- Email: [email protected]
Cone penetration-induced pore pressure distribution and dissipation
Computers and Geotechnics 57 (2014) 105–113
Contents lists available at ScienceDirect
Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo
Cone penetration-induced pore pressure distribution and dissipation Jin-Chun Chai a,⇑, Md. Julfikar Hossain a, John Carter b, Shui-Long Shen c a
Graduate School of Science and Engineering, Saga University, 1 Honjo, Saga 840-8502, Japan Faculty of Engineering and Built Environment, the University of Newcastle, NSW 2308, Australia c Department of Civil Engineering, Shanghai Jiao Tong University and State Key Laboratory of Ocean Engineering, 800 Dong Chuan Road, Minhang District, Shanghai 200240, China b
a r t i c l e
i n f o
Article history: Received 31 October 2013 Received in revised form 16 January 2014 Accepted 18 January 2014 Available online 8 February 2014 Keywords: Piezocone test Model test Coefficient of consolidation Excess pore pressure Cavity expansion
a b s t r a c t The excess pore water pressure distribution (u) induced by the penetration of a piezocone into clay and its dissipation behaviour have been investigated by laboratory model tests, theoretical analysis and numerical simulation. Based on the results of the tests and the analysis, a semi-theoretical method has been proposed to predict the piezocone penetration-induced pore pressure distribution in the radial direction from the shoulder of the cone. The method can consider the effect of the undrained shear strength (su), over-consolidation ratio (OCR) and rigidity index (Ir) of the soil. With a reliably predicted initial distribution of u and the measured curve of dissipation of pore water pressure at the shoulder of the cone (u2), the coefficient of consolidation of the soil in the horizontal direction (ch) can be back-fitted by analysis of the pore pressure dissipation. Comparing the back-fitted values of ch with the values directly estimated by a previously proposed method indicates that the previously proposed method can be used reliably to estimate ch values from non-standard dissipation curves (where u2 increases initially and then dissipates with time). Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The piezocone is now widely used as an in situ site investigation tool. From the results of a piezocone penetration test, the soil profile and the undrained shear strength (su) of a clayey deposit can be estimated, normally quite reliably (e.g., [2]). Numerous research results have also been published on estimating the in situ hydraulic conductivity (e.g., [3]) and the coefficient of consolidation of soil in the horizontal direction (ch) (e.g., [4,16]) from the results of piezocone penetration and dissipation tests. For a standard piezocone with the filter for pore water pressure measurement located at the shoulder of the cone (u2 type), two types of piezocone dissipation curves have been reported in the literature. One displays monotonic reduction of the measured pore water pressure (u2) with time (e.g., [16]), i.e., the so called ‘‘standard’’ dissipation curve; and the other is a ‘‘non-standard’’ curve, for which the measured value of u2 increases initially and then reduces with time [1,4,15]. The reason for a non-standard dissipation curve is that at the beginning of the dissipation the pore pressure at the filter element location is lower than the pore pressures in the soil nearby. The causes for this kind of initial pore water pressure distribution are thought to be: (1) the shear-induced ⇑ Corresponding author. Tel.: +81 952288580. E-mail addresses: [email protected] (J.-C. Chai), [email protected] (J. Carter), [email protected] (S.-L. Shen). http://dx.doi.org/10.1016/j.compgeo.2014.01.008 0266-352X/Ó 2014 Elsevier Ltd. All rights reserved.
dilatancy effect for overconsolidated clay or dense sandy soil, which results in lower initial pore water pressure being generated in zones of soil with significant shear strain, i.e., in the zone close to the surface of the cone (e.g., [1,4]); and (2) the partial unloading effect when a soil element moves from the face to the shoulder of the cone during cone penetration (e.g., [4]). Kim et al. [10] reported laboratory model test results of the piezocone penetration-induced pore water pressure distribution (u) in the radial direction at the level of the shoulder of the cone. The measured data show that for the normally consolidated case, values of u reduced with radial distance, but for overconsolidated cases (OCR > 5) values of u at the shoulder of the cone (the filter location) are lower. Peak values of u were reached at a radial distance of about 1.4–2.2 times the radius of the cone and then u reduced with increasing radial distance. Unfortunately, the dissipation curves for these tests were not reported. The numerical results of Chai et al. [4] indicate that even for a slightly overconsolidated clayey soil, the initial value of u at the shoulder of the cone is lower than values in the nearby soil region. It is clear that knowledge of the initial distribution of u induced by piezocone penetration is very important for establishing a suitable method to evaluate ch from the piezocone dissipation test results. However, due to physical restrictions, such as the size of a piezometer, the limited number of piezometers that can be installed in the ground or in a laboratory test specimen, it is difficult to measure a precise distribution of u around a cone, even in a
106
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
laboratory model test. However, by combining the limited measured data related to the initial distribution of u and the dissipation curve for u2, a more complete picture of the initial distribution of u induced by piezocone penetration can be deduced. In this study, laboratory model tests were conducted using a piezocone and these involved measurements of the pore pressures generated during penetration and then their subsequent dissipation. Pore water pressure measurements were made at the shoulder of the cone and at three points in the model ground specimen. A method for predicting the radial distribution of excess pore water pressure induced by piezocone penetration (u) from the shoulder of the cone is proposed and validated using the model test results, as well as some other results available in the literature. Finally, a method for estimating the coefficient of consolidation of a deposit in the horizontal direction (ch) from non-standard dissipation curves is discussed, making reference to the predicted initial distribution of u caused by the piezocone penetration. 2. Laboratory model tests 2.1. Equipment The device used for the model tests is shown in Fig. 1. The cylindrical container (chamber) is made of PVC and has an inner diameter of 0.485 m and a height of 1.0 m. A piston system driven by air
pressure was used to apply consolidation pressure to the soil sample. The sealing between the piston and the container was achieved by using a rubber ‘‘O’’-ring placed in a slot around the piston as well as a rubber sleeve installed above the piston. The piezocone used in these experiments has a diameter of 30 mm with a cone tip angle of 60°. The filter for pore water pressure measurement was installed on the shoulder of the cone. The set-up of the test is illustrated in Fig. 1. The penetration system consists of a reaction frame, a motor and a speed control unit. The penetration rate adopted was 25 mm/min. A servo motor is used to control the penetration rate. Since the penetration depth is relatively small and in order to reach a steady rate in a short time period, a rate of 50% of the maximum rate of the motor was adopted. Although the rate is lower than that adopted in the standard field test, i.e., 20 mm/s, Kim et al. [9] reported that for a saturated clayey soil and when the penetration rates are about 0.1–20 mm/s, there is no obvious effect on the measured penetration tip resistance and the generated pore water pressure. Three piezometers with a diameter of 20 mm and length of 25 mm were placed in the model ground at different radial distances from the centreline of the cone, but on the same level, in order to monitor the pore water pressure distribution and its variation during the piezocone penetration and dissipation tests (Fig. 1(b)). For the configuration adopted, the ratio of the diameter of the model ground and the cone is about 16. This ratio is relatively small and the pore water pressures measured by the piezometer near the periphery of the cylindrical chamber may be influenced by the boundary (wall of the chamber). This point will be further discussed in presenting the measured and calculated results. The settlement of the model ground was measured by a dial gauge. During piezocone penetration and the subsequent dissipation process, the tip resistance and pore water pressures at the shoulder of the cone and at the locations of the three piezometers installed in the model ground were monitored using a computer through a data logger. 2.2. Test procedure
(a)
(b) Fig. 1. Schematic diagram of laboratory model test. (a) Illustration of the set-up of the test and (b) plane view of the locations of piezometers (P1, P2 and P3).
