that captures the main compressive layers, and the significant components of inward lateral displacement induced by vacuum pressure occur mainly in this zone. However, for the components of outward lateral displacement induced by embankment pressure, a representative value of su would normally involve those layers through which any potential failure surface might pass. These two zones of interest may not always be coincident. Nevertheless, for simplicity and ease of use of the proposed method, the authors propose the adoption of an average value of su as determined for the PVD-improved soft clayey layers in equation (4). The effects of the magnitudes of both the embankment and vacuum

LATERAL DISPLACEMENT UNDER COMBINED LOADING pressure loading, the rate of embankment loading, and the strength and consolidation properties of the soft subsoil are effectively included in the definition of the parameter RLS. For a soft clayey deposit, the ratio between the undrained Young’s modulus (Eu ) and the representative strength su (Eu /su ) is also an important parameter influencing the shear-induced deformation of the ground. It is considered that the effect of Eu /su can be implicitly taken into account via the parameter NLD. If two soils have the same value of su , but different values of Eu , in general their absolute lateral displacements will be different. However, it is assumed that the ratio between the lateral displacement and the settlement is about the same. The same assumption has been used in developing the embankment stability control chart proposed by Matsuo & Kawamura (1977). Based on the above discussions, it is proposed to use RLS as a key parameter for estimating the value of the normalised maximum net lateral displacement, NLD. Thus, if the values of NLD and Sf are known, a value of nm can be simply calculated from equation (2). Suggested methods for evaluating U and su are given in the following section, after which a relationship between RLS and NLD will be established from both published and some previously unpublished field data. The intention is to develop a relationship that is applicable only for embankments with a sufficient FS against overall shear failure: that is, the proposed method is specifically unsuited for cases where FS approaches unity.

Vacuum-drain method

3 Airtight sheet method

Vertical and radial

Vertical

Radial

Radial

PVD

Vertical

EVALUATION OF U AND su Degree of consolidation (U) In practice, a vacuum pressure can be fully applied over a short period of time, and so it can be considered as an instantaneous load. On the other hand, embankments are normally constructed in stages. For PVD-improved subsoil subjected to time-dependent loading, there are solutions for the degree of consolidation for the special case where the deposit is uniform (e.g. Tang & Onitsuka, 2000). However, most natural deposits are not uniform, but are inhomogeneous and often layered. Estimating representative consolidation parameters for a layered deposit is a difficult task. In this study, a simplified model for the consolidation analysis of a PVD-improved, layered deposit, as illustrated in Fig. 1, is adopted. When evaluating values of U and su to be substituted into equations (3) and (4), the bottom layer without PVD improvement does not need to be considered. However, when it comes to calculating the value of Sf required in equation (2), the compression of the bottom layer does need to be included, and therefore the degree of consolidation of this layer also needs to be calculated. These issues are considered in the following treatment, where each of the layers shown in Fig. 1 is considered in turn. The surface layer. In cases where a vacuum pressure is applied by the airtight sheet method (Chai et al., 2010), both vertical and radial drainage need to be considered. When considering the effect of vertical drainage, it is simply assumed for convenience that the drainage path length is the same as the thickness of the surface layer, and the average degree of consolidation due to the vertical drainage (Uv1 ) can be calculated by Terzaghi’s one-dimensional consolidation theory. The average degree of consolidation due to the effect of the PVDs (Uh1 ) can be calculated by Hansbo’s (1981) solution. In calculating the well resistance, it is assumed that the drainage length of the PVDs is the same as the length of the PVDs themselves. With these assumptions, the average degree of consolidation of the surface layer (U1 ) can be evaluated by Carrillo’s (1942) equation as

Permeable or impermeable

Fig. 1. Consolidation model of prefabricated vertical drain (PVD)-improved layered deposit

U 1 ¼ 1 [(1 U v1 )(1 U h1 )]

(5)

In cases where the vacuum-drain method is adopted (Chai et al., 2010), only the vertical drainage needs to be considered. However, in this case the water flows toward the PVDs, and there is no simple analytical solution for this situation. It is recommended to use the empirical method proposed by Ong et al. (2012) for such cases, in which the average degree of consolidation of the layer is expressed as U 1 ¼ Æ2 U T

(6)

where UT is the degree of the consolidation of the layer (without PVDs) calculated by Terzaghi’s one-dimensional consolidation theory for two-way drainage conditions, and Æ2 is a multiplier, which can be calculated as 0:07 k h =k s Æ2 ¼ (0:05U 2p þ 0:48U p þ 0:3) (7) 2 where Up is the average degree of consolidation of the layer with PVDs, located below the surface layer, kh /ks is the hydraulic conductivity ratio, and kh and ks are the hydraulic conductivities of the natural deposit in the horizontal direction and the smear zone around a PVD respectively. Equations (6) and (7) can be used whenever U1 is smaller than the degree of the consolidation (Up ) of the PVD-improved layer below the surface layer. The criteria for judging the applicability of these equations can be found in Ong et al. (2012). Middle layer(s). Only the effect of radial drainage due to the

4


PVDs needs to be considered for this case, using Hansbo (1981)’s solution for calculating the degree of consolidation. Bottom layer without PVDs. Only vertical drainage needs to be considered, and again it is suggested that the method of Ong et al. (2012) should be used for estimating the average degree of consolidation. However, in calculating UT using Terzaghi’s one-dimensional consolidation theory, two-way drainage conditions should be assumed for the case where the bottom of the layer is a permeable boundary (PB). Conversely, for the case where the bottom of the layer is an impermeable boundary (IB), one-way drainage conditions should be adopted. When adopting two-way drainage conditions, the value of Æ2 is calculated from equation (7) assuming the value of Up applicable to the layer with PVDs, located above the bottom layer. When one-way drainage conditions are assumed, the value of Æ2 is calculated by the equation 0:07 0:3 k h =k s D0 2 : : : (8) Æ2 ¼ (0 33U p þ 0 20U p þ 0 1) 2 De where De is the equivalent diameter of a single PVD-improved area (i.e. the diameter of a unit cell), and D0 is a constant (¼ 1.5 m). Terzaghi’s one-dimensional consolidation theory and Hansbo’s (1981) solution are for the case of instantaneous loading. In order to consider the time-dependent embankment construction process, application of the embankment pressure is simulated as a stepwise loading. The degree of consolidation for each loading step is calculated as follows. (a) Suppose that at time t i the total applied load is pi , and the degree of consolidation with respect to pi is Ui : A load increment ˜p j is applied instantaneously at time t i , so that the degree of consolidation (U j ) with respect to the loading p j ¼ pi + ˜p j at time t i is U i pi (9) Uj ¼ pj (b) With U j known, an imaginary time t j0 (or the time factor T j0 ) can be obtained from the corresponding consolidation theory. (c) Under the loading p j , at time t i + ˜t, the degree of consolidation is calculated using a time of t j0 + ˜t.

