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Surcharge loading rate for minimizing lateral displacement of PVD improved deposit with vacuum pressure
Geotextiles and Geomembranes 43 (2015) 558e566
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Surcharge loading rate for minimizing lateral displacement of PVD improved deposit with vacuum pressure Jinchun Chai*, Steeva Gaily Rondonuwu Department of Civil Engineering and Architecture, Saga University, 1 Honjo, Saga 840-8502, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 February 2015 Received in revised form 1 April 2015 Accepted 7 July 2015 Available online 10 August 2015
A series of laboratory radial drainage odometer and triaxial tests were conducted to investigate the deformation behaviour of clayey soils under combined vacuum pressure and surcharge loads. Based on the test results, a method for determining the optimum surcharge loading rate (SLR) which will result in minimum lateral displacement of a deposit under combined loads has been proposed. The method using a dimensionless parameter, a, defined as the ratio of SLR and the parameters controlling the rate of consolidation of a deposit improved by prefabricated vertical drains (PVDs). The ratio between surcharge load (Dss) to the vacuum pressure (Dsvac) is designated as ðLR ¼ Dss =jDsvac jÞ. Values for the optimum SLR increase with increasing of initial effective stress in the soil and with reducing LR. It is suggested that the method can be used for design the preloading project with combined vacuum and surcharge loads. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Preloading Consolidation Vacuum pressure Lateral displacement Loading rate
1. Introduction Preloading clayey deposits improved by prefabricated vertical drain (PVD) with combination of vacuum pressure and surcharge load has been widely used in engineering practice (e.g. Artidteang et al., 2011; Indraratna et al., 2012). The combined load offers several advantages and one of them is it can reduce preloading induced lateral displacement of a deposit (e.g., Bergado et al., 1998; Yan and Chu, 2005; Kelly and Wong, 2009; Indraratna et al., 2011; Long et al., 2013; Chai et al., 2013a; Xu and Chai, 2014). Vacuum pressure is an isotropic incremental consolidation pressure and it will result in settlement and inward lateral displacement (toward the centre of the loading area). This inward lateral displacement sometimes may cause surface cracks around the treatment area (Shang et al., 1998; Chu et al., 2000; Chai et al., 2005). While a surcharge (embankment) load will induce settlement and outward lateral displacement of a deposit. Therefore, combining a vacuum pressure with a surcharge load may minimize lateral displacement of a deposit, which is an important design issue, especially in an urban environment.
* Corresponding author. Tel./fax: þ81 952 288580. E-mail addresses: [email protected] (J. Chai), [email protected] (S.G. Rondonuwu). http://dx.doi.org/10.1016/j.geotexmem.2015.07.012 0266-1144/© 2015 Elsevier Ltd. All rights reserved.
The factors influencing lateral displacement induced by embankment and/or vacuum loadings are: (1) the magnitude and loading rate of the loads; (2) the load ratio (LR) of a surcharge load (Dss) to a vacuum pressure (Dsvac) ðLR ¼ Dss =jDsvac jÞ; (3) the initial stress state in and the undrained shear strength (su) of the subsoil; and (4) the consolidation and deformation characteristics of the subsoil. Ong and Chai (2011) reported that for a given subsoil condition, LR and surcharge loading rate (SLR) are two main influence factors on the lateral displacement of a deposit under combined loading. The smaller the SLR and LR values, the smaller the outward lateral displacement. For applying the preloading with combined loads to road or railway embankment constructions, in most cases, the achievable magnitude of vacuum pressure is limited, and the final height of an embankment is pre-specified, i.e. LR may be decided prior to construction. While value of SLR can be controlled during the construction process to minimize the lateral displacement. However, there has been no such design method available yet. In this study a series of laboratory consolidation tests under both modified odometer and triaxial tests with radial drainage (drain was located at the centre of specimens) were conducted to investigate the tendency of lateral displacement of the samples under the combination of a vacuum pressure and a surcharge load. Based on the test results, a method is proposed to determine the optimum SLR with which the lateral displacement of a deposit can be minimized in the field condition.
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List of notations
s
ch cv ds dw k kh ks K
SLR su t Τr ua
coefficient of consolidation in the horizontal direction coefficient of consolidation in the vertical direction diameter of the smear zone diameter of the drain hydraulic conductivity horizontal hydraulic conductivity of natural soil horizontal hydraulic conductivity of a smear zone ratio of horizontal effective stress to the value in the vertical direction coefficient of earth pressure on the wall of the consolidation ring coefficient of at-rest lateral earth pressure drainage length of a PVD ratio of loading atmospheric pressure discharge capacity of a PVD radial radial distance of pore water pressure measurement radius of a unit cell of PVD improvement radius of smear zone equivalent radius of the vertical drain
Kw K0 L LR pa qw r ra re rs rw
559
ratio of radius of smear zone to the equivalent radius of the vertical drain surcharge loading rate undrained shear strength time a time factor dimensionless pore water pressure measurement on the radial distance ra measured excess pore water pressure a dimensionless parameter a dimensionless multiple applied surcharge load increment applied vacuum pressure increment horizontal effective stress initial horizontal effective stress vertical effective stress horizontal stress (effective or total) acting on the wall of consolidation ring measured total horizontal earth pressure on the wall initial vertical effective stress a parameter considering the effect of PVD spacing, smear and well resistance
ue
a b Dss Dsvac s0h s0h0 s0v s0hw
sep
s0v0
m
2. Methodologies
2.2. Odometer condition
2.1. Stress ratio and lateral displacement
Under odometer condition, outward lateral displacement is restricted and only inward lateral displacement is allowed. While horizontal effective stress is changeable. To judge the lateral displacement tendency of a specimen, Chai et al. (2013b) proposed a parameter called coefficient of earth pressure on the wall of the consolidation ring (Kw). Consider the normal stress acting on the wall of the ring ðs0hw Þ, and designate the pressure change transmitted by the solid skeleton of the soil specimen as a positive component of the effective stress (Fig. 1(a)), and the suction (vacuum) pressure as a negative stress change acting on the wall (Fig. 1(b)). Then Kw is defined as follows:
Let's define the ratio of horizontal effective stress (s0h ) to the value in the vertical direction (s0v ) as stress ratio and designated as K: 0
K¼
sh 0 sv
(1)
For a field condition under combined vacuum and surcharge loadings, in case that a surcharge (embankment) load dominates, the load can induce outward lateral displacement and the soil under the toe of the embankment will be in a tendency of passive state and result in K > K0 (K0 is the coefficient of at-rest earth pressure). While, for a case dominated by a vacuum pressure, the lateral displacement will be inward, but for soil under the loading area, K > K0 condition can be created also due to isotropic effective stress (suction) increment in the soil mass. Therefore, sometimes, it may be difficult to only use the stress ratio K to judge the tendency of lateral displacement of a deposit (Chai et al., 2013b).
Surcharge load
Soil
(a) Surcharge load
Pressure on the wall
Vacuum pressure Soil
(b) Vacuum pressure
Fig. 1. Illustration of the pressure change on the wall of a consolidation ring (after Chai et al., 2013b).
0
Kw ¼
shw 0 sv
(2)
The value of s0hw is calculated as follows: 0
shw ¼
sep ue sep
ðue > 0Þ ðue 0Þ
(3)
where sep ¼ the measured total horizontal earth pressure on the wall; and ue ¼ the measured excess pore water pressure at the same level (height) of the earth pressure gauge. It will be explained in the next section that the consolidation ring used has an earth pressure transducer and a pore water pressure transducer inserted on the wall. The vertical effective stress is calculated as follows: 0
sv ¼ Dss ue
(4)
Then when Kw > K0, there will be a tendency for outward lateral displacement, and when Kw < K0, the tendency will be for inward lateral displacement under a field condition. If Kw < 0, there is likely to be a micro-gap formed between the soil specimen and the consolidation ring and inward displacement occurred under the odometer condition.