2.2.1. Preparing model ground Three layers of non-woven geotextile (about 138 g/m2) were first placed at the bottom of the cylindrical chamber to act as a drainage layer. Then six 0.1 m wide geotextile strips were lined vertically along the inner periphery of the chamber to facilitate drainage by outward radial flow of the pore water. In the field condition, the radial boundary is neither drained nor undrained, and so the laboratory set-up is an approximation of the field situation. Thoroughly remoulded clay soil with a water content about 1.2 times its liquid limit was placed in the chamber, layer by layer. To avoid possible air-bubbles being trapped in the sample, each soil layer was thoroughly stirred by a stainless rod. When the soil deposit was about 0.5 m thick, the three piezometers were installed. Then further soil was added until the layer was about 0.8 m thick. Finally, three layers of non-woven geotextile were placed on top of the cylindrical soil specimen to act as a drainage layer, and the piston and air-pressure system were setup. A pre-determined air pressure was applied to pre-consolidate the model ground. Once the degree of pre-consolidation was more than 90%, the air-pressure was adjusted to result in a specimen with the desired over-consolidation ratio (OCR). For cases where OCR > 1.0, there may have been some negative pore water pressure in the ground at this stage. A piezocone penetration and dissipation test was conducted once the unloading-induced negative pore pressures had the opportunity to dissipate (which generally took a few days). 2.2.2. Piezocone penetration and dissipation test After pre-consolidation, the thickness of the model ground was about 0.60 m, and it is estimated that the three piezometers were
107
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
then located about 0.225 m below the surface of the sample. The piezocone was then pushed into the sample so that the pore pressure filter at the shoulder of the cone was located at a depth of 0.225 m from the surface of the model ground. A dissipation test was then conducted by holding the cone stationary. 2.3. Materials used and cases tested The soil used was remoulded Ariake clay [12]. The physical properties of this clay are listed in Table 1. The initial water content of the soil was adjusted to about 133.0% and the sample was thoroughly mixed before putting it into the chamber. Three tests were conducted, as listed in Table 2. The air pressure applied during pre-consolidation was 100 kPa, but there was a shaft installed on the top of the piston, and so the area on which the air pressure could be applied is annular. After correcting for the area of the shaft, the effective consolidation stress transmitted to the soil was estimated to be about 96 kPa. Samples with relatively low values of OCR were tested because most natural soft clayey deposits are found in such conditions. For all cases, after the penetration and dissipation test, soil samples from the model ground were taken for oedometer testing and laboratory mini vane shear tests. The mini vane used has a diameter of 20 mm and height of 40 mm and the shearing speed adopted was 3 degrees/min. 2.4. Test results The test results presented here are: (1) initial distributions of u before starting the dissipation tests, (2) u2 dissipation curves, and (3) dissipation curves recorded by the three piezometers embedded in the model ground. (1) Initial distributions of u The initial distributions of u for samples with OCR = 1, 2 and 4 are shown in Fig. 2. Generally the initial values of u reduced with an increase of OCR. The measurements also show that u reduces with radial distance. It is not possible to discern whether the values of u are actually higher in a zone adjacent to the shoulder of the cone than right on the shoulder (r = r0), since the location of P1 (r1) is not close enough to the cone face to allow such a determination. Locating P1 closer to the centre of the model ground was not attempted as it was thought that the piezometer may be damaged during the cone penetration process or it may influence the outcome of the piezocone dissipation test. As shown in Fig. 2(c) for
Table 1 Physical properties of the Ariake clay used.