Equivalent loading The application of a vacuum pressure (pvac ) will induce negative excess pore water pressure (u) in the underlying soil, whereas the embankment loading (pem ) will induce positive values of u. However, if considering only the vertical effective stress changes in the ground, the combined effect of pvac and pem is the same as the effect of applying a loading of magnitude |pvac | + pem : It is proposed to use this loading, |pvac | + pem , to calculate the average degree of consolidation, and therefore the vertical effective stress in the ground at the end of embankment construction. In calculating the surface settlement, as well as the average value of su under the centre of an embankment, it is suggested that the distribution of vertical stress change in the soil due to an embankment load can be calculated approximately by Osterberg’s (1957) method. For the case of vacuum pressure applied to the ground surface using the airtight sheet method, a constant value of mean effective stress change may be assumed throughout the PVD-improved zone. Whenever vacuum pressure is applied by adopting the vacuum-drain method, which uses a surface or subsurface

soil layer as a sealing layer, it is suggested that the method proposed by Chai et al. (2010) be used for calculating the approximate final vacuum pressure distribution in the ground. Method for calculating su When the average degree of consolidation at the end of embankment construction is known for each soil layer, the average vertical effective stress increment in each layer (˜ v9 Z) can be estimated, and therefore the operative value of su can also be calculated. It is recommended that the average value of su of each soil layer can be estimated to sufficient accuracy by the empirical equation proposed by Ladd (1991), as m

su ¼ S v9 ðOCRÞ

(10)

where v9 is the representative vertical effective stress in the soil layer, OCR is the overconsolidation ratio, and S and m are constants. Ladd (1991) proposed that the range of appropriate values for S is 0.162–0.25, and for m it is 0.75– 1.0. For most cases, at the end of embankment construction the soft clayey deposit will be either normally consolidated or close to it (i.e. OCR 1.0), and the effect of the parameter m will therefore be insignificant. In this study it is assumed for simplicity that m ¼ 1.0. As for the value of S, it is suggested that it can be calibrated using measured initial values of su for the deposit. The initial value of su can be measured by field vane shear tests or laboratory unconfined compression tests on undisturbed samples, whichever is most convenient and readily available. If no such data are available, a value of S ¼ 0.25 is suggested, based on experience. Conceptually, the effect of vacuum pressure on the value of su is different from that of a surcharge pressure applied under one-dimensional or plane-strain loading conditions. However, the literature indicates that the magnitude of this difference is not very significant in practice (e.g. Mesri & Khan, 2012). In addition, the method suggested for estimating su (equation (10)) is an empirical equation, and if necessary, this difference could be considered implicitly when selecting the value of the constant, S, to be substituted into that empirical equation. FIELD CASE HISTORIES Eighteen case histories at 12 different sites in Thailand, China, Australia, Japan and Vietnam have been collected to investigate empirically the relationship between RLS and NLD. The soil profile, embankment geometry and loading history, as well as the measured lateral displacement profile at the end of the embankment construction and the ground surface settlement (Sf ) at the end of the vacuum pressure application, are summarised for each of these cases, and the corresponding values of parameters NLD and RLS are calculated. The relationship between the values of RLS and NLD is then investigated, and an equation is proposed based on the results of these field case histories. In analysing the case histories, the following assumptions and procedures for evaluating the soil properties have been adopted. (a) Unless otherwise specified, the swelling index (Cs ) was taken as one tenth of the corresponding compression index (Cc ). (b) In cases where there is no measured value of the overconsolidation ratio (OCR), a value was backcalculated using the measured compression of each soil layer or the surface settlement.

LATERAL DISPLACEMENT UNDER COMBINED LOADING

5

(c) If there were no reported values of the coefficients of consolidation in the vertical direction (cv ) and the horizontal direction (ch ), values have been back-calculated by fitting the measured settlement curves and assuming ch ¼ 2cv : In cases where the hydraulic conductivities (k) are known, the corresponding values of the coefficients of consolidation were calculated using the known value of k and the coefficient of volume compressibility (mv0 ), which was calculated from the known values of Cc and the initial void ratio (e0 ) at the stress state corresponding to the initial yielding condition (i.e. the maximum consolidation pressure). (d ) Values of the horizontal hydraulic conductivity (kh ) were used in calculating the well resistance applicable in cases of PVD-assisted consolidation. If no measured value of kh was reported, a value was calculated from the known values of ch and mv0 :

immediately adjacent to the toe of the embankment, and if there were no side berms. It is considered that the data from these three cases might be of doubtful value in assessing the relationship between RLS and NLD, because of the particular locations of the measurement points. For Case 13, the values of RLS and NLD were calculated by considering only the soft soil layer above the 6.7 m thick middle sand layer, and the compression of this soft soil layer was calculated with reference to the measured surface settlement; it was not a directly measured value. It is therefore questionable whether this data point should be included in any assessment of the relationship between RLS and NLD (a question mark is placed beside the data point in Fig. 14). If the data points corresponding to Cases 3, 4 and 5 at the SBIA site are excluded from the analysis, a regression line can be established from the remaining field data plotted in Fig. 14, as NLD ¼ 0:05 þ 0:168RLS for 1:5 , RLS , 0:75