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Considering the field condition, the odometer condition discussed above may be applicable to a soil element under the centre of an embankment, but not for the condition under the toe of the embankment. As illustrated in Fig. 2, for two soil elements, A and B, assuming the horizontal effective stresses are the same for both the elements, the stress ratio of element B will be larger than that of element A, KB > KA. This implies that even for KA < K0, it is possible for KB > K0 and still results in outward lateral displacement. Chai et al. (2005) proposed that under odometer condition, if there is no effective confinement from the consolidation ring, and vacuum pressure alone can maintain K0 condition of the sample, there will be still no gap occurring between the consolidation ring and the soil sample. This condition is the same as Kw ¼ 0. Considering the soils under an embankment, and assuming the initial effective stress state is in a K0 stress condition, and if the vacuum pressure alone can maintain K0 condition for the applied vacuum and surcharge loads, the applied loads will not induce horizontal earth pressure increment to the soils outside the toe of the embankment, and consequently no outward lateral displacement. Therefore, it is considered that to judge the lateral displacement tendency in the field using the odometer test results, the condition of Kw ¼ 0 may be more suitable then Kw ¼ K0. In case a soil specimen has no zero initial effective stresses before the vacuum and surcharge loads application, to use Kw ¼ 0 criterion, the stress increments caused by the applied loads should be used to calculate Kw value.
r2 r4 ln rrwe 34 þ rw2 4rw4 e e b¼ 2 2 2 rw 1 rrw2 ln rrwa ra2r 2 e
(6)
e
Conceptually, b is a multiple to convert the measured excess pore water pressure of ua to the average pore water pressure in the specimen. Then for a combined vacuum and surcharge loading, s0v can be calculated as:
0 0 sv ¼ sv0 þ Dss þ Dsvac ðua þ jDsvac jÞ$b
(7)
where s0v0 ¼ the initial vertical effective stress; Dss ¼ the applied surcharge load; and Dsvac ¼ the applied vacuum pressure. The value of s0h can be expressed as:
0 0 sh ¼ sh0 þ Dsvac ðua þ jDsvac jÞ$b
(8)
where s0h0 ¼ the initial horizontal effective stress. Note, K (Eq. (1)) is defined as the ratio of total effective stresses in the sample, while Kw (Eq. (2)) is defined as the ratio of effective stress increments.
2.3. Triaxial condition For an ordinary triaxial test, the total confining pressure is a constant, but there is no restriction on horizontal displacement. Thus if the horizontal effective stress (s0h ) is less than the stress ðK0 $s0v Þ required to maintain a no horizontal deformation (K0) state, there will be outward lateral deformation. And if s0h > K0 s0v , there will be inward lateral displacement. Therefore, the tendency of lateral displacement can be easily judged using the stress ratio (K) (Eq. (1)). For a triaxial test with a drain at the centre of the soil specimen, to calculate the average effective stress in the specimen, the consolidation theory for vertical drain needs to be used. In Hansbo's (1981) solution for the consolidation due to the effect of a vertical drain, assuming an equal vertical strain condition, the excess pore water pressure distribution in the radial (r) direction is:
2 r r 2 rw uðrÞf re2 ln rw 2
water pressure is measured at a location with a radial distance of ra ¼ 17 mm on the base pedestal, and the value is designated as ua. To calculate the average pore pressure in the specimen from the measured value of ua, the radial distribution given by Eq. (5) has to be considered. By integrating Eq. (5) with cross-sectional area, a parameter b is introduced as:
(5)
where re ¼ the radius of a unit cell of PVD improvement (here the radius of the soil specimen); and rw ¼ the equivalent radius of the vertical drain. For the triaxial test conducted in this study, the pore
2.4. Time for calculating Kw and/or K In the field, surcharge load induced outward lateral displacement mainly occurs immediately after the load application, i.e. undrained shear deformation, while vacuum pressure induced lateral displacement occurs during consolidation process. For a given geometrical condition, the loading rate will influence the excess pore water pressure generated in the specimen, and therefore the values of Kw and K during loading, but may not significantly influence the final (end of consolidation) values of Kw and K. Considering most outward lateral displacement occurs during the surcharge load application process, the end of surcharge load application is chosen as a critical point for calculating Kw or K from laboratory tests, and use them to judge the tendency of lateral displacement. 2.5. Loading rate parameter a The effect of SLR on lateral displacement of a deposit is related to the consolidation properties of the deposit and the spacing of PVDs. For a PVD improved subsoil, the degree of consolidation is controlled by a dimensionless time factor of Tr:
Tr ¼
ch t 4re2 m
(9)
where ch ¼ coefficient of consolidation in the horizontal direction, and t ¼ time. Using Hansbo (1981)’s solution, the expression of m is:
m ¼ lnðre =rs Þ þ ðkh =ks ÞlnðsÞ
Fig. 2. Illustration of stress ratio change near the toe of an embankment.
3 2p$l2 $kh þ 4 3qw
(10)
where s ¼ rs/rw (rs is the radius of smear zone); l ¼ drainage length of a PVD; kh and ks ¼ the horizontal hydraulic conductivities of natural soil and smear zone respectively; and qw ¼ the discharge
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capacity of a PVD. In Eq. (9), except t, all parameters are basic soil properties of a deposit or the geometric parameter of PVD improvement. Let's define a dimensionless parameter (a) as:
a¼
SLR 4$SLR$re2 m t¼ Tr pa ch pa
(11)
where pa ¼ atmospheric pressure. It is aimed at establish aeKw and/ or aeK relationships from the test results. It is considered that a a value corresponding to Kw ¼ 0 (odometer condition) or K ¼ K0 (triaxial condition) will result in minimum lateral displacement. Then the corresponding value of SLR will be the optimum value for the purpose of minimizing the lateral displacement under the field condition.
3. Laboratory test 3.1. Material tested Remolded Ariake clay was used for the tests. Majority of Ariake clay is marine formation with smectite as main clay mineral (Ohtsubo et al., 1995). Natural Ariake clay deposit has a high compressibility and low strength (Miura et al., 1998). Some physical and mechanical properties of the Ariake clay tested are listed in Table 1. Both incremental loading (IL) and constant rate of strain (CRS) consolidation tests with a strain rate of 0.02%/min were conducted. The CRS tests were conducted with either vertical or horizontal drainages (Chai et al., 2012), and a ratio of the coefficients of consolidation in the horizontal direction (ch) to that in the vertical direction (cv) of 1.63 was obtained from the test results. While, the CRS test resulted in a relative lower cv value than that of IL test. The values listed in Table 1 are cv value from the IL test and ch ¼ 1.63cv. 3.2. Modified odometer test (1) Equipment The modified odometer device used is shown in Fig. 3. The detailed description of the test device has been reported by Chai et al. (2013b), and here only a brief description is given. The device consists of an odometer ring 60 mm in diameter and nominal height of 20 mm. At the middle height of the wall of the ring a pore pressure transducer and an earth pressure transducer were inserted into the wall and opposite each other. A hollow cylindrical metal porous stone wrapped with filter paper was inserted in a predrilled hole at centre of the specimen as a vertical drain. The diameter of the drain (dw) was 4 mm or 8 mm. The vacuum pressure was applied to the specimen through the central drain and the surcharge load was applied using air pressure. The settlement gauge was installed on the top of the loading piston. Settlement, pore water pressure and total lateral earth pressure were recorded by a computer through a data logger.