the case where OCR = 4, P2 was damaged and only the results of P1 and P3 can be presented. (2) Piezocone dissipation curves The dissipation curves for u2 at the shoulder of the cone are shown in Fig. 3. All measured curves are non-standard, i.e., u2 increased initially and then dissipated with time. From the measured dissipation curves, interpreted values of the time (tmax) for u2 to reach its maximum value (umax), and the time increment (t50) for u2 to reduce to 50% of umax are summarized in Table 3. It can be seen that tmax increased with the increase of OCR. (3) Dissipation curves at P1, P2 and P3 The pore pressure dissipation curves measured at the locations of the three piezometers embedded in the model ground are depicted in Fig. 4. All measured curves show a tendency of initial increase in the value of u followed by dissipation to a value close to zero. The measured maximum value of u also reduced with increasing radial distance from the cone. 3. Predicting the distribution of excess pore pressure 3.1. Proposed method It is generally accepted that during a cone penetration process, values of u generated around the cone consists two parts arising from: (1) the change of mean stress (Dup); and (2) the change of shear stress (Dus) (e.g., [1,10,13]). For a normally consolidated clayey soil or loose sand, Dus is normally positive, while for a heavily over-consolidated clayey soil or dense sand, Dus may be negative. The generation of shear-induced negative values of Dus around the shoulder of the cone is generally considered as the main reason for the existence of non-standard dissipation curves [1,4,15]. However, the numerical results from Chai et al. [4] also show that even for a clayey deposit that is close to normally consolidated, at the very beginning (may be for only the first few seconds) of the dissipation process, the pore water pressure at the shoulder of the cone may increase and then decrease, i.e., producing a non-standard dissipation curve. A possible reason for this phenomenon is the partial unloading effect in the vertical direction when (relatively speaking) a soil element moves from the face to the shoulder of a cone, and during this process, the vertical strain increment in the soil element is indeed tensile [16]. This partial unloading effect tends to reduce the value of u near the shoulder of a cone. Its value arising from this cause alone is designated here as Duul. Hence u can be expressed as:
u ¼ Dup þ Dus þ Duul
Soil properties
Liquid limit, LL (%)
Plastic limit, PL (%)
Finer than 2 lm (%)
Water content, Wn (%)
Values
114.0
60.6
63.5
133.0
ð1Þ
where the various components are explained as follows. Using an elastic-perfectly plastic soil model and based on undrained cylindrical cavity expansion theory, the excess pore water
Table 2 Model test conditions. Case
r0v m a (kPa)
r0v 0 (kPa)
OCR
su (kPa)
Radial locations of piezometer (mm) r1
r2
r3
1 2 3
96 96 96
96 48 24
1 2 4
30 26 23
45 45 54
90 90 107
135 135 161
a r0v m is the maximum vertical consolidation stress, r0v 0 is the initial vertical effective stress in the model ground during piezocone penetration and dissipation tests, and su is the estimated undrained shear strength.
108
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
120
Measured
100
Predicted
80
Excess pore pressure (kPa)
140
Cone
Initial excess pore pressure (kPa)
140
60 40 20 0 0
0.05
0.1
0.15
0.2
80 60 40 20 0.01
0.1
1
Radial distance (m)
Time (h)
(a)
(a)
10
100
1000
100
Excess pore pressure (kPa)
100
Measured
80
Predicted 60
Cone
Initial excess pore pressure (kPa)
Predicted
100
0 0.001
0.25
Measured
120
40
20
0.05
0.1
0.15
0.2
0.25
Predicted
60
40
20
0 0.001
0 0
Measured 80
0.01
0.1
1
10
100
1000
Time (h)
Radial distance (m)
(b)
(b) 80
Excess pore pressure (kPa)
Measured 80
Predicted
60
Cone
Initial excess pore pressure (kPa)
100
40
20
0
Measured
40
20
0 0.001 0
0.05
0.1
0.15
0.2
Predicted
60
0.01
0.25
0.1
1
10
100
1000
Time (h)
Radial distance (m)
(c)
(c)
Fig. 3. Piezocone dissipation curves: (a) OCR = 1, (b) OCR = 2, (c) OCR = 4. Fig. 2. Initial u distribution with radial distance from the cone: (a) OCR = 1, (b) OCR = 2, (c) OCR = 4.
pressure due to the change of mean stress (Dup) can be expressed as follows:
Dup ¼ 2 su lnðR=rÞ ðr 0 < r < RÞ
ð2Þ
where su = the undrained shear strength of the soil; r0 = the radius p of the cylindrical cavity (cone); r = radial distance; R = r0 Ir is the outer radius of the annular plastic zone surrounding the cylindrical cavity and Ir = G/su is the rigidity index of soil, with G = the elastic shear modulus of the soil. For the magnitude of shear-induced excess pore water pressure, Dus, there is no well-accepted method of prediction. Several researchers (e.g., [10,13]) attempted to use the Modified Cam Clay
Table 3 Summary of the laboratory piezocone dissipation test results. Test No.
OCR
tumax (min)
umax (kPa)
t50 (min)
t50m (min)
Ir
1 2 3
1 2 4
0.35 0.75 1.40
128.9 93.7 73.5
83.65 79.59 107.76
60.48 47.94 59.26
100 100 100
(MCC) model [14] to predict the magnitude of Dus. Randolph et al. [13] proposed the following equation to calculate the value of Dus.