Summary of the case histories The 18 case histories and their sources are summarised in Table 1. In this table the loading procedure (history) for each case and the methods for determining values of the parameters for the consolidation and deformation analyses are also listed. The soil profiles, embankment geometries and PVD installation depths are shown in Figs 2(a)–13(a) for Case 1 to Case 18. Values of initial total unit weight (ªt ), void ratio (e0 ), compression index (Cc ), overconsolidation ratio (OCR), coefficient of consolidation (cv ) and available undrained shear strength (su ) are indicated in the corresponding figures. For the case histories in Japan, reported su values are derived from unconfined compression tests on undisturbed soil samples, and for all other cases the values are field vane shear test results. Values of the unit weight of embankment fill (ªem ) and groundwater level are also indicated in these figures. The lateral displacement profiles at the end of embankment construction are also depicted in Figs 2(b)–13(b). Vacuum pressures, embankment loadings and the parameters required for the PVD consolidation analysis are given in Table 2. Values of the effective diameter of the PVD unit cell (De ) were determined from the field installation pattern and PVD spacing, and the values of the equivalent diameter of the PVD (dw ) are either actual values of the PVDs used or assumed after referring to the dimensions of commonly used commercial PVDs. The ground surface settlements (Sf ) at the end of the vacuum pressure application are listed in Table 3. In addition to the information given in Tables 1–3 and Figs 2–13, for completeness, some additional explanation is warranted for some cases, and this has been provided in the Appendix. Given this information, the values of RLS and NLD for each case history were calculated, and these are listed in Table 3.

(11)

RLS–NLD RELATIONSHIP The relationship between the values of RLS and NLD analysed from the measured results of the 18 field cases described above is plotted in Fig. 14. Before proposing a relationship between RLS and NLD, some additional points warrant further explanation. As illustrated in Fig. 3, for Cases 3, 4 and 5, the inclinometer casings used to measure the lateral displacements were located about 6.0 m away from the toe of each of these embankments, and each casing passed through a side berm about 1.0 m thick. Therefore it is reasonable to expect that in each of these cases the measured maximum lateral displacement is likely to be smaller than it might otherwise have been, had the measurement been made

The correlation given by equation (11) provides a general trend for the field-measured data, but considerable scatter about this average trend is noted. The 18 cases from the 12 different project sites had different soft soil profiles, different embankment geometries and different construction sequences, and different magnitudes of applied and effective vacuum pressures. Taking all these factors into account, it is considered that estimating a range of likely values of NLD for use in design may be more meaningful than adopting a unique relationship with RLS. It is therefore proposed that the operative field value of NLD is likely to be the value estimated by equation (11) 0.05. This proposed range of likely values for NLD is also indicated in Fig. 14. The 15 data points used in the regression analysis are within the range or very close to the bounds of the range proposed for use in design. Only data points corresponding to Cases 11 and 16 are located considerably outside this range. Both these cases have a thick (9.4–17.0 m), very soft peat layer at the ground surface. Therefore it is suggested that caution should be applied when applying the method to any deposit with a thick, very soft peat layer located at or near the ground surface. Furthermore, in Case 11, shown in Fig. 7, the maximum lateral displacement was observed at the elevation of the end of the sheet pile. It is therefore uncertain whether the bending movement of the sheet pile might have affected the observed maximum lateral displacement of the soil in this case. The proposed range of design values of NLD can then be used together with equation (2) and the predicted value of settlement (Sf ) to calculate the likely range of values for the maximum net lateral displacement (nm ). This approach seems reasonable for values of RLS between 1.5 and 0.75, which is the approximate range covered by the available field data. The parameter RLS includes the main factors influencing the lateral displacement of a deposit – that is, the magnitude of embankment loading as well as the vacuum pressure, the loading rate, the consolidation properties and the operative undrained shear strength of the soil deposit. But there are other factors that may also have an effect on the maximum value of net lateral displacement, such as the slope of the embankment. For the cases investigated in this study, the embankment slopes (i.e. the values of the ratio V:H) are from 1:0.8 to 1:2.5, and therefore at present the applicability of equation (11) should be limited to values of V:H within the investigated range. Although the relative magnitudes of the vacuum pressure and the embankment pressure are indirectly reflected in the

Cai Mep International Terminal Project at Baria-Vung Tau, Vietnam, Section I North-South Expressway Project, Nhon Trach-Dong Nai, Vietnam, Section C1

Embankment at Maizuru-Wakasa Expressway, Japan Embankment at Ishikarigawa, Hokkaido, Japan Embankment at Kushiro City, Hokkaido, Japan Test section at Ebetsu, Hokkaido, Japan Mihara Bypass, Hokkaido, Japan

78

25 64

7

73

68

30

7

44 90

40 120 25 40 50 54 20 79

80 15 50 20

– – 45 45

– 24 320

–

ªt , e0 , Cc , OCR, cv e0 , OCR, cv cv ªt , OCR, cv

ªt , Cc , e0 , cv ªt , Cc , e0 , cv

195

OCR, ch ¼ 4.0cv

OCR, ch ¼ 4.5cv

ds , kh /ks , qw ds , kh /ks , qw ds , kh /ks , qw ds , kh /ks

ªt , cv , OCR

e0 , Cc – ªt , Cc –

OCR, ds , qw , cv (for sand layer) ds , kh /ks , qw

–

ªt , e0 , Cc , cv , ch

147 65

84 60 123 48

75

320

cv

ds , qw

–

cv ¼ ch /2

–

A

ªt , e0 , Cc , OCR

ªt , e0 , Cc (Bergado OCR (Bergado et et al., 2002) al., 1998) ªt , e0 , Cc , OCR cv

OCR, cv

ªt , e0 , Cc

,40 79

C

M

Parameter determination method

tv-a

– 46 97 57 100 7 120 ,173

– 55

40 21

35

tv-b tem

– 45

ts

Construction history: days

ds , kh /ks , qw

ds , kh /ks , qw

– – ªt , e0 , Cc Cc , e0 , qw

–

kh /ks

kh /ks (Indraratna et al., 2011)

ds , kh /ks , qw

ch , ds , kh /ks , qw

ds , kh /ks , qw

R

Long et al. (2012); Long (personal communication, 2012)