Table 1 Basic soil properties. Parameter Plastic limit Liquid limit Compression Coefficient of consolidation wp (%) (m2/day) wl (%) index Cc
Value
56.8
120.3
0.821
Vertical, cv
Horizontal, ch
5 103
8.15 103
561
(2) Specimen preparation To prepare the specimen, firstly, the clay slurry with a water content of about 1.2 times of its liquid limit was de-aired with approximately 100 kPa vacuum pressure. Then the de-aired slurry was put into a consolidation container of 60 mm in diameter and 60 mm in height (consolidation ring þ 40 mm height of a collar), and consolidated under 20 kPa pressure. Next 20 mm thick specimen was cut from the pre-consolidated sample for further consolidation test. Finally, a hole of 8 mm or 4 mm in diameter (dw) was drilled manually for installing the vertical drain at the center of the specimen. (3) Cases tested All cases tested are summarized in Table 2. For all cases the surcharge load adopted was 80 kPa, while vacuum pressure used was either 80 kPa or 40 kPa. And the resulting final value of LR is 1e2. For all tests, the vacuum pressure was fully applied at the start of the test, but the surcharge load was applied in a stepwise manner to simulate the field construction process. The incremental load for each step was 10 kPa, and the time interval between adjacent two steps was varied from 10 min to 360 min, which resulting in values of SLR from 10 kPa/360 min to 10 kPa/10 min. 3.3. Modified triaxial test (1) Equipment An ordinary triaxial compression test device was modified to conduct the consolidation under combined vacuum and surcharge loads. The sketch and the photo of the device are shown in Fig. 4 (a) and (b) respectively. There are two main modifications. (a) Instead of a conventional solid cylindrical specimen, using an annular shaped soil specimen with a drain inserted in the centre to simulate a unit cell of prefabricated vertical drain (PVD) improved soil layer. The nominal outer diameter of the specimen was 50 mm, inner diameter of 8 mm, and height of 100 mm. (b) Adding a system for applying vacuum pressure to the centreedrain inserted into the specimen. (2) Test procedure (a) Specimen preparation. First, a cylinder soil specimen as for ordinary triaxial test was made with pre-consolidated Ariake clay (from slurry) under 20 kPa vertical consolidation pressure. Then the specimen was fixed on a frame (guide) and an 8 mm in diameter central hole was made using a drilling tool manually. A vertical drain made by a steel spring and wrapped by filter paper was inserted into the central hole as a vertical drain. The spring is made of 0.6 mm in diameter steel wire with a pitch between two adjacent coils of about 2.7 mm. The outer diameter of the spring is about 8 mm. The stiffness of the spring is very low, and its influence on the vertical stress can be ignored. (b) Saturating the specimen. Soil specimen with the drain installed was put into the rubber membrane sleeve with a diameter of 50 mm. Then the specimen with the rubber membrane was placed into a container to which vacuum pressure can be applied, and de-aired water was put around the specimen till the water level reached the height of the specimen. A vacuum pressure of about 20 kPa was applied to the container for about 1 h to eliminate possible trapped air
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Displacement
Air pressure
(Unit: mm)
Porous stone tube Pore pressure gauge
60 20
Specimen
10
Earth pressure gauge To vacuum pump
(a) Sketch
(b) Photo
Fig. 3. Laboratory odometer test device.
bubbles between the rubber membrane, the drain, and the soil specimen. (c) Pre-consolidation. The specimen was set into the triaxial cell, and a cell pressure of about 5 kPa was applied, and de-aired water was flowed from the bottom to the top of the specimen to remove any air bubbles in the drainage system. Then anisotropic consolidation stresses were applied to consolidate the specimen for 1 day. For the cases tested, a K0 value of 0.6 was assumed in this step. The isotropic part of the consolidation stresses was applied using air-pressure and the deviational part by dead load. To avoid excessive shear deformation in the pre-consolidation process, the preconsolidation pressures were applied in a stepwise manner with a vertical stress increment of 10 kPa and horizontal stress increment of 6 kPa and a time interval of 2 hours. (d) Consolidation under combined loads. Firstly, vacuum pressure of 60 kPa was applied through the central drain. Then the surcharge load increment (10 kPa for each step) was applied stepwise with desired loading rate using dead load.
The total surcharge load applied was 60 kPa. Due to the capacity of vacuum pressure generation system adopted for the triaxial tests, the magnitude of the vacuum pressure applied was smaller than that for the odometer tests. The consolidation test generally lasted for about 2e4 days. The vertical settlement, excess pore water pressure at the bottom of the specimen and at a radial distance ra ¼ 17 mm (Fig. 4(a)) was measured and recorded using a data logger and a computer. During the pre-consolidation, the amount of water drained out from the specimen was also measured and used for calculating the diameter of the specimen before the consolidation under the combined loads. Further, the final average diameter of the specimen was measured after the consolidation test, and the value is used for calculating the horizontal strain of the specimen caused by the consolidation of the combined loads. (3) Cases tested Totally nine (9) tests were conducted using triaxial device, and the initial stress and loading conditions are listed in Table 3.
Table 2 Cases tested using the modified odometer.
4. Test results
Case
s0v0 (kPa)
dw (mm)
Dss (kPa)
Dsvac (kPa)
LR
SLR (kPa/min)
O-1a O-1b O-1c O-1d O-2a O-2b O-2c O-3a O-3b O-3c O-3d O-4a O-4b O-4c O-5a O-5b O-5c O-6a O-6b O-6c
0
8
80
80
1
10/10 10/60 10/120 10/360 10/60 10/90 10/360 10/10 10/15 10/90 10/360 10/30 10/60 10/90 10/30 10/60 10/90 10/30 10/60 10/90
0
8
80
40
2
0
4
80
80
1
20
8
80
80
1
40
8
80
80
1
80
8
80
80
1
4.1. Modified odometer test results (1) Typical test results The test results of LR ¼ 1, diameter of the central drain, dw ¼ 8 mm, SLR of 10 kPa/10 min and 10 kPa/60 min are shown in Figs. 5e7 for the variations of settlement, pore water pressure and total earth pressure, respectively. The negative total earth pressure indicates possible formation of micro-gap between the consolidation ring and the soil specimen. With increase of SLR, the settlement rate, maximum pore water pressure and total horizontal earth pressure were increased. The applied vacuum pressure was 80 kPa, but the measured values are about 50 kPa (Fig. 6). Since the gauge was calibrated carefully before the tests, the possible reason considered is that under the laboratory condition, due to vacuum (suction) pressure, mini-drain can become unsaturated and at the interface between
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563
Fig. 4. Photo of the triaxial device.
Table 3 Cases tested using the modified triaxial device. Case
T-1a T-1b T-1c T-1d T-2a T-2b T-2c T-2d T-3a T-3b T-3c T-3d
Initial stresses s0v0 (kPa)
s0h0 (kPa)
20
12
Dss (kPa)
Dsvac (kPa)
LR
SLR (kPa/min)
60
60
1
10/30 10/60 10/90 10/480 10/30 10/60 10/90 10/480 10/30 10/60 10/90 10/480
the mini-drain and soil forming convex meniscuses, which can reduce the efficiency of the vacuum pressure transferring into the soil sample. (2) Effect of SLR on Kw value
40
24
60
60
1
60
36
60
60
1
Fig. 5. Settlementetime curves (LR ¼ 1; dw ¼ 8 mm).
Fig. 8 shows the variation of the values of Kw for the cases of LR ¼ 1.0, dw ¼ 8 mm, but different SLR. It can be seen that (1) with increase of SLR, the values of Kw are increased during the surcharge loading process; and (2) influence of SLR on the final value of Kw is not significant. It can also be observed that when Dss is larger than about 40 kPa, for each surcharge load increment, the maximum Kw value not varied much. The mechanism for this may be that the surcharge loading induced shear stress increment and the consolidation induced shear strength increment are somehow balanced each other under the odometer condition.
Fig. 6. Variation of pore water pressure (LR ¼ 1; dw ¼ 8 mm).
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Fig. 7. Variation of total lateral earth pressures (LR ¼ 1; dw ¼ 8 mm).
(3) Kw versus a relationship For both the odometer and triaxial tests, the central drains were inserted into a pre-drilled hole and there should be no significant disturbance to the surrounding soil, and therefore no obvious smear zone existed. However, the soil around the central drain would be consolidated much faster, and the void ratio and therefore the hydraulic conductivity (k) of the soil around the drain would be reduced considerably. Also, as mentioned previously, in the laboratory condition, the central drains in the samples can become unsaturated. Consequently, there might be a thin soil layer around the drain became partially saturated, and its k value might be reduced significantly. The effect of faster consolidation and partial unsaturation induced k reduction, is analogous to “smear” effect. Back analysis is conducted to quantitatively evaluate the “smear” effect. Assuming the diameter of the “smear” zone (ds ) is 2 times of the diameter of the drain, by fitting the settlement curves of the odometer test results, a kh/ks ratio of about 10 was obtained. Then ds/dw ¼ 2 and kh/ks ¼ 10 are used for calculating a values for both the odometer and triaxial test results. Kw versus a relationship evaluated from the test results at the end of surcharge load application are summarized in Fig. 9. It can be clearly seen that for a given LR, Kw increased with the increase of a. Comparing LR ¼ 1 and 2 cases shows that the larger the LR, the
Fig. 8. Variation of Kw values (LR ¼ 1.0; dw ¼ 8 mm).