Dus ¼ p0i p0f
ð3Þ
where p0i and p0f = the values of mean effective stresses at the initial and failure states, respectively. Using the MCC model and consider-
109
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
Excess pore pressure (kPa)
120
M¼
80
Measured P1 P2 P3
60
Predicted P1
100
su ¼
P3
20 0 0.001
0.01
0.1
1
10
100
1000
Excess pore pressure (kPa)
100 Measured P1 P2 P3 Predicted P1 P2
40
P3
20
0 0.001
0.01
0.1
1
10
100
1000
Time (h)
(b)
Excess pore pres sure (kPa)
60 Measured P1 P3 40
Predicted P1 P3
20
0 0.001
0.01
0.1
1
10
100
ðTriaxial conditionsÞ
ð6Þ
ðPlane strain conditionsÞ
ð7Þ
It can be observed from Eq. (3) that the component (p0i p0f ) does not change with radial distance, and for this reason Randolph et al. [13] proposed that the pore pressure contribution expressed by Eq. (3) should be added to the value of u generated throughout the plastic zone. It is noted that first yielding and material failure coincide in an elastic-perfectly plastic model. But with a strain hardening elasto-plastic model, like MCC, yielding does not necessarily coincide with material failure. As illustrated in Fig. 5, if a deviator stress qif is considered, Points B and C would be considered to be at failure according to an elastic-perfectly plastic model. However, according to the MCC model Points B and C have not yet failed, although at each of these points the soil is yielding plastically. Path YBA can be considered as an effective stress path for undrained compression. Path YC may occur due to internal pore water movement even if the boundary conditions of the soil sample allow no flow, i.e., undrained conditions overall for the soil body. Therefore within the plastic zone predicted by an elasticperfectly plastic model, shear stress-induced excess pore water pressure may vary with radial distance. Based on the results of laboratory model test, Kim et al. [10] assumed that the shear stress induced excess pore water pressure mainly occurs in a shear zone with a radius, rs = (1.5–2.2)r0 < R. They further assumed that the shear induced excess pore water pressure has a maximum value at r = r0, and linearly reduces to zero at r = rs. Chai et al. [4] conducted numerical simulations of piezocone penetration and the results indicate that a zone within which the excess pore water pressure is significantly influenced by the shear deformation is about 10–15 mm thick from the surface of the cone, which is comparable with that proposed by Burns and Mayne [1] of about 10 mm. It is proposed that the value of rs is a portion of the radius of the plastic zone (R) induced by a cavity expansion and a function of OCR. By further assuming that the minimum value of rs is (r0 + 5) mm, rs can be expressed as:
(a)
60
Mp0f 2
Mp0f su ¼ pffiffiffi 3
Time (h)
80
ð5Þ
The value of the undrained shear strength, su, can also be predicted from knowledge of the value of p0f . Conversely, if the value of su is known, p0f can be estimated, and their relationships are as follows
P2 40
6 sin /0 3 sin /0
1000
Time (h)
rs ¼ a ðOCRÞb R ðrs 6 r 0 þ 5 ðmmÞÞ
(c) Fig. 4. Dissipation curves at P1, P2 and P3 locations: (a) OCR = 1, (b) OCR = 2, (c) OCR = 4.
ð8Þ
where a and b = constants. Based on the results of back analysis of limited laboratory model test results (to be discussed in the next
q
M
ing an undrained compression stress path, p0f can be predicted as follows:
p0f
¼
p0i
M2 þ g2i
2K
M2
!K ðOCRÞK
ð4Þ
where K = 1 j/k, while j and k are the slopes of unloading– reloading and virgin loading curves in an e ln(p0 ) plot (e is void ratio and p0 is mean effective stress); gi = qi/p0i (qi is the initial deviator stress); and M = the slope of critical state line in a p0 –q plot. For triaxial compression, M is related to the effective friction angle of soil (/0 ) as follows:
qif
A
B C Y O
p’f
p’i
Fig. 5. Illustration of different effective stress paths.
p’
110
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
vertical effective stress to the (current) initial vertical effective stress (r0v 0 ). The assumed conditions are given in Table 4. Values of the shear modulus in Table 4 are calculated from [13]:
Table 4 Stress and strength conditions for Scenario-1.
r0v 0 (kPa)
K0
OCR
e0
j
Plane strain su (kPa)
G (kPa)
R (m)
50.0 25.0 12.5 3.1
0.50 0.71 1.0 1.0
1 2 4 16
2 2 2 2
0.05 0.05 0.05 0.05
12.5 12.5 12.5 12.5
1000 1000 1000 1000
0.16 0.16 0.16 0.16
G ¼ 0:5
j: slope of unloading–reloading curve in e ln(p0 ) plot (e is void ratio and p0 is consolidation mean stress); K0: at-rest earth pressure coefficient; G: shear modulus.
section), the suggested values are a = 0.15 and b = 0.1. If Ir = 100 (R = 10r0), Eq. (8) will result in a value of rs of 1.5r0 for OCR = 1, and about 2r0 for OCR of about 10. Regarding the variation of Dus with radial distance, it is assumed that Dus has a maximum value at r = r0, and zero at r = rs, but it varies with 1/r. Finally, Dus can be expressed as:
r 0 r s 1 rs r0 r
ð9Þ
In determining the value of Duul, it is considered that the stiffer the soil and the lower the confining pressure, the more significant will be the unloading effect. If the stiffness of a clayey soil is related to the maximum consolidation pressure, then both the effects of stiffness and confining pressure can be considered using the relevant value of OCR. Designating the absolute maximum value of Duul as (Duul)max, and then assuming (Duul)max is a portion of the maximum cavity expansion induced value of u at r = r0, the following empirical equation is proposed for calculating the value of (Duul)max
ðDuul Þmax ¼ m ðDup Þr¼r0 ðOCRÞn
ð10Þ
where m and n = constants. In order to get reasonable agreement between the calculated excess pore water pressure distribution and the limited test data available from this study and in the literature [10], sensitivity analysis indicates that the range of m is 0.15– 0.2, and n of 0.2–0.3. It is suggested that m = 0.2 and n = 0.25 are appropriate. It is further assumed that Duul has a maximum absolute value at the shoulder of a cone and zero at r = rs and varies with 1/r, the same as for Dus.