Hirata et al. (2010); Kawaida et al. (2012); Kosaka et al. (2011) Takahashi et al. (2008) Yamazoe et al. (2003); Mitachi et al. (2010) Yamazoe & Mitachi (2007) Hayashi & Nishimoto (2012); Hatashi (personal communication, 2012)

Indraratna et al. (2011)

Indraratna et al. (2009); Kelly & Wong (2009); Wong (personal communication, 2011)

Saowapakpiboon et al. (2008, 2010); Bergado (personal communication, 2011) Yan & Chu (2005); Rujikiatkamjorn et al. (2007)

Bergado et al. (1998)

Source

M ¼ measured value; C ¼ back-calculated or calculated from other known values of the related parameters; A ¼ assumed; R ¼ obtained from the source reference; OCR, overconsolidation ratio. Measured vacuum pressure was practically zero after the end of embankment construction.

18

17

12 13 14 15, 16

11

10

7 8, 9

6

Embankments at Ballina bypass, Australia: settlements, SP5 and SP7, lateral displacements, I2 and I3 Preloading project at Port of Brisbane, Australia

Test embankments 1 and 2 at Second Bangkok International Airport (SBIA), Thailand Third runway and taxi road construction at SBIA, Section EW16, Thailand Embankments at Tianjin Port, Sections I and II, China

1, 2

3–5

Project and section

Case

Table 1. Summary of case histories and parameter determination methods

6


LATERAL DISPLACEMENT UNDER COMBINED LOADING 36·00 0·8 γem ⫽ 18 kN/m

2·50

1

3

Sand mat

0·30 Surface layer

1·00

7

Groundwater level: ⫺0·5

16

1·8

0·69

5·0

0·118

14·5

2·8

1·68

1·7

0·015 9–15

⫺0·05

0

Lateral displacement: m 0·05 0·10

0·15

11 Case 1

Very soft to soft clay

7·50

Inclinometer casing

Case 2

PVD

2·00

Soft clay

15

2·4

1·15

1·7

0·017

16

2·50

Medium clay

16

1·8

0·69

1·7

0·012

27

18

1·2

0·23

1·7

0·01

–

5·00

Stiff clay

Cc

OCR

γt: e0 kN/m3

End of embankment construction

cv: su: m2/day kPa

Surface layer, ch ⫽ cv; other ch ⫽ 2cv (a)

(b)

Fig. 2. (a) Cross-section of embankment and soil profile for Case 1 (dimensions in m; OCR, overconsolidation ratio; PVD, prefabricated vertical drain); (b) lateral displacement profiles for Cases 1 and 2 ~30·0 2 2·8

γem ⫽ 18 kN/m3

1

Sand mat 1·0

0·50

⫺0·05

0·10


2·0

Weathered clay

Hose 18·5

0·35

5·0

0·0048

3·0

Very soft clay

Cap

13·8

0·40

1·7

0·0048

5·0

Soft clay 1

14·0

0·35

1·7

Inclinometer 0·0048 casing

PVD

Lateral displacement: m 0·05 0

Case 5 Case 3

Case 4 3·0

Soft clay 2

15·0

0·30

1·7

0·0048

2·0

Medium clay

15·7

0·20

1·7

0·0048

5·00

γ t: Cc / OCR kN/m3 (1 ⫹ e0)

Stiff clay

cv : m2/day

ch ⫽ 2cv su values are not available (a)

(b)

Fig. 3. (a) Cross-section of embankment and soil profile for Case 3 (dimensions in m; OCR, overconsolidation ratio; PVD, prefabricated vertical drain); (b) lateral displacement profiles for Cases 3 to 5

parameter RLS, whether the proposed equation can be applied to cases of vacuum pressure alone (pem ) or embankment loading alone (pvac ) is still not clear, and further investigation of this issue is needed. For the cases investigated here, the ratio between the magnitude of vacuum pressure and embankment load, |pvac |/pem , varied from 0.31 to 0.64. Based on this observation, it is recommended that the use of equation (11) should also be restricted to cases for which 0.3 , |pvac |/pem , 0.7. CONCLUSIONS In preloading soft clayey deposits, combining a vacuum pressure with an embankment loading has been widely used

in practice to increase the effective preloading pressure and minimise the lateral displacement of the ground improved by PVDs. Based on observations of 18 field cases at 12 different sites in Thailand, China, Australia, Japan and Vietnam, a method has been proposed to estimate the range of the maximum value of the net lateral displacement of the ground (nm ). nm is defined as the maximum value of the net outward lateral displacement, discounted by the maximum value of the net inward lateral displacement. This method considers the effects of the magnitudes of the embankment loading and vacuum pressure, the loading rate, and the undrained shear strength and consolidation properties of the soft subsoil on the lateral displacement, and combines these into a newly defined parameter, which is


8 Assumed ~1·5 1

2·53

30·00

⫺0·40 ⫺0·35 ⫺0·30 ⫺0·25 ⫺0·20 ⫺0·15 ⫺0·10 ⫺0·05

0·3 3·50

Silty clay consolidated from slurry

γ t: e0 kN/m3

Cc

Lateral displacement: m

Sand mat

γem ⫽ 17·1 kN/m3 OCR

cv: su: m2/day kPa

18·3

1·21 0·28

1·0

0·0024 20–38

1·0

0

0·05

Case 6

Case 7 5·00

Muddy clay

18·8

0·32

1·2

0·0105 20–60

7·50

Soft silt to silty clay

17·5 1·35 0·46

1·2

0·0084 18–50 Inclinometer casing

18·5

1·1

0·0046

PVD

4·00

Stiff silty clay

0·9

0·23

–

ch ⫽ 3cv (a)

(b)

Fig. 4. (a) Cross-section of embankment and soil profile for Case 6 (dimensions in m; OCR, overconsolidation ratio; PVD, prefabricated vertical drain); (b) lateral displacement profiles for Cases 6 and 7