Fig. 9. Kwea relationship.
higher the Kw. Although the data are scattered, for s0v0 ¼ 0, cases, using Kw ¼ 0 criterion, for LR ¼ 1, a value of about 2.3 can be estimated and for LR ¼ 2 cases, the value is about 1.0, i.e. for a larger LR case, a smaller a value (lower loading rate) is required to minimize the lateral displacement. The test results also indicate that increase the initial effective stresses in the sample, reduced Kw value. Higher initial effective stresses in the sample means higher initial undrained shear strength, and for a given surcharge load, it will result in less undrained shear deformation. 4.2. Modified triaxial test results (a) Typical test results Fig. 10 presents some settlement curves of s0v0 ¼ 20 kPa cases. It can be seen that increase SLR increased settlement significantly due to more shear deformation. In Fig. 11, apparently SLR ¼ 10 kPa/ 90 min case had higher pore water pressures (u) for a given time, but at the end of the surcharge load application, the higher the SLR, the higher the u value. The difference of u values between three (3) cases before elapsed time of 50 min can be considered as the scatter of the measured data. The applied vacuum pressure to the central drain was 60 kPa, but the measured final value was about 45 kPa.
Fig. 10. Settlement curves (s0v0 ¼ 20 kPa).
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565
Pore pressure (kPa)
10 0 -10 -20 -30 -40 -50 0.01
SLR (kPa/min) 10/30 10/60 10/90
0.1
1
10 100 Elapsed time (min)
1000
10000
Fig. 11. Excess pore pressure variations (s0v0 ¼ 20 kPa).
Fig. 13. aeK relationships.
The calculated K values by Eqs. (1), (7) and (8) are depicted in Fig. 12. For these three cases, K values gradually reduced with the application of the surcharge load. At the end of the surcharge load application, K values were less than 0.3. For remoulded Ariake clay, the coefficient of at-rest earth pressure is about 0.4 (Chai and Kawaguchi 2011), and K < K0 means that the sample would deform lateral in the direction of increase the diameter of the sample (i.e. tensile horizontal strain) at that time. With the progress of consolidation and increase of vacuum pressure, K values were gradually increased and at the time of termination of the tests the values are about 0.45. (b) K versus a relationships
aeK relationships from the results of modified triaxial test are shown in Fig. 13 corresponding to the end of surcharge load application. It clearly shows that K increased with the reducing of a (or SLR). The same tendency as that of the odometer test results, K increased with the increase of initial effective stresses in the sample. Using the K ¼ K0 (z0.4 for the samples tested) criterion, for s0v0 ¼ 20 kPa, a a value which may result in minimum lateral displacement, of about 0.8 can be estimated, which is smaller than that from the odometer test results.
(c) a versus horizontal strain For the modified triaxial test, the shapes of the samples after the consolidation test were measured and the horizontal strains were calculated and the results are shown in Fig. 14. Comparing with the estimated diameters after the pre-consolidation, all samples were bulged, i.e. had tensile horizontal strain. However, the absolute magnitude of the horizontal strain reduced with the reducing of the a value and increasing of initial effective stresses in the samples. From the results in Fig. 13 and the method we proposed, under s0v0 ¼ 20 kPa, and at a of about 0.8, zero horizontal strain is predicted, but Fig. 14 shows it had about 1% horizontal strain. There are two possible reasons for this apparent inconsistency. One is that after dismounted the sample, unloading will result in certain increase of its size. Another one is that during the consolidation test, a sustained deviator stress was existed in the samples, and it may cause certain creep deformation. Further the target considered is the end of surcharge load application and in term of horizontal strain, it may be different from the final condition. 4.3. Discussion The odometer test results give larger a values than that from the triaxial test results and the exact reason(s) is not clear yet. For the device used, the lateral earth pressure gauge has a diameter of
0.6
K
0.5 0.4 0.3 0.2 0.1 0.01
SLR (kPa/min) 10/30 10/60 10/90
0.1
1 10 100 Elapsed time (min) Fig. 12. Variations of K with time.
1000
10000 Fig. 14. a versus horizontal strains (triaxial test results).
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10 mm with a flat surface. While, the consolidation ring has an arc inner surface, i.e. the surface of the earth pressure gauge is not matched the inner surface of the ring. To ensure a good contact between the sample and the ring, the remoulded soil was reconstituted directly inside the ring as explained previous. However, during the consolidation process, the soil around the earth pressure gauge will experience not only vertical compression, but also some complicated shear deformation and that may influence the measured earth pressure (possibly lower than the value supposed to be), and therefore possibly the lower calculated Kw value. Further investigation on this issue is required. Nevertheless, considering two different tests with different boundary condition and sample size, the results are in the same order is quite encouraging. Let's consider a practical case, for which, the PVD spacing is 1.0 m with a square pattern; equivalent diameter of the PVD, dw ¼ 0.05 m; the diameter of smear zone, ds ¼ 0.2 m; and kh/ks ¼ 2; discharge capacity of a PVD, qw ¼ 100 m3/year; hydraulic conductivity in the horizontal direction, kh ¼ 2 109 m/s; coefficient of consolidation in the horizontal direction, ch ¼ 10 m2/year; and the drainage length of PVD, l ¼ 5 m. From the results of the triaxial test, in case of a deposit has an average initial vertical effective stress of about 20 kPa, if LR ¼ 1.0 and the magnitude of vacuum pressure of 60 kPa, to minimize the lateral displacement a z 0.8 can be obtained, and the corresponding surcharge loading rate will be about 0.5 kPa/day for this case, i.e. a rate of filling of 1.0 m/40 days. 5. Conclusions A series of laboratory radial drainage odometer and triaxial tests were conducted to investigate the deformation behaviour of clayey soils under combined vacuum pressure and surcharge loading. For odometer condition, a parameter, Kw, defined as the ratio of the horizontal effective stress acting on the inner wall of the consolidation ring divided by the vertical effective stress in the soil sample, and for triaxial condition, the ratio of horizontal effective stress to that in the vertical direction, K, are used to determine the tendency of the lateral displacement of the samples, i.e. inward or outward. A dimensionless parameter a, define as a function of surcharge loading rate (SLR) and the parameters controlling the rate of consolidation of a prefabricated vertical drain (PVD) improved deposits has been introduced and linked to Kw ¼ 0 and/or K ¼ K0 (coefficient of at-rest earth pressure)values to determine optimum value of SLR, which will result in minimum lateral displacement. The ratio between surcharge load (Dss) to vacuum pressure (Dsvac) is designated as LRð¼ Dss =jDsvac jÞ. The test results indicate that values for the optimum SLR increase with increasing of initial effective stresses in the soil and with reducing LR. The established
optimum a value from the odometer test results is larger than that from the triaxial test results, but they are in the same order. One possible reason considered is the difference of the magnitude of the applied vacuum pressure. It is suggested that further investigation on this issue is required.