Considering a standard piezocone with a diameter of 35.7 mm (r0 = 17.8 mm), two scenarios are assumed and their distributions of u around the cone in the radial direction are calculated by the method presented above. Scenario-1 is that the soils have the same maximum consolidation pressure (p0max ), but different OCR values of 1, 2, 4 and 16. The OCR is defined as the ratio of the maximum
ð11Þ
where e0 = initial void ratio. Adopting axisymmetric plane strain conditions, the calculated distributions of u around a cone are shown in Fig. 6. In these calculations, in Eq. (8), a = 0.15, b = 0.1; in Eq. (10), m = 0.20 and n = 0.25 are used. If only the excess pore water pressures due to cavity expansion and shearing are considered (Fig. 6(a)), then only for the case with OCR = 16 is the initial value of u at the shoulder of the cone less than the values in the immediately adjacent zone of soil. But if the effect of partial unloading is included (Fig. 6(b)), all other cases, except the case of OCR = 1, show that the value of u at the shoulder location is lower than values in the adjacent area. Scenario-2 assumes that the soils have the same (current) initial vertical effective stress but different maximum pre-consolidation pressures, which results in the different OCR values of 1, 2, 4 and 16. The conditions are listed in Table 5 and the calculated distributions of u are shown in Fig. 7. For Scenario-2, cases with higher OCR have a higher value of su, and therefore, higher values of u. As for Scenario-1, if the effect of partial unloading is considered (Fig. 7(b)), then for OCR P 2 the value of u at the shoulder of the cone is lower than the values at locations slightly away from the shoulder. 4. Comparison of simulated and measured pore pressures 4.1. Analysis of model test results To predict the initial distribution of u around a cone, values of Ir and undrained shear strength (su) of the soil are needed. For the three model tests as listed in Table 2, a value of Ir of 100 was assumed. For the undisturbed soil samples at about 225 mm depth from the surface of the model ground, the average value of su measured by the mini vane shear test was about 19 kPa. Considering the effect of initial effective stress on su, the values given in Table 2 are estimated using Ladd [11]’s equation
ð12Þ
where r0v = vertical effective stress; and S and m are constants. For the sample used in the mini vane shear test, the mechanically applied initial total stress was close to zero, but there was suction pore water pressure in the sample. Assuming the suction (effective) stress is about 10 kPa, then the value of OCR for the vane shear sample would be about 10. Further, referring to Ladd’s suggestion of using m = 0.8, and adopting the measured value of su of 19 kPa, a va-
100
100
Cone
75 50
Δup+Δus+Δuul
Scenario-1 OCR 1 2 4 16
75
u (kPa)
Δup +Δus
u (kPa)
p0max
su ¼ S r0v ðOCRÞm
3.2. Performance of the proposed method
50
Scenario-1 OCR 1 2 4 16
25
25 0
j
Cone
Dus ¼ ðp0i p0f Þ
1 þ e0
0
0.1
0.2
0
0
0.1
Radial distance, r (m)
Radial distance, r (m)
(a)
(b)
0.2
Fig. 6. Calculated excess pore water pressure distributions (Scenario-1): (a) Cavity expansion + shear and (b) cavity expansion + shear + unloading.
111
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113 Table 5 Stress and strength conditions for Scenario-2.
r0v 0 (kPa)
K0
OCR
e0
j
Plane strain su (kPa)
G (kPa)
R (m)
50.0 50.0 50.0 50.0
0.50 0.71 1.0 1.0
1 2 4 16
2 2 2 2
0.05 0.05 0.05 0.05
12.5 25.0 50.0 200.0
1000 2000 4000 16,000
0.16 0.16 0.16 0.16
lue of 0.31 can be estimated for the parameter S. With S = 0.31, and m = 0.8 and the values of r0v 0 shown in Table 2, the corresponding values of su were estimated for each sample. These are also listed in Table 2. The simulated initial distributions of u are compared with the measured values in Fig. 2(a), (b) and (c) for OCR = 1, 2 and 4, respectively. It can be seen that only for OCR = 4 is there good agreement between the predictions and measurements. For OCR = 1, at the locations P1, P2 and P3, and for OCR = 2 at the location P3 the measured values of u are higher than the predicted values. Assuming axisymmetric plane strain conditions (i.e., no vertical heaving), and considering a horizontal slice of the model ground, penetration of the cylindrical rod attached to the cone into this slice should have induced an outward radial displacement and thus displacement of a volume of soil. In a horizontal slice the outward displacement caused by the penetration of the cone is equivalent to 0.38% of the volume of the original sample. However, the cone penetration process is close to undrained, with almost no immediate volume change in the soil, which was confirmed by the measured heaving, i.e., the volume of heaved soil was almost the same as the volume of the penetrating cone and rod. This means that for the geometric conditions adopted there may be a possible boundary effect on the test results, which would result in higher measured values of u. The higher the applied vertical stress (r0v 0 ) (i.e., smaller OCR), the greater the constraint on the sample and the larger the effect of the horizontal boundary (i.e., the wall of the model chamber) is likely to be. Comparison of the predicted and measured distributions of u provided in Fig. 2 shows the same tendency. It is also worth noting that the simulated initial distributions of u for the cases where OCR = 2 and 4 show that the value of u at the shoulder of the cone is lower than values in the nearby area, but due to the limited number of experimental measurement points, this trend cannot be directly confirmed by the measured data. However, it has been checked indirectly by comparing the simulated and measured dissipation curves for u2, as shown in Fig. 3. This simulation was carried out using an uncoupled consolidation analysis and the finite difference technique assuming only outward radial drainage. The coefficient of consolidation in the horizontal direction (ch) used in the numerical simulation was a back-fitted value. A method for directly estimating ch values from the
dissipation curves will be discussed later. For all three cases, the simulated dissipation curves compared very well with the measured data, except for OCR = 1, in which case the simulation does not result in a non-standard dissipation curve, but the measurements do. The simulated and the measured dissipation curves for the piezometers at P1, P2 and P3 are compared in Fig. 4. For OCR = 1 and 2 (Fig. 4(a) and (b)), there are considerable discrepancies between the measured and simulated dissipation curves, while for OCR = 4 (Fig. 4(c)), the comparison can be judged as good or at least fair. The main reason for these discrepancies is considered to be the boundary effect, as discussed previously, and this effect is more profound for lower values of OCR. It is noted that the measurements show an initial increase of u and then dissipation at P1, P2 and P3. But the simulation does not clearly show this phenomenon for P1 and P2. The reason is not very clear, but a possible cause may be a delay in the pore water pressure response. Chai et al. [6] reported similar observations from laboratory oedometer tests conducted with pore water pressure measurement; after applying an incremental load under undrained conditions a time period of about 2 h was needed for the measured pore water pressure to reach more than 90% of the applied load. Furthermore, the process involved in a piezocone dissipation test is not a constant total stress process. As discussed by Fahey and Lee Goh [7] and Chai et al. [4], during the consolidation process the soil immediately around the cone tends to displace toward the cone, and some unloading (or swelling) may also occur in the soil more remote from the cone. None of these factors has been considered in the numerical simulation. The comparisons presented here between the simulated and measured distributions of u and the dissipation in a horizontal plane indicate that generally the proposed method for estimating the initial distribution of u is reasonable. Further validation of the method has been achieved by comparing predicted and measured data [10] reported in the literature, as described in the following section.