Case 8

Case 9 15

15

1·5 1·5 6·15

1

1

γem ⫽ 18·0 kN/m3

Sand mat 0·0 0·5

5·00 m

2·00m 14·5

Clayey silt

PVD

Soft silty clay

14·5

4·0

Groundwater level: ⫺0·2 ⫺0·1

2·9

1·3

2·9

1·3

Lateral displacement: m 0

0·1

0·2

0·3

0·4

2·0 0·003

1·7 0·003

5–10 Case 8

Inclinometer Inclinometer 9·0 Middle silty clay

10·0

11·7

15·0

Stiff silty clay

2·6

γ t: e0 kN/m3

1·1 Cc

1·1 0·0015 10–20 OCR


Case 9

cv: su: m2/day kPa

14·7 m ch ⫽ 2cv

(a)

(b)

Fig. 5. Cases 8 and 9: (a) cross-section of embankments and soil profiles (OCR, overconsolidation ratio; PVD, prefabricated vertical drain); (b) lateral displacement profiles

the ratio of an index pressure to the representative undrained shear strength of the soil (RLS). Explicit equations are provided for calculating values of RLS. Then by defining the ratio of nm to the surface settlement (Sf ) under the centre of an embankment as the normalised maximum net lateral displacement (NLD), a relationship between RLS and NLD with a range has been proposed, using 15 of the 18 data points deduced from the field data considered in this study. With a value of RLS obtained in this way and a value of Sf ,

usually calculated using existing methods of consolidation and deformation analysis, the values of nm can easily be estimated. It is suggested that the proposed method can be used as a first approach, to estimate the likely range of the NLD, in designing the preloading of soft clayey deposits for cases where a combination of vacuum pressure and embankment pressure as well as PVD improvement are employed, and there is a sufficient factor of safety against bearing capacity


9

~50

1·5

Connected to another test section

γt: kN/m3

Cc/ (1 ⫹ e0)

γem ⫽ 20 kN/m3

cv: m2/day

ch: m2/day

su: kPa

3·2

Lateral displacement/total change in applied stress: mm/kPa

1·0 0 7·8

Dredged sand

0·2

0·4

0·6

0·8

2·0 5

0·235

0·0022

0·0027

19

0·01

0·0548

0·0548 10–15

Upper Holocene sand 2·0

16

0·18

0·0027

0·0054 15–20

Upper Holocene clay

16

0·200

0·0022

0·0052 20–35

5·0

0

Relative level: m

5–15

Dredged mud

14

RL ⫹3·5

3·0

Lower Holocene clay

⫺5

6·0 Inclinometer ⫺10

Pleistocene over consolidated clay

⫺15

(a)

(b)

Fig. 6. Case 10: (a) cross-section; (b) normalised lateral displacement profile

~ 100 Groundwater level: ⫺0·5 m Vacuum pump

Surface settlement plate

~24 ~1·0

γem ⫽ 18·6 kN/m3

Sheet pile (L ⫽ 10)

24

Surface deformation marks 0 0

Clay 1

⫺3·8

20

Peat 1

Sand 1

PVD (1·2 ⫻ 1·2) two times

Peat 3 Sand 2

⫺9·8

⫺17·7

34

Peat 2

Clay 2

1·0

PVD (1·2 ⫻ 1·2)

⫺25·7 ⫺31·0

Peat 1

Sandy gravel or bed rock

PVD-improved zone

⫺42·7

Lateral displacement: m 0·5 1·0

1·5

13·8 3·00 1·41 2·00 0·009 10 ⫺7·0

14·1 2·38 1·40 1·35 0·024 30 10

13·4 3·00 1·78 1·35 0·038 19–52 Inclinometer casing ⫺17·0 16·3 1·50

m 20

14·1 2·38 2·10 1·35 0·042 29–40 16·3 1·50 ⫺30·0 16·3 1·50 0·33 1·35 0·100 50 11·9 5·85 4·54 2·0 0·090 82 Pore pressure γt: e0 Cc OCR cv: su: gauge kN/m3 m2/day kPa Settlement gauge

(a)

30

40

ch ⫽ 2cv (b)

Fig. 7. Case 11: (a) soil profile and cross-section of embankment (OCR, overconsolidation ratio; PVD, prefabricated vertical drain); (b) lateral displacement profile

failure. It is emphasised that estimating the lateral displacement of the ground is an important design consideration, especially when the preloading area is adjacent to existing buildings or structures. ACKNOWLEDGEMENTS This research has been partially supported by the Kajima Foundation, Japan, and the Australian Research Council. The

authors are grateful to Dr P. V. Long, of Vina Mekong Engineering Consultants JS Company, Vietnam, and Dr H. Hayashi, of the Civil Engineering Research Institute for Cold Region, Sapporo, Japan. Dr Long generously provided the unpublished information about the embankment geometries of Cases 17 and 18 and their construction histories, as well as the surface settlement data for Case 18. Dr Hayashi kindly provided the data for lateral displacement for Cases 15 and 16.


10 6·0 Old embankment

2·5

γem ⫽ 18·0 kN/m3 (assumed)

Sand mat

9·80

1


1·80 Groundwater level: ⫺0·3

γt: kN/m3

e0

Cc

OCR

11·0

7·65

3·75

14·2

2·65

11·8 Impermeable sheet 17·7

Peat 1

Hose

⫺0·1

3·0

2·5

cv: m2/day 0·014

1·0

1·2

0·0047

4·5

4·08

2·0

1·2

0·006

0·7

1·10

–

–

–

1·30

0·5

1·2

0·006

0

0·1

0·2

0·3

0·4

Cap Clayey peat

Peat 2 Sandy soil

PVD

Clay

16·8

2·7

9·1 End of embankment construction

Inclinometer casing

1·0 ch ⫽ 2cv su values are not available

Sandy soil (a)

(b)