References Artidteang, S., Bergado, D.T., Saowapakpiboon, J., Teerachaikulpanich, N., Kumar, A., 2011. Enhancement of efficiency of prefabricated vertical drains using surcharge, vacuum and heat preloading. Geosynth. Int. 18 (1), 35e47. Bergado, D.T., Chai, J.-C., Miura, N., Balasubramaniam, A.S., 1998. PVD improvement of soft Bangkok clay with combined vacuum and reduced sand embankment preloading. Geotech. Eng. Southeast Asian Geotech. Soc. 29 (1), 95e121. Chai, J.-C., Carter, J.P., Hayashi, S., 2005. Ground deformation induced by vacuum consolidation. J. Geotechn. Geoenviron. Eng. ASCE 131 (12), 1552e1561. Chai, J.-C., Kawaguchi, Y., 2011. Vacuum Consolidation Induced Deformation under Odometer Condition. Proc. of the 14th Asian Regional Conference on Soil Mechanics and Foundation Engineering. Hong Kong, China. Paper No. 270, CD Rom. Chai, J.-C., Jia, R., Hino, T., 2012. Anisotropic consolidation behavior of Ariake clay from three different CRS tests. Geotech. Test. J. ASTM 35 (6), 1e9. Chai, J.-C., Ong, C.Y., Carter, J.P., Bergado, D.T., 2013a. Lateral displacement under combined vacuum pressure and embankment loading. Geotechnique 63 (10), 842e856. Chai, J.-C., Carter, J., Saito, A., Hino, T., 2013b. Behaviour of clay subjecting to vacuum and surcharge loading in an odometer. Geotech. Eng. J. SEAGS AGSSEA 44 (4), 1e8. Chu, J., Yan, S.W., Yang, H., 2000. Soil improvement by the vacuum preloading method for an oil storage station. Geotechnique 50 (6), 625e632. Hansbo, S., 1981. Consolidation of Fine-grained Soils by Prefabricated Drain, vol. 3, pp. 677e682. Proceedings 10th International Conference Soil Mechanics and Foundation Engineering. Indraratna, B., Rujikiatkamjorn, C., Ameratunga, J., Boyle, P., 2011. Performance and prediction of vacuum combined surcharge consolidation at port of Brisbane. J. Geotech. Geoenviron. Eng. ASCE 137 (1), 1009e1018. Indraratna, B., Rujikiatkamjorn, C., Balasubramaniam, A.S., McIntosh, G., 2012. Soft ground improvement via vertical drains and vacuum assisted preloading. Geotext. Geomembr. 30, 16e23. Kelly, R.B., Wong, P.K., 2009. An embankment constructed using vacuum consolidation. Aust. Geomech. 44 (2), 55e64. Long, P.V., Bergado, D.T., Nguyen, L.V., Balasubramaniam, A.S., 2013. Design and performance of soft ground improvement using PVD with and without vacuum consolidation. Geotech. Eng. J. SEAGS AGSSEA 44 (4), 37e52. Miura, N., Chai, J.-C., Hino, T., Shimoyama, S., 1998. Depositional environment and geotechnical properties of soft deposit in Saga plain. Indian Geotech. J. 2 (2), 121e146. Ohtsubo, K., Egashira, K., Kashima, K., 1995. Depositional and post-depositional geochemistry, and its correlation with the geotechnical properties of marine clays in Ariake Bay, Japan. Geotechnique 45 (3), 509e523. Ong, C.Y., Chai, J.-C., 2011. Lateral displacement of soft ground under vacuum pressure and surcharge load. Front. Archit. Civ. Eng. China 5 (2), 239e248. http://dx.doi.org/10.1007/s11709-011-0110-1. Shang, J.Q., Tang, M., Miao, Z., 1998. Vacuum preloading consolidation of reclaimed land: a case study. Can. Geotech. J. 35 (4e6), 740e751. Xu, F., Chai, J.-C., 2014. Lateral displacement of PVD-improved deposit under embankment loading. Geosynth. Int. 21 (5), 286e300. Yan, S.W., Chu, J., 2005. Soil improvement for a storage yard using the combined vacuum and fill preloading method. Can. Geotech. J. 42 (4), 1094e1104.
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Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
Surcharge loading rate for minimizing lateral displacement of PVD improved deposit with vacuum pressure Jinchun Chai*, Steeva Gaily Rondonuwu Department of Civil Engineering and Architecture, Saga University, 1 Honjo, Saga 840-8502, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 February 2015 Received in revised form 1 April 2015 Accepted 7 July 2015 Available online 10 August 2015
A series of laboratory radial drainage odometer and triaxial tests were conducted to investigate the deformation behaviour of clayey soils under combined vacuum pressure and surcharge loads. Based on the test results, a method for determining the optimum surcharge loading rate (SLR) which will result in minimum lateral displacement of a deposit under combined loads has been proposed. The method using a dimensionless parameter, a, defined as the ratio of SLR and the parameters controlling the rate of consolidation of a deposit improved by prefabricated vertical drains (PVDs). The ratio between surcharge load (Dss) to the vacuum pressure (Dsvac) is designated as ðLR ¼ Dss =jDsvac jÞ. Values for the optimum SLR increase with increasing of initial effective stress in the soil and with reducing LR. It is suggested that the method can be used for design the preloading project with combined vacuum and surcharge loads. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Preloading Consolidation Vacuum pressure Lateral displacement Loading rate
1. Introduction Preloading clayey deposits improved by prefabricated vertical drain (PVD) with combination of vacuum pressure and surcharge load has been widely used in engineering practice (e.g. Artidteang et al., 2011; Indraratna et al., 2012). The combined load offers several advantages and one of them is it can reduce preloading induced lateral displacement of a deposit (e.g., Bergado et al., 1998; Yan and Chu, 2005; Kelly and Wong, 2009; Indraratna et al., 2011; Long et al., 2013; Chai et al., 2013a; Xu and Chai, 2014). Vacuum pressure is an isotropic incremental consolidation pressure and it will result in settlement and inward lateral displacement (toward the centre of the loading area). This inward lateral displacement sometimes may cause surface cracks around the treatment area (Shang et al., 1998; Chu et al., 2000; Chai et al., 2005). While a surcharge (embankment) load will induce settlement and outward lateral displacement of a deposit. Therefore, combining a vacuum pressure with a surcharge load may minimize lateral displacement of a deposit, which is an important design issue, especially in an urban environment.
* Corresponding author. Tel./fax: þ81 952 288580. E-mail addresses: [email protected] (J. Chai), [email protected] (S.G. Rondonuwu). http://dx.doi.org/10.1016/j.geotexmem.2015.07.012 0266-1144/© 2015 Elsevier Ltd. All rights reserved.
The factors influencing lateral displacement induced by embankment and/or vacuum loadings are: (1) the magnitude and loading rate of the loads; (2) the load ratio (LR) of a surcharge load (Dss) to a vacuum pressure (Dsvac) ðLR ¼ Dss =jDsvac jÞ; (3) the initial stress state in and the undrained shear strength (su) of the subsoil; and (4) the consolidation and deformation characteristics of the subsoil. Ong and Chai (2011) reported that for a given subsoil condition, LR and surcharge loading rate (SLR) are two main influence factors on the lateral displacement of a deposit under combined loading. The smaller the SLR and LR values, the smaller the outward lateral displacement. For applying the preloading with combined loads to road or railway embankment constructions, in most cases, the achievable magnitude of vacuum pressure is limited, and the final height of an embankment is pre-specified, i.e. LR may be decided prior to construction. While value of SLR can be controlled during the construction process to minimize the lateral displacement. However, there has been no such design method available yet. In this study a series of laboratory consolidation tests under both modified odometer and triaxial tests with radial drainage (drain was located at the centre of specimens) were conducted to investigate the tendency of lateral displacement of the samples under the combination of a vacuum pressure and a surcharge load. Based on the test results, a method is proposed to determine the optimum SLR with which the lateral displacement of a deposit can be minimized in the field condition.
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List of notations
s
ch cv ds dw k kh ks K
SLR su t Τr ua
coefficient of consolidation in the horizontal direction coefficient of consolidation in the vertical direction diameter of the smear zone diameter of the drain hydraulic conductivity horizontal hydraulic conductivity of natural soil horizontal hydraulic conductivity of a smear zone ratio of horizontal effective stress to the value in the vertical direction coefficient of earth pressure on the wall of the consolidation ring coefficient of at-rest lateral earth pressure drainage length of a PVD ratio of loading atmospheric pressure discharge capacity of a PVD radial radial distance of pore water pressure measurement radius of a unit cell of PVD improvement radius of smear zone equivalent radius of the vertical drain
Kw K0 L LR pa qw r ra re rs rw
559
ratio of radius of smear zone to the equivalent radius of the vertical drain surcharge loading rate undrained shear strength time a time factor dimensionless pore water pressure measurement on the radial distance ra measured excess pore water pressure a dimensionless parameter a dimensionless multiple applied surcharge load increment applied vacuum pressure increment horizontal effective stress initial horizontal effective stress vertical effective stress horizontal stress (effective or total) acting on the wall of consolidation ring measured total horizontal earth pressure on the wall initial vertical effective stress a parameter considering the effect of PVD spacing, smear and well resistance
ue
a b Dss Dsvac s0h s0h0 s0v s0hw
sep
s0v0
m
2. Methodologies
2.2. Odometer condition
2.1. Stress ratio and lateral displacement
Under odometer condition, outward lateral displacement is restricted and only inward lateral displacement is allowed. While horizontal effective stress is changeable. To judge the lateral displacement tendency of a specimen, Chai et al. (2013b) proposed a parameter called coefficient of earth pressure on the wall of the consolidation ring (Kw). Consider the normal stress acting on the wall of the ring ðs0hw Þ, and designate the pressure change transmitted by the solid skeleton of the soil specimen as a positive component of the effective stress (Fig. 1(a)), and the suction (vacuum) pressure as a negative stress change acting on the wall (Fig. 1(b)). Then Kw is defined as follows:
Let's define the ratio of horizontal effective stress (s0h ) to the value in the vertical direction (s0v ) as stress ratio and designated as K: 0
K¼
sh 0 sv
(1)
For a field condition under combined vacuum and surcharge loadings, in case that a surcharge (embankment) load dominates, the load can induce outward lateral displacement and the soil under the toe of the embankment will be in a tendency of passive state and result in K > K0 (K0 is the coefficient of at-rest earth pressure). While, for a case dominated by a vacuum pressure, the lateral displacement will be inward, but for soil under the loading area, K > K0 condition can be created also due to isotropic effective stress (suction) increment in the soil mass. Therefore, sometimes, it may be difficult to only use the stress ratio K to judge the tendency of lateral displacement of a deposit (Chai et al., 2013b).