4.2. Data of Kim et al. [10] Kim et al. [10] reported measured radial distributions of u obtained from laboratory model tests. The tests were conducted using a mixture of kaolinite and Joomoonjin (Korea) sand (in equal portions), and a standard u2 type cone (1000 mm2 projected cone area and 60° cone apex angle, and the filter for excess pore water pressure measurement was on the shoulder of the cone). The model chamber had a diameter of 1.2 m and a height of 1.0 m. For the conditions adopted, and assuming axisymmetric plane strain conditions, for a horizontal slice of the model ground the cone penetration produced a volumetre displacement less than 0.09% of the original volume of the slice, and so the boundary effect should be
800
200 0
0
400 200
0.1
0.2
0
Scenario-2 OCR 1 2 4 16
Cone
400
Δup+Δus+Δuul
600
Cone
u (kPa)
600
800 Scenario-2 OCR 1 2 4 16
u (kPa)
Δup+Δus
0
0.1
Radial distance, r (m)
Radial distance, r (m)
(a)
(b)
0.2
Fig. 7. Calculated excess pore water pressure distributions (Scenario-2): (a) Cavity expansion + shear and (b) cavity expansion + shear + unloading.
112
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
Table 6 Stress, strength and stiffness of model ground of Kim et al.’s [10] tests. Case
r0v 0 (kPa)
K0
OCR
Triaxial su (kPa)
Ira (kPa)
Rb (m)
1 2 3 4
200 40 20 10
0.50 1.1 1.6 2.2
1 5 10 20
70 54 48 43
100 100 100 100
0.178 0.178 0.178 0.178
Assumed. Calculated.
much less than that observed in the model tests conducted in this study. The stress conditions adopted and the corresponding strength and stiffness of the soils tested are listed in Table 6. The values of K0, OCR and su are from Kim et al. [10]. Kim et al. also reported the values of shear modulus (G) from which the rigidity index (Ir) could be estimated, but their suggested value of G for the case of OCR = 1 was more than 10 times the value suggested for the other cases with higher OCR values, which seems inconsistent. The measured zones where u > 0 had outer radii about 10 times the radius of the cone, and so a value of Ir of 100 was simply assumed here. The simulated initial distributions of u are compared with measured values in Fig. 8(a)–(d) for OCR = 1, 5, 10 and 20, respectively. From these figures, the following points can be observed: (a) The estimated size of the shear zone (rs) given by Eq. (8) seems quite reasonable. (b) Except for OCR = 1, the cases where both the effects of shear and partial unloading are considered resulted in better simulations.
The results presented in the previous section show that the pore water pressure distribution in the radial direction from the shoulder of the cone can be reliably predicted. It is suggested that the coefficient of consolidation of the soil in the horizontal direction (ch) can also be estimated by back analysis of the dissipation curve for the pore pressure measured at the shoulder of the cone, u2. The back fitted value should be a reliable estimate of the ‘‘true’’ value of ch of the soil. As such, it proves a convenient reference for evaluating other proposed methods for directly estimating values of ch from measured dissipation curves. For example, for a non-standard dissipation curve, Chai et al. [4] proposed a method for estimating the value of ch. The basic idea of this method is to correct the measured time taken for the excess pore water pressure to dissipate from its maximum value to 50% of the maximum value, t50. The correct time is defined as t50c, and then this value of t50c is used in the equation proposed by Teh and Houlsby [16] for standard dissipation curves to calculate directly the value of ch. The equation proposed by Chai et al. for evaluating t50c is as follows:
t50c ¼ 1 þ 18:5
pffiffiffiffi Ir
ð14Þ
OCR = 5 Measured Δup +Δus+Δuul Δup +Δus Δup
Cone
200
u (kPa)
Cone
u (kPa)
0:245 r 20 t 50c
300 200 100
100
0
0.1
0
0.2
0
0.1
0.2
Radial distance, r (m)
Radial distance, r (m)
(a)
(b)
400
400
OCR = 10 Measured Δup +Δus+Δuul Δup +Δus Δup
200
OCR = 20 Measured Δup +Δus+Δu ul Δup +Δus Δup
300
u (kPa)
Cone
300
u (kPa)
ð13Þ
Ir 0:3 200
400
OCR = 1 Measured Δup+Δus+Δuul Δup+Δus Δup
300
100 0
0:67
Applying Eqs. (13) and (14) to the three model dissipation test results (Fig. 3), values of ch have been estimated, and in Table 7 these are compared with: (a) values of the coefficient of consolidation of the soil in the vertical direction, cv, measured directly in
400
0
t50
t u max t 50
For a piezocone with a filter element for pore water pressure measurement located at the shoulder of the cone, the equation for calculating the value of ch is as follows [16]:
ch ¼ The reasonable comparisons between the predicted and measured distributions of u for Kim et al.’s model tests further reinforces the statement that the proposed method is capable of predicting the piezocone penetration-induced excess pore water pressure distributions in the radial direction.
Cone
a b
5. Estimating ch from non-standard dissipation curves
200 100
0
0.1
0.2
0
0
0.1
Radial distance, r (m)
Radial distance, r (m)
(c)
(d)
0.2
Fig. 8. Simulated distributions of u for Kim et al.’s model tests: (a) OCR = 1, (b) OCR = 5, (c) OCR = 10, (d) OCR = 20.