15·50


1·05 γem ⫽ 18·0 kN/m3

6·60

1·00

0·80

Sand mat

2·35

Peat 1

10·5

13·8

6·59

5·0

0·058

~3

1·65

Clay 1

15·0

2·2

0·64

1·3

0·013

21

0·95 1·00

Peat 2 Clay 2

10·5

13·8

3·75

1·3

0·058

15·0

2·2

0·64

1·3

0·026

16 –

6·70

Sand 1

7·95

Clay 3

0·83

1·3

0·032

–

Sand 2

3·80

Clay 4

⫺0·20

Lateral displacement: m ⫺0·15 ⫺0·10 ⫺0·05 0

0·05

0·10

Consider only this zone

γt ⫽ 17·0 kN/m3

15·0

2·2


PVD 0·80

⫺0·25

γt ⫽ 17·0 kN/m3 15·0

2·2

0·90

1·3

γ t: kN/m3

e0

Cc

OCR

0·011

–

cv: su: kPa m2/day

For all layers, ch ⫽ 2cv (a)

(b)



11

24·4 1·13 γem ⫽ 17·0 kN/m3

13·5

1·0

Peat

10·3

9·7

6·00

2·8

0·071

10

⫺9·0

Clay 1

14·3

2·16

0·77

1·4

0·019

12

⫺11·8

Sand 1

18·0

⫺14·4

Silt 1

17·4

1·05

0·38

1·4

0·024

25

⫺17·5

Clay 2u

16·3

1·48

0·57

1·4

0·020

24

⫺21·0

Clay 2m

16·6

1·19

0·49

1·4

0·044

20

⫺23·0

Silt 2

19·1

0·67

0·27

1·4

0·052

29

⫺25·5

Clay 2l

17·1

1·44

0·78

1·4

0·011

35

⫺30·5

Clay 3u

18·4

0·80

0·33

1·4

0·049

47

Clay 3l

16·2 γt: kN/m3

0·92

0·44

1·4

0·036

–

e0

Cc

OCR

⫺40·1

⫺0·4 0

⫺0·9

⫺0·2

0

0·2

⫺5

Ground level: m

GL ⫺3·8


3·7

Sand mat (0·5 m)

⫺10 ⫺15 ⫺20 ⫺25

End of construction

Inclinometer casing

(b)

cv: su: kPa m2/day

Sandy gravel For all layers, ch ⫽ 2cv (a)

Case 15

Case 16

11·0

13·0

Assumed γt ⫽ 18 kN/m3

~1

10·7

·1

~0·5 sand mat

3 ⫺1·0

⫺3·0

⫺5·3

Upper clay

⫺8·0

⫺9·4

⫺10·7

Sand

⫺14·0

Sandy silt

e0

Cc OCR

10·7

12·36 6·2

7·0

0·062

12·5

5·40

3·7

2·5

0·017

15·8

1·63

0·9

2·5

0·013

1·0 m Inclinometer

⫺14·5

Lower clay

⫺0·3 ⫺0·2 ⫺0·1 0

0

0·1

0·2

0·3

cv: m2/day

⫺11·5

PVD ⫺20·3

γt: kN/m3

Peat Clayey peat

⫺5·0


3

GL: m

5

Case 16 Case 15

Depth: m

10·8

~1

·1


10

15 PVD Inclinometer

⫺20·9

20

1·0 m

Sand (b) ch ⫽ 2cv su values are not available (a)

Fig. 11. Cases 15 and 16: (a) soil profiles and cross-sections of embankments (OCR, overconsolidation ratio; PVD, prefabricated vertical drain); (b) lateral displacement profiles

APPENDIX: DETAILS OF SELECTED CASE HISTORIES

Vacuum pressure variations for Cases 1 and 2

For completeness, further explanation is warranted in relation to the interpretation of the field data reported for some of the case histories, and this additional material is provided in this Appendix.

For these two cases, the applied vacuum pressures varied significantly before, during and after embankment construction (possibly due to leakages). The vacuum pressure before embankment construction was increased from about 30 kPa to about 60 kPa


12

Vacuum ⫹ surcharge area 57

19 15

1:2

Cut-off wall

Very soft clay

⫹12·0

Geotextile reinforcement Geomembrane

⫹9·2

River side

Surcharge area

1:2

3

γem ⫽ 18·0 kN/m (assumed) Assumed ⫹2·0

Settlement gauge


6·2

0·4 0

⫹3·0

14·5

2·5

1·20

5·0

0·0033

14·5

2·5

1·20

2·2

0·0033

15·0

2·2

0·90

1·3

0·0022

15·5

1·9

0·90

1·1

0·0022

16·0

1·7

0·85

1·1

0·0022

⫺4

0·3

0·2

0·1

0

⫺10

m ⫺20 Soft clay

Inclinometer

γt: kN/m3 e0

PVD spacing 0·9 m square pattern

Cc

OCR cv: m2/day

Outward ⫺30

⫺33·4 ch ⫽ 4·5cv su values are not available

Stiff clay

⫺40

(a)

(b)

Fig. 12. Case 17: (a) soil profile and cross-section of embankment (OCR, overconsolidation ratio; PVD, prefabricated vertical drain); (b) lateral displacement profile CL 13·75 Sand mat

1:2

γem ⫽ 18·0 kN/m3 (assumed)

4·75

8·0 Lateral displacement: m

1:2

2·0

⫺0·2 0

0 14·0

2·8

1·0

5·0

0·0033

14·0

2·8

1·0

5·0

0·0018

15·0

2·2

0·8

1·3

0·0022

Assumed ⫺1·0

⫺0·1

0

0·1

0·2

0·3

Very soft clay

⫺6·0 ⫺10

15·4

2·0

0·8

1·1

Soft clay

0·0026

m

15·4 γt: kN/m ⫺24

PVD spacing 0·9 m triangular pattern

3

2·0

0·6

e0

Cc

1·1

0·0026

OCR cv: m2/day

⫺20 Inclinometer

ch ⫽ 4·0cv su values are not available

Middle stiff clay

⫺30 (a)

(b)


(with an average value of about 40 kPa) for Case 1, and from about 40 kPa to about 60 kPa (with an average value of about 50 kPa) for Case 2. During embankment construction, the vacuum pressure was reduced from about 60 kPa to about 20 kPa (with an average value of about 40 kPa) for Case 1, and from about 60 kPa to about 40 kPa (with an average value of about 50 kPa) for Case 2 respectively. About 4 months after the beginning of the vacuum loading, the vacuum pressure was only about 10 to 20 kPa (Bergado et al., 1998). In calculating values of pn using

equation (3), the magnitudes of the sum of |pvac | and pem , corresponding to the end of the embankment construction, were assumed to be 65 kPa and 85 kPa for Cases 1 and 2 respectively.