Surcharge load
Soil
(a) Surcharge load
Pressure on the wall
Vacuum pressure Soil
(b) Vacuum pressure
Fig. 1. Illustration of the pressure change on the wall of a consolidation ring (after Chai et al., 2013b).
0
Kw ¼
shw 0 sv
(2)
The value of s0hw is calculated as follows: 0
shw ¼
sep ue sep
ðue > 0Þ ðue 0Þ
(3)
where sep ¼ the measured total horizontal earth pressure on the wall; and ue ¼ the measured excess pore water pressure at the same level (height) of the earth pressure gauge. It will be explained in the next section that the consolidation ring used has an earth pressure transducer and a pore water pressure transducer inserted on the wall. The vertical effective stress is calculated as follows: 0
sv ¼ Dss ue
(4)
Then when Kw > K0, there will be a tendency for outward lateral displacement, and when Kw < K0, the tendency will be for inward lateral displacement under a field condition. If Kw < 0, there is likely to be a micro-gap formed between the soil specimen and the consolidation ring and inward displacement occurred under the odometer condition.
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Considering the field condition, the odometer condition discussed above may be applicable to a soil element under the centre of an embankment, but not for the condition under the toe of the embankment. As illustrated in Fig. 2, for two soil elements, A and B, assuming the horizontal effective stresses are the same for both the elements, the stress ratio of element B will be larger than that of element A, KB > KA. This implies that even for KA < K0, it is possible for KB > K0 and still results in outward lateral displacement. Chai et al. (2005) proposed that under odometer condition, if there is no effective confinement from the consolidation ring, and vacuum pressure alone can maintain K0 condition of the sample, there will be still no gap occurring between the consolidation ring and the soil sample. This condition is the same as Kw ¼ 0. Considering the soils under an embankment, and assuming the initial effective stress state is in a K0 stress condition, and if the vacuum pressure alone can maintain K0 condition for the applied vacuum and surcharge loads, the applied loads will not induce horizontal earth pressure increment to the soils outside the toe of the embankment, and consequently no outward lateral displacement. Therefore, it is considered that to judge the lateral displacement tendency in the field using the odometer test results, the condition of Kw ¼ 0 may be more suitable then Kw ¼ K0. In case a soil specimen has no zero initial effective stresses before the vacuum and surcharge loads application, to use Kw ¼ 0 criterion, the stress increments caused by the applied loads should be used to calculate Kw value.
r2 r4 ln rrwe 34 þ rw2 4rw4 e e b¼ 2 2 2 rw 1 rrw2 ln rrwa ra2r 2 e
(6)
e
Conceptually, b is a multiple to convert the measured excess pore water pressure of ua to the average pore water pressure in the specimen. Then for a combined vacuum and surcharge loading, s0v can be calculated as:
0 0 sv ¼ sv0 þ Dss þ Dsvac ðua þ jDsvac jÞ$b
(7)
where s0v0 ¼ the initial vertical effective stress; Dss ¼ the applied surcharge load; and Dsvac ¼ the applied vacuum pressure. The value of s0h can be expressed as:
0 0 sh ¼ sh0 þ Dsvac ðua þ jDsvac jÞ$b
(8)
where s0h0 ¼ the initial horizontal effective stress. Note, K (Eq. (1)) is defined as the ratio of total effective stresses in the sample, while Kw (Eq. (2)) is defined as the ratio of effective stress increments.
2.3. Triaxial condition For an ordinary triaxial test, the total confining pressure is a constant, but there is no restriction on horizontal displacement. Thus if the horizontal effective stress (s0h ) is less than the stress ðK0 $s0v Þ required to maintain a no horizontal deformation (K0) state, there will be outward lateral deformation. And if s0h > K0 s0v , there will be inward lateral displacement. Therefore, the tendency of lateral displacement can be easily judged using the stress ratio (K) (Eq. (1)). For a triaxial test with a drain at the centre of the soil specimen, to calculate the average effective stress in the specimen, the consolidation theory for vertical drain needs to be used. In Hansbo's (1981) solution for the consolidation due to the effect of a vertical drain, assuming an equal vertical strain condition, the excess pore water pressure distribution in the radial (r) direction is:
2 r r 2 rw uðrÞf re2 ln rw 2
water pressure is measured at a location with a radial distance of ra ¼ 17 mm on the base pedestal, and the value is designated as ua. To calculate the average pore pressure in the specimen from the measured value of ua, the radial distribution given by Eq. (5) has to be considered. By integrating Eq. (5) with cross-sectional area, a parameter b is introduced as:
(5)
where re ¼ the radius of a unit cell of PVD improvement (here the radius of the soil specimen); and rw ¼ the equivalent radius of the vertical drain. For the triaxial test conducted in this study, the pore
2.4. Time for calculating Kw and/or K In the field, surcharge load induced outward lateral displacement mainly occurs immediately after the load application, i.e. undrained shear deformation, while vacuum pressure induced lateral displacement occurs during consolidation process. For a given geometrical condition, the loading rate will influence the excess pore water pressure generated in the specimen, and therefore the values of Kw and K during loading, but may not significantly influence the final (end of consolidation) values of Kw and K. Considering most outward lateral displacement occurs during the surcharge load application process, the end of surcharge load application is chosen as a critical point for calculating Kw or K from laboratory tests, and use them to judge the tendency of lateral displacement. 2.5. Loading rate parameter a The effect of SLR on lateral displacement of a deposit is related to the consolidation properties of the deposit and the spacing of PVDs. For a PVD improved subsoil, the degree of consolidation is controlled by a dimensionless time factor of Tr:
Tr ¼
ch t 4re2 m
(9)
where ch ¼ coefficient of consolidation in the horizontal direction, and t ¼ time. Using Hansbo (1981)’s solution, the expression of m is:
m ¼ lnðre =rs Þ þ ðkh =ks ÞlnðsÞ
Fig. 2. Illustration of stress ratio change near the toe of an embankment.
3 2p$l2 $kh þ 4 3qw
(10)
where s ¼ rs/rw (rs is the radius of smear zone); l ¼ drainage length of a PVD; kh and ks ¼ the horizontal hydraulic conductivities of natural soil and smear zone respectively; and qw ¼ the discharge
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capacity of a PVD. In Eq. (9), except t, all parameters are basic soil properties of a deposit or the geometric parameter of PVD improvement. Let's define a dimensionless parameter (a) as:
a¼
SLR 4$SLR$re2 m t¼ Tr pa ch pa
(11)
where pa ¼ atmospheric pressure. It is aimed at establish aeKw and/ or aeK relationships from the test results. It is considered that a a value corresponding to Kw ¼ 0 (odometer condition) or K ¼ K0 (triaxial condition) will result in minimum lateral displacement. Then the corresponding value of SLR will be the optimum value for the purpose of minimizing the lateral displacement under the field condition.
3. Laboratory test 3.1. Material tested Remolded Ariake clay was used for the tests. Majority of Ariake clay is marine formation with smectite as main clay mineral (Ohtsubo et al., 1995). Natural Ariake clay deposit has a high compressibility and low strength (Miura et al., 1998). Some physical and mechanical properties of the Ariake clay tested are listed in Table 1. Both incremental loading (IL) and constant rate of strain (CRS) consolidation tests with a strain rate of 0.02%/min were conducted. The CRS tests were conducted with either vertical or horizontal drainages (Chai et al., 2012), and a ratio of the coefficients of consolidation in the horizontal direction (ch) to that in the vertical direction (cv) of 1.63 was obtained from the test results. While, the CRS test resulted in a relative lower cv value than that of IL test. The values listed in Table 1 are cv value from the IL test and ch ¼ 1.63cv. 3.2. Modified odometer test (1) Equipment The modified odometer device used is shown in Fig. 3. The detailed description of the test device has been reported by Chai et al. (2013b), and here only a brief description is given. The device consists of an odometer ring 60 mm in diameter and nominal height of 20 mm. At the middle height of the wall of the ring a pore pressure transducer and an earth pressure transducer were inserted into the wall and opposite each other. A hollow cylindrical metal porous stone wrapped with filter paper was inserted in a predrilled hole at centre of the specimen as a vertical drain. The diameter of the drain (dw) was 4 mm or 8 mm. The vacuum pressure was applied to the specimen through the central drain and the surcharge load was applied using air pressure. The settlement gauge was installed on the top of the loading piston. Settlement, pore water pressure and total lateral earth pressure were recorded by a computer through a data logger.