113
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113 Table 7 Comparison of ch and cv values of the model tests. Case
OCR
cv (m2/min)
Estimated ch (m2/min)
Back fitted ch (m2/min)
(ch)back/(ch)estimated
1 2 3
1 2 4
2.28E06 3.60E06 6.00E06
9.11E06 1.15E05 9.30E06
1.4E05 1.5E05 1.6E05
1.5 1.3 1.7
laboratory oedometer tests conducted at the appropriate initial vertical effective stress r0v 0 ); and (b) numerically back fitted values of ch. It can be seen that the values of ch estimated by Eqs. (13) and (14) are smaller but close to the back fitted ch values obtained from the dissipation simulations. It can be observed from Fig. 3 that although the simulated curves compared well with the measured ones, for OCR = 2 and 4, the simulated values of tumax are larger than the corresponding measurements. As can be seen from Eq. (13), the larger the value of tumax, the smaller t50c will be, and consequently a larger value of ch will be interpreted. This comparison suggests that Eqs. (13) and (14) can be used to interpret values of ch from measured non-standard dissipation curves. The estimated ch values are about 1.5–4 times the corresponding laboratory values of cv. The behaviour of a remoulded clayey soil may be initially isotropic, but after consolidation under onedimensional (1D) conditions with a pressure of 96 kPa, it is very likely to exhibit stress-induced anisotropic consolidation behaviour. The stress-induced anisotropy is stronger for a remoulded soil than an undisturbed soil sample because the remoulded soil has a weak or even no inter-aggregate bonding [8]. For undisturbed Ariake clay samples, the ratio of ch/cv is known to be about 1.5 [5], and for a remoulded Ariake clay sample consolidated under 1D condition and a pressure of 96 kPa, a ratio ch/cv of about 1.5–4 may be reasonable. 6. Conclusion The distribution of piezocone penetration-induced excess pore water pressure (u), as well as its dissipation behaviour, have been investigated by laboratory model tests, theoretical analysis and numerical simulation. Based on the test and analysis results, the following conclusions can be drawn. (1) A semi-theoretical method has been proposed to predict the radial distribution of excess pore pressure, u, induced at the level of the shoulder of a cone. In the method, the effects of the undrained shear strength (su), over-consolidation ratio (OCR) and rigidity index (Ir) of the soil have been considered. The validity of the method has been checked by using the model test results from this study and other experimental data available in the literature. (2) With a reliably predicted initial distribution of u and the measured dissipation curve of pore water pressure at the shoulder of the cone (u2), the coefficient of consolidation of the soil in the horizontal direction (ch) can be back fitted by dissipation analysis. Comparing the back fitted values of
ch with values estimated from the dissipation curve by a previously proposed method indicates that the previously proposed method can result in a good estimation of ch from non-standard dissipation curves (in which u2 initially increases and then dissipates with time).
Acknowledgement Mr. A. Saito, technician at Saga University, Japan, assisted the laboratory tests reported in this article. References [1] Burns SE, Mayne PW. Monotonic and dilatory pore pressure decay during piezocone tests in clay. Can Geotech J 1998;35(6):1063–73. [2] Campanella RG, Robertson PK. Current status of the piezocone test. In: Ruiter J, editor. Penetration testing. Rotterdam: Balkema; 1988. p. 93–116. [3] Chai J-C, Agung PMA, Hino T, Igaya Y, Carter JP. Estimating hydraulic conductivity from piezocone soundings. Geotechnique 2011;61(8):699–708. http://dx.doi.org/10.1680/ geot.10.P.009. [4] Chai J-C, Sheng D-C, Carter JP, Zhu H-H. Coefficient of consolidation from nonstandard piezocone dissipation curves. Comput Geotech 2012;41:13–22. http://dx.doi.org/10.1016/j.compgeo.2011.11.005. [5] Chai J-C, Jia R, Hino T. Anisotropic consolidation behavior of Ariake clay from three different CRS tests. Geotech Test J ASTM 2012;35(6):1–9. http:// dx.doi.org/10.1520/GTJ103848. [6] Chai J-C, Carter JP, Saito A, Hino T. Behaviour of clay subjecting to vacuum and surcharge loading in an oedometer. Geotech Eng J, SEAGS AGSSEA 2013;44(4):1–8. [7] Fahey, M, Lee Goh, A. A comparison of pressuremeter and piezocone methods of determining the coefficient of consolidation. In: Proceedings 4th international symposium on pressuremeters, Sherbrooke, Quebec, Canada, Balkema, Rotterdam; 1995. p. 153–60. [8] Hattab M, Hammad T, Fleureau J-M, Hicher P-Y. Behaviour of a sensitive marine sediment: microstructural investigation. Geotechnique 2013;63(1):71–84. http://dx.doi.org/10.1680/geot.10.P.10. [9] Kim K, Prezzi M, Salgado R, Lee W. Effect of penetration rate on cone penetration resistance in saturated clayey soils. J Geotech Geoenviron Eng 2008;134(8):1142–53. [10] Kim T, Kim N, Tumay MT, Lee W. Spatial distribution of excess pore-water pressure due to piezocone penetration in overconsolidated clay. J Geotech Geoenviron Eng 2007;133(6):674–83. [11] Ladd CC. Stability evaluation during staged construction. J Geotech Geoenviron Eng ASCE 1991;117(4):540–615. [12] Miura N, Chai J-C, Hino T, Shimoyama S. Depositional environment and geotechnical properties of Ariake clay. Indian Geotech J 1998;28(2):121–46. [13] Randolph MF, Carter JP, Wroth CP. Driven piles in clay – the effects of installation and subsequent consolidation. Geotechnique 1979;29(4):361–93. [14] Roscoe KH, Burland JB. On the generalized stress-strain behavior of wet clay. In: Heyman J, Leckie FA, editors. Engineering plasticity. Cambridge University Press; 1968. p. 535–609. [15] Sully JP, Robertson PK, Campanella RG, Woeller DJ. An approach to evaluation of field CPTU dissipation data in overconsolidated fine-grained soils. Can Geotech J 1999;36:369–81. [16] Teh CI, Houlsby GT. An analytical study of the cone penetration test in clay. Geotechnique 1991;41:17–34.