PVD lengths in Cases 8, 9 and 10 The lengths of PVDs installed in the field were not reported in the sources for these three cases. From the values of the factor


13

Table 2. Loading conditions and parameters for prefabricated vertical drain (PVD) consolidation Case

pvac : kPa

Hem : m

40 (60 to 20) 50 (60 to 40) 60 60 60 80 80 70 70 65 54 75 60 60 60 60 55 65

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ªem : pem : kPa kN/m3

2.50 2.50 2.80 2.80 2.80 2.53 3.50 6.15 7.00 3.20 24.0y 9.80 6.6 13.5 10.8 10.7 6.2 4.75

18.0 18.0 18.0 18.0 18.0 17.1 17.1 18.0 18.0 20.0 18.6 18.0 18.0 17.0 18.0 18.0 18.0 18.0

PVD parameters

45 45 50 50 50 43 60 111 126 64 348 176 119 230 194 193 112 86

De : m

dw : m

ds : m

kh /ks

1.05 1.05 0.89 0.89 0.89 1.13 1.13 1.13 1.13 1.36 0.96, 1.36 0.90 0.90 0.90 0.90 0.90 1.05 0.96

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.034 0.034 0.034 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05

0.30 0.30 0.19 0.19 0.19 0.20 0.20 0.20 0.20 0.20 0.30 0.30 0.30 0.30 0.30 0.30 0.22 0.22

10 10 6 6 6 3 3 2 2 2 5 5 5 5 5 5 2 2

Remark qw : m3 /day HL : m 0.137 0.137 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.346 0.346 0.274 0.274

15 12 10 10 10 20 20 9 10 18 20, 34 19 25 19.6 19.3 19.9 34 24

Bangkok, Thailand Bangkok, Thailand Bangkok, Thailand Bangkok, Thailand Bangkok, Thailand Tianjin Port, China Tianjin Port, China Ballina, Australia Ballina, Australia Brisbane, Australia Fukui, Japan Hokkaido, Japan Hokkaido, Japan Hokkaido, Japan Hokkaido, Japan Hokkaido, Japan Cai Mep, Vietnam Nhon Trach-Dong Nai, Vietnam

Numbers in parentheses are the range of the pressure during the embankment construction. About 10 m fill was submerged.

y

Table 3. Values of the ratio of index pressure to representative shear strength (RLS) and normalised maximum (net) lateral displacment (NLD) calculated from field case histories Case

U: %

pn : kPa

su : kPa

RLS

Sf : m

mo : m

mi : m

NLD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

48.3 54.6 35.3 35.3 35.3 84.0 85.6 62.0 60.0 39.0 91.8 65.0 83.0 80.8 84.0 74.0 70.7 66.1

13.6 1.4 11.4 11.4 11.4 60.3 59.9 1.3 8.4 13.7 21.0 13.0 29.6 4.1 19.3 5.7 7.9 13.8

18.4 21.5 17.7 17.7 17.7 46.3 50.0 33.0 35.2 33.2 96.0 43.7 34.8 67.3 55.7 49.1 53.3 39.4

0.739 0.066 0.644 0.644 0.644 1.302 1.197 0.040 0.239 0.412 0.219 0.297 0.851 0.061 0.346 0.116 0.147 0.351

0.74 0.97 1.06 1.1 1.15 1.21 1.61 2.7 2.8 1.22 10.6 3.48 1.94 4.60 2.63 2.32 3.8 2.45

0.14 0.06 0.04 0.09 0.06 0 0 0.12 0.35 0.07 1.00 0.35 0.05 0.10 0.25 0.10 0.25 0.21

0 0 0 0 0 0.21 0.35 0 0 0 0 0 0.21 0.22 0.16 0.22 0 0.08

0.189 0.062 0.041 0.084 0.052 0.174 0.217 0.044 0.125 0.059 0.094 0.101 0.082 0.027 0.034 0.052 0.066 0.053

NLD

0·1

x ⫽ RLS y ⫽ NLD

y ⫽ 0·1 ⫹ 0·168x

Case 11 y ⫽ 0·05 ⫹ 0·168x

0

⫺0·1 ⫺0·2 ⫺0·3 ⫺1·5

Case 14

?

y ⫽ 0·168x

⫺1·0

⫺0·5

RLS

0

Cases 3, 4 and 5 Case 16 TH CN AU JP VN 0·5

Bangkok, Thailand Bangkok, Thailand Bangkok, Thailand Bangkok, Thailand Bangkok, Thailand Tianjin Port, China Tianjin Port, China Ballina, Australia Ballina, Australia Brisbane, Australia Fukui, Japan Hokkaido, Japan Hokkaido, Japan Hokkaido, Japan Hokkaido, Japan Hokkaido, Japan Cai Mep, Vietnam Nhon Trach-Dong Nai, Vietnam

( ¼ ld H=D2e , where ld is the length of the PVD, H is the fill thickness, and De is the diameter of the zone of influence of a PVD) reported by Indraratna et al. (2009), the lengths of the PVDs were evaluated to be about 9.0 m and 10.0 m for Cases 8 and 9 respectively. As for Case 10, in the treated area, the lengths of the PVDs varied from about 14.0 m to 26.5 m, and at the inclinometer location it was assumed to be 18.0 m (to the bottom of the Holocene clay layer).