Table 1 Basic soil properties. Parameter Plastic limit Liquid limit Compression Coefficient of consolidation wp (%) (m2/day) wl (%) index Cc
Value
56.8
120.3
0.821
Vertical, cv
Horizontal, ch
5 103
8.15 103
561
(2) Specimen preparation To prepare the specimen, firstly, the clay slurry with a water content of about 1.2 times of its liquid limit was de-aired with approximately 100 kPa vacuum pressure. Then the de-aired slurry was put into a consolidation container of 60 mm in diameter and 60 mm in height (consolidation ring þ 40 mm height of a collar), and consolidated under 20 kPa pressure. Next 20 mm thick specimen was cut from the pre-consolidated sample for further consolidation test. Finally, a hole of 8 mm or 4 mm in diameter (dw) was drilled manually for installing the vertical drain at the center of the specimen. (3) Cases tested All cases tested are summarized in Table 2. For all cases the surcharge load adopted was 80 kPa, while vacuum pressure used was either 80 kPa or 40 kPa. And the resulting final value of LR is 1e2. For all tests, the vacuum pressure was fully applied at the start of the test, but the surcharge load was applied in a stepwise manner to simulate the field construction process. The incremental load for each step was 10 kPa, and the time interval between adjacent two steps was varied from 10 min to 360 min, which resulting in values of SLR from 10 kPa/360 min to 10 kPa/10 min. 3.3. Modified triaxial test (1) Equipment An ordinary triaxial compression test device was modified to conduct the consolidation under combined vacuum and surcharge loads. The sketch and the photo of the device are shown in Fig. 4 (a) and (b) respectively. There are two main modifications. (a) Instead of a conventional solid cylindrical specimen, using an annular shaped soil specimen with a drain inserted in the centre to simulate a unit cell of prefabricated vertical drain (PVD) improved soil layer. The nominal outer diameter of the specimen was 50 mm, inner diameter of 8 mm, and height of 100 mm. (b) Adding a system for applying vacuum pressure to the centreedrain inserted into the specimen. (2) Test procedure (a) Specimen preparation. First, a cylinder soil specimen as for ordinary triaxial test was made with pre-consolidated Ariake clay (from slurry) under 20 kPa vertical consolidation pressure. Then the specimen was fixed on a frame (guide) and an 8 mm in diameter central hole was made using a drilling tool manually. A vertical drain made by a steel spring and wrapped by filter paper was inserted into the central hole as a vertical drain. The spring is made of 0.6 mm in diameter steel wire with a pitch between two adjacent coils of about 2.7 mm. The outer diameter of the spring is about 8 mm. The stiffness of the spring is very low, and its influence on the vertical stress can be ignored. (b) Saturating the specimen. Soil specimen with the drain installed was put into the rubber membrane sleeve with a diameter of 50 mm. Then the specimen with the rubber membrane was placed into a container to which vacuum pressure can be applied, and de-aired water was put around the specimen till the water level reached the height of the specimen. A vacuum pressure of about 20 kPa was applied to the container for about 1 h to eliminate possible trapped air
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Displacement
Air pressure
(Unit: mm)
Porous stone tube Pore pressure gauge
60 20
Specimen
10
Earth pressure gauge To vacuum pump
(a) Sketch
(b) Photo
Fig. 3. Laboratory odometer test device.
bubbles between the rubber membrane, the drain, and the soil specimen. (c) Pre-consolidation. The specimen was set into the triaxial cell, and a cell pressure of about 5 kPa was applied, and de-aired water was flowed from the bottom to the top of the specimen to remove any air bubbles in the drainage system. Then anisotropic consolidation stresses were applied to consolidate the specimen for 1 day. For the cases tested, a K0 value of 0.6 was assumed in this step. The isotropic part of the consolidation stresses was applied using air-pressure and the deviational part by dead load. To avoid excessive shear deformation in the pre-consolidation process, the preconsolidation pressures were applied in a stepwise manner with a vertical stress increment of 10 kPa and horizontal stress increment of 6 kPa and a time interval of 2 hours. (d) Consolidation under combined loads. Firstly, vacuum pressure of 60 kPa was applied through the central drain. Then the surcharge load increment (10 kPa for each step) was applied stepwise with desired loading rate using dead load.
The total surcharge load applied was 60 kPa. Due to the capacity of vacuum pressure generation system adopted for the triaxial tests, the magnitude of the vacuum pressure applied was smaller than that for the odometer tests. The consolidation test generally lasted for about 2e4 days. The vertical settlement, excess pore water pressure at the bottom of the specimen and at a radial distance ra ¼ 17 mm (Fig. 4(a)) was measured and recorded using a data logger and a computer. During the pre-consolidation, the amount of water drained out from the specimen was also measured and used for calculating the diameter of the specimen before the consolidation under the combined loads. Further, the final average diameter of the specimen was measured after the consolidation test, and the value is used for calculating the horizontal strain of the specimen caused by the consolidation of the combined loads. (3) Cases tested Totally nine (9) tests were conducted using triaxial device, and the initial stress and loading conditions are listed in Table 3.
Table 2 Cases tested using the modified odometer.
4. Test results
Case
s0v0 (kPa)
dw (mm)
Dss (kPa)
Dsvac (kPa)
LR
SLR (kPa/min)
O-1a O-1b O-1c O-1d O-2a O-2b O-2c O-3a O-3b O-3c O-3d O-4a O-4b O-4c O-5a O-5b O-5c O-6a O-6b O-6c
0
8
80
80
1
10/10 10/60 10/120 10/360 10/60 10/90 10/360 10/10 10/15 10/90 10/360 10/30 10/60 10/90 10/30 10/60 10/90 10/30 10/60 10/90
0
8
80
40
2
0
4
80
80
1
20
8
80
80
1
40
8
80
80
1
80
8
80
80
1
4.1. Modified odometer test results (1) Typical test results The test results of LR ¼ 1, diameter of the central drain, dw ¼ 8 mm, SLR of 10 kPa/10 min and 10 kPa/60 min are shown in Figs. 5e7 for the variations of settlement, pore water pressure and total earth pressure, respectively. The negative total earth pressure indicates possible formation of micro-gap between the consolidation ring and the soil specimen. With increase of SLR, the settlement rate, maximum pore water pressure and total horizontal earth pressure were increased. The applied vacuum pressure was 80 kPa, but the measured values are about 50 kPa (Fig. 6). Since the gauge was calibrated carefully before the tests, the possible reason considered is that under the laboratory condition, due to vacuum (suction) pressure, mini-drain can become unsaturated and at the interface between
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563
Fig. 4. Photo of the triaxial device.
Table 3 Cases tested using the modified triaxial device. Case
T-1a T-1b T-1c T-1d T-2a T-2b T-2c T-2d T-3a T-3b T-3c T-3d
Initial stresses s0v0 (kPa)
s0h0 (kPa)
20
12
Dss (kPa)
Dsvac (kPa)
LR
SLR (kPa/min)
60
60
1
10/30 10/60 10/90 10/480 10/30 10/60 10/90 10/480 10/30 10/60 10/90 10/480
the mini-drain and soil forming convex meniscuses, which can reduce the efficiency of the vacuum pressure transferring into the soil sample. (2) Effect of SLR on Kw value
40
24
60
60
1
60
36
60
60
1
Fig. 5. Settlementetime curves (LR ¼ 1; dw ¼ 8 mm).
Fig. 8 shows the variation of the values of Kw for the cases of LR ¼ 1.0, dw ¼ 8 mm, but different SLR. It can be seen that (1) with increase of SLR, the values of Kw are increased during the surcharge loading process; and (2) influence of SLR on the final value of Kw is not significant. It can also be observed that when Dss is larger than about 40 kPa, for each surcharge load increment, the maximum Kw value not varied much. The mechanism for this may be that the surcharge loading induced shear stress increment and the consolidation induced shear strength increment are somehow balanced each other under the odometer condition.