0·3

0·2

Remark

1·0

Fig. 14. Ratio of index pressure to representative shear strength– normalised maximum (net) lateral displacement (RLS–NLD) relationship

Embankment load and PVD spacing of Case 11 Although vacuum pressure was applied under the base of the embankment, given that the settlement was more than 10 m, the buoyancy effect on the embankment fill (above the airtight sheet) could not be avoided. Assuming that about 10 m of the fill material was submerged, the estimated maximum embankment load is 348 kPa. For this case, first, PVDs arranged in a square pattern at 1.2 m spacing were installed to 34 m depth. Then the additional PVDs were installed between the already installed PVDs with a spacing also of 1.2 m to 20 m depth.


14

Effects of middle sandy layers For Cases 11 to 16, there are sandy soil layers in the middle-depth ranges of the deposits. These sandy soil layers could have influenced the vacuum pressure distributions in the deposits and drainage paths of the clayey soil layers adjacent to them. For Case 11, based on the measured vacuum pressures at depths of 7.0 m and 17.0 m from the ground surface, a vacuum pressure of 54 kPa was assumed in the soil layers above the Sand 1 layer (Fig. 7(a)). However, considering the fact that there were two thin sandy layers in the deposit, and that the spacing of the PVDs changed at 20.0 m depth, in calculating the average value of su for the soil layers with PVD improvement at the end of embankment construction, vacuum pressures of about 37 kPa and 27 kPa were assumed in the layers between the Sand 1 and Sand 2 layers, and from the Sand 2 layer to about 34.0 m depth respectively. The excess pore water pressure gauge at 17.0 m depth was located at the top of the Sand 1 layer, where the relatively high vacuum pressures were measured, and therefore in the consolidation calculations the Sand 1 and Sand 2 layers were not treated as free-draining materials. For Case 12, Takahashi et al. (2008) reported that the middle sand layer (Fig. 8(a)) had a hydraulic conductivity of about 2 3 105 m/s, and in the consolidation analysis it was treated as a fully drained layer. However, to avoid vacuum leakage through the middle sand layer, an impermeable sheet was glued to the surface of that part of the PVDs passing through the sand layer. The final measured vacuum pressures were about 75 kPa in the clayey peat layer and about 50 kPa and 30 kPa in the upper and lower clay layers below the middle sand layer. For Case 13, considering the effect of the middle sand layer (Fig. 9(a)), it was assumed that the vacuum pressure varied from a value of 60 kPa at the ground surface to about 30 kPa (50% of the surface value) at the bottom of the Clay 2 layer (top of Sand 1). In the Clay 3 and Clay 4 layers a value of 10 kPa was adopted. Based on the measured vacuum pressure in the Clay 3 layer, it was considered that the Sand 1 and Sand 2 layers had relatively high hydraulic conductivities, but were not free-drainage layers. Because of the existence of the middle sandy layer (Sand 1), only the deformations and values of su of the soil layers above the Sand 1 layer were considered in the analysis. This is clearly a simplifying assumption, but following its adoption it was estimated that about 1.94 m of the 2.5 m of observed surface settlement was due to compression of the soil layers above the Sand 1 layer. For Case 14, since a maximum vacuum pressure of about 60 kPa was measured in the Clay 2 layer (below the Silt 1 layer; Fig. 10(a)), when calculating the degree of consolidation of the clayey layers any vertical drainage resulting from the presence of the sand layers was ignored: that is, only radial drainage in the clayey subsoil layers was considered. For Cases 15 and 16, since there is a thick middle sand and sandy silt layer, and the settlements (compressions) of each subsoil layer were measured (personal communication with Dr H. Hayashi), in the analyses only the soft layers above the middle sand layer were considered.

coefficient of consolidation in horizontal direction coefficient of consolidation in vertical direction diameter of a unit cell of prefabricated vertical drain (PVD) area equivalent diameter of PVD installation mandrel diameter of smear zone diameter of vertical drain undrained Young’s modulus initial void ratio embankment height thickness of PVD-improved zone hydraulic conductivity hydraulic conductivity in horizontal direction hydraulic conductivity of smear zone hydraulic conductivity in vertical direction constant for calculating undrained shear strength initial coefficient of volume compressibility normalised maximum value of net lateral displacement overconsolidation ratio pressure due to embankment fill pressure at ith step pressure at jth step index pressure vacuum pressure discharge capacity of PVD ratio of index pressure to representative shear strength ground surface settlement under centre of embankment constant for calculating undrained shear strength undrained shear strength imaginary time factor time time period for embankment construction imaginary time consolidation time of sand mat vacuum loading period after embankment construction vacuum consolidation period before embankment construction U average degree of consolidation Uh average degree of consolidation due to radial drainage Ui average degree of consolidation at ith step U j average degree of consolidation at jth step Up average degree of consolidation of a layer with PVD UT average degree of consolidation from Terzaghi’s onedimensional consolidation theory Uv average degree of consolidation due to vertical drainage Æ2 constant ªem unit weight of embankment fill ªt total unit weight of soil ˜p j pressure increment at jth step ˜t time increment mi maximum value of net inward lateral displacement mo maximum value of net outward lateral displacement nm maximum value of net lateral displacement v9 vertical effective stress

ch cv De dm ds dw Eu e0 Hem HL k kh ks kv m mv0 NLD OCR pem pi pj pn pvac qw RLS Sf s su T j0 t tem t j0 ts tv-a tv-b

Measured vacuum pressures for Cases 17 and 18 For Case 17, vacuum pressures were measured only in the sand blanket. All measurements indicated that at the beginning the vacuum pressure was about 70 kPa, and it gradually reduced to about 55 kPa at the end of the embankment construction. For Case 18, the vacuum-drain method was used, and shortly after the end of embankment construction the measured vacuum pressure inside the PVDs was practically zero (Long et al., 2012; personal communication with Dr P. V. Long). However, monitoring continued for a total time period of about 300 days, and the settlement corresponding to the elapsed time of 300 days was used in the analysis. For both Cases 17 and 18, since there are no measured data to allow estimation of the variation of the vacuum pressure in the ground, in the analysis it was assumed that the vacuum pressure at the bottom of the PVDs was 80% of the value in the sand blanket for Case 17, consistent with past experience (Chai et al., 2005), and the value inside the instrumented PVD for Case 18.

NOTATION Cc Cs

compression index swelling index

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