Fig. 6. Variation of pore water pressure (LR ¼ 1; dw ¼ 8 mm).
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Fig. 7. Variation of total lateral earth pressures (LR ¼ 1; dw ¼ 8 mm).
(3) Kw versus a relationship For both the odometer and triaxial tests, the central drains were inserted into a pre-drilled hole and there should be no significant disturbance to the surrounding soil, and therefore no obvious smear zone existed. However, the soil around the central drain would be consolidated much faster, and the void ratio and therefore the hydraulic conductivity (k) of the soil around the drain would be reduced considerably. Also, as mentioned previously, in the laboratory condition, the central drains in the samples can become unsaturated. Consequently, there might be a thin soil layer around the drain became partially saturated, and its k value might be reduced significantly. The effect of faster consolidation and partial unsaturation induced k reduction, is analogous to “smear” effect. Back analysis is conducted to quantitatively evaluate the “smear” effect. Assuming the diameter of the “smear” zone (ds ) is 2 times of the diameter of the drain, by fitting the settlement curves of the odometer test results, a kh/ks ratio of about 10 was obtained. Then ds/dw ¼ 2 and kh/ks ¼ 10 are used for calculating a values for both the odometer and triaxial test results. Kw versus a relationship evaluated from the test results at the end of surcharge load application are summarized in Fig. 9. It can be clearly seen that for a given LR, Kw increased with the increase of a. Comparing LR ¼ 1 and 2 cases shows that the larger the LR, the
Fig. 8. Variation of Kw values (LR ¼ 1.0; dw ¼ 8 mm).
Fig. 9. Kwea relationship.
higher the Kw. Although the data are scattered, for s0v0 ¼ 0, cases, using Kw ¼ 0 criterion, for LR ¼ 1, a value of about 2.3 can be estimated and for LR ¼ 2 cases, the value is about 1.0, i.e. for a larger LR case, a smaller a value (lower loading rate) is required to minimize the lateral displacement. The test results also indicate that increase the initial effective stresses in the sample, reduced Kw value. Higher initial effective stresses in the sample means higher initial undrained shear strength, and for a given surcharge load, it will result in less undrained shear deformation. 4.2. Modified triaxial test results (a) Typical test results Fig. 10 presents some settlement curves of s0v0 ¼ 20 kPa cases. It can be seen that increase SLR increased settlement significantly due to more shear deformation. In Fig. 11, apparently SLR ¼ 10 kPa/ 90 min case had higher pore water pressures (u) for a given time, but at the end of the surcharge load application, the higher the SLR, the higher the u value. The difference of u values between three (3) cases before elapsed time of 50 min can be considered as the scatter of the measured data. The applied vacuum pressure to the central drain was 60 kPa, but the measured final value was about 45 kPa.
Fig. 10. Settlement curves (s0v0 ¼ 20 kPa).
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Pore pressure (kPa)
10 0 -10 -20 -30 -40 -50 0.01
SLR (kPa/min) 10/30 10/60 10/90
0.1
1
10 100 Elapsed time (min)
1000
10000
Fig. 11. Excess pore pressure variations (s0v0 ¼ 20 kPa).
Fig. 13. aeK relationships.
The calculated K values by Eqs. (1), (7) and (8) are depicted in Fig. 12. For these three cases, K values gradually reduced with the application of the surcharge load. At the end of the surcharge load application, K values were less than 0.3. For remoulded Ariake clay, the coefficient of at-rest earth pressure is about 0.4 (Chai and Kawaguchi 2011), and K < K0 means that the sample would deform lateral in the direction of increase the diameter of the sample (i.e. tensile horizontal strain) at that time. With the progress of consolidation and increase of vacuum pressure, K values were gradually increased and at the time of termination of the tests the values are about 0.45. (b) K versus a relationships
aeK relationships from the results of modified triaxial test are shown in Fig. 13 corresponding to the end of surcharge load application. It clearly shows that K increased with the reducing of a (or SLR). The same tendency as that of the odometer test results, K increased with the increase of initial effective stresses in the sample. Using the K ¼ K0 (z0.4 for the samples tested) criterion, for s0v0 ¼ 20 kPa, a a value which may result in minimum lateral displacement, of about 0.8 can be estimated, which is smaller than that from the odometer test results.
(c) a versus horizontal strain For the modified triaxial test, the shapes of the samples after the consolidation test were measured and the horizontal strains were calculated and the results are shown in Fig. 14. Comparing with the estimated diameters after the pre-consolidation, all samples were bulged, i.e. had tensile horizontal strain. However, the absolute magnitude of the horizontal strain reduced with the reducing of the a value and increasing of initial effective stresses in the samples. From the results in Fig. 13 and the method we proposed, under s0v0 ¼ 20 kPa, and at a of about 0.8, zero horizontal strain is predicted, but Fig. 14 shows it had about 1% horizontal strain. There are two possible reasons for this apparent inconsistency. One is that after dismounted the sample, unloading will result in certain increase of its size. Another one is that during the consolidation test, a sustained deviator stress was existed in the samples, and it may cause certain creep deformation. Further the target considered is the end of surcharge load application and in term of horizontal strain, it may be different from the final condition. 4.3. Discussion The odometer test results give larger a values than that from the triaxial test results and the exact reason(s) is not clear yet. For the device used, the lateral earth pressure gauge has a diameter of
0.6
K
0.5 0.4 0.3 0.2 0.1 0.01
SLR (kPa/min) 10/30 10/60 10/90
0.1
1 10 100 Elapsed time (min) Fig. 12. Variations of K with time.
1000
10000 Fig. 14. a versus horizontal strains (triaxial test results).
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10 mm with a flat surface. While, the consolidation ring has an arc inner surface, i.e. the surface of the earth pressure gauge is not matched the inner surface of the ring. To ensure a good contact between the sample and the ring, the remoulded soil was reconstituted directly inside the ring as explained previous. However, during the consolidation process, the soil around the earth pressure gauge will experience not only vertical compression, but also some complicated shear deformation and that may influence the measured earth pressure (possibly lower than the value supposed to be), and therefore possibly the lower calculated Kw value. Further investigation on this issue is required. Nevertheless, considering two different tests with different boundary condition and sample size, the results are in the same order is quite encouraging. Let's consider a practical case, for which, the PVD spacing is 1.0 m with a square pattern; equivalent diameter of the PVD, dw ¼ 0.05 m; the diameter of smear zone, ds ¼ 0.2 m; and kh/ks ¼ 2; discharge capacity of a PVD, qw ¼ 100 m3/year; hydraulic conductivity in the horizontal direction, kh ¼ 2 109 m/s; coefficient of consolidation in the horizontal direction, ch ¼ 10 m2/year; and the drainage length of PVD, l ¼ 5 m. From the results of the triaxial test, in case of a deposit has an average initial vertical effective stress of about 20 kPa, if LR ¼ 1.0 and the magnitude of vacuum pressure of 60 kPa, to minimize the lateral displacement a z 0.8 can be obtained, and the corresponding surcharge loading rate will be about 0.5 kPa/day for this case, i.e. a rate of filling of 1.0 m/40 days. 5. Conclusions A series of laboratory radial drainage odometer and triaxial tests were conducted to investigate the deformation behaviour of clayey soils under combined vacuum pressure and surcharge loading. For odometer condition, a parameter, Kw, defined as the ratio of the horizontal effective stress acting on the inner wall of the consolidation ring divided by the vertical effective stress in the soil sample, and for triaxial condition, the ratio of horizontal effective stress to that in the vertical direction, K, are used to determine the tendency of the lateral displacement of the samples, i.e. inward or outward. A dimensionless parameter a, define as a function of surcharge loading rate (SLR) and the parameters controlling the rate of consolidation of a prefabricated vertical drain (PVD) improved deposits has been introduced and linked to Kw ¼ 0 and/or K ¼ K0 (coefficient of at-rest earth pressure)values to determine optimum value of SLR, which will result in minimum lateral displacement. The ratio between surcharge load (Dss) to vacuum pressure (Dsvac) is designated as LRð¼ Dss =jDsvac jÞ. The test results indicate that values for the optimum SLR increase with increasing of initial effective stresses in the soil and with reducing LR. The established
optimum a value from the odometer test results is larger than that from the triaxial test results, but they are in the same order. One possible reason considered is the difference of the magnitude of the applied vacuum pressure. It is suggested that further investigation on this issue is required.
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