Contents lists available at ScienceDirect
Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo
Cone penetration-induced pore pressure distribution and dissipation Jin-Chun Chai a,⇑, Md. Julfikar Hossain a, John Carter b, Shui-Long Shen c a
Graduate School of Science and Engineering, Saga University, 1 Honjo, Saga 840-8502, Japan Faculty of Engineering and Built Environment, the University of Newcastle, NSW 2308, Australia c Department of Civil Engineering, Shanghai Jiao Tong University and State Key Laboratory of Ocean Engineering, 800 Dong Chuan Road, Minhang District, Shanghai 200240, China b
a r t i c l e
i n f o
Article history: Received 31 October 2013 Received in revised form 16 January 2014 Accepted 18 January 2014 Available online 8 February 2014 Keywords: Piezocone test Model test Coefficient of consolidation Excess pore pressure Cavity expansion
a b s t r a c t The excess pore water pressure distribution (u) induced by the penetration of a piezocone into clay and its dissipation behaviour have been investigated by laboratory model tests, theoretical analysis and numerical simulation. Based on the results of the tests and the analysis, a semi-theoretical method has been proposed to predict the piezocone penetration-induced pore pressure distribution in the radial direction from the shoulder of the cone. The method can consider the effect of the undrained shear strength (su), over-consolidation ratio (OCR) and rigidity index (Ir) of the soil. With a reliably predicted initial distribution of u and the measured curve of dissipation of pore water pressure at the shoulder of the cone (u2), the coefficient of consolidation of the soil in the horizontal direction (ch) can be back-fitted by analysis of the pore pressure dissipation. Comparing the back-fitted values of ch with the values directly estimated by a previously proposed method indicates that the previously proposed method can be used reliably to estimate ch values from non-standard dissipation curves (where u2 increases initially and then dissipates with time). Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The piezocone is now widely used as an in situ site investigation tool. From the results of a piezocone penetration test, the soil profile and the undrained shear strength (su) of a clayey deposit can be estimated, normally quite reliably (e.g., [2]). Numerous research results have also been published on estimating the in situ hydraulic conductivity (e.g., [3]) and the coefficient of consolidation of soil in the horizontal direction (ch) (e.g., [4,16]) from the results of piezocone penetration and dissipation tests. For a standard piezocone with the filter for pore water pressure measurement located at the shoulder of the cone (u2 type), two types of piezocone dissipation curves have been reported in the literature. One displays monotonic reduction of the measured pore water pressure (u2) with time (e.g., [16]), i.e., the so called ‘‘standard’’ dissipation curve; and the other is a ‘‘non-standard’’ curve, for which the measured value of u2 increases initially and then reduces with time [1,4,15]. The reason for a non-standard dissipation curve is that at the beginning of the dissipation the pore pressure at the filter element location is lower than the pore pressures in the soil nearby. The causes for this kind of initial pore water pressure distribution are thought to be: (1) the shear-induced ⇑ Corresponding author. Tel.: +81 952288580. E-mail addresses: [email protected] (J.-C. Chai), [email protected] (J. Carter), [email protected] (S.-L. Shen). http://dx.doi.org/10.1016/j.compgeo.2014.01.008 0266-352X/Ó 2014 Elsevier Ltd. All rights reserved.
dilatancy effect for overconsolidated clay or dense sandy soil, which results in lower initial pore water pressure being generated in zones of soil with significant shear strain, i.e., in the zone close to the surface of the cone (e.g., [1,4]); and (2) the partial unloading effect when a soil element moves from the face to the shoulder of the cone during cone penetration (e.g., [4]). Kim et al. [10] reported laboratory model test results of the piezocone penetration-induced pore water pressure distribution (u) in the radial direction at the level of the shoulder of the cone. The measured data show that for the normally consolidated case, values of u reduced with radial distance, but for overconsolidated cases (OCR > 5) values of u at the shoulder of the cone (the filter location) are lower. Peak values of u were reached at a radial distance of about 1.4–2.2 times the radius of the cone and then u reduced with increasing radial distance. Unfortunately, the dissipation curves for these tests were not reported. The numerical results of Chai et al. [4] indicate that even for a slightly overconsolidated clayey soil, the initial value of u at the shoulder of the cone is lower than values in the nearby soil region. It is clear that knowledge of the initial distribution of u induced by piezocone penetration is very important for establishing a suitable method to evaluate ch from the piezocone dissipation test results. However, due to physical restrictions, such as the size of a piezometer, the limited number of piezometers that can be installed in the ground or in a laboratory test specimen, it is difficult to measure a precise distribution of u around a cone, even in a
106
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
laboratory model test. However, by combining the limited measured data related to the initial distribution of u and the dissipation curve for u2, a more complete picture of the initial distribution of u induced by piezocone penetration can be deduced. In this study, laboratory model tests were conducted using a piezocone and these involved measurements of the pore pressures generated during penetration and then their subsequent dissipation. Pore water pressure measurements were made at the shoulder of the cone and at three points in the model ground specimen. A method for predicting the radial distribution of excess pore water pressure induced by piezocone penetration (u) from the shoulder of the cone is proposed and validated using the model test results, as well as some other results available in the literature. Finally, a method for estimating the coefficient of consolidation of a deposit in the horizontal direction (ch) from non-standard dissipation curves is discussed, making reference to the predicted initial distribution of u caused by the piezocone penetration. 2. Laboratory model tests 2.1. Equipment The device used for the model tests is shown in Fig. 1. The cylindrical container (chamber) is made of PVC and has an inner diameter of 0.485 m and a height of 1.0 m. A piston system driven by air
pressure was used to apply consolidation pressure to the soil sample. The sealing between the piston and the container was achieved by using a rubber ‘‘O’’-ring placed in a slot around the piston as well as a rubber sleeve installed above the piston. The piezocone used in these experiments has a diameter of 30 mm with a cone tip angle of 60°. The filter for pore water pressure measurement was installed on the shoulder of the cone. The set-up of the test is illustrated in Fig. 1. The penetration system consists of a reaction frame, a motor and a speed control unit. The penetration rate adopted was 25 mm/min. A servo motor is used to control the penetration rate. Since the penetration depth is relatively small and in order to reach a steady rate in a short time period, a rate of 50% of the maximum rate of the motor was adopted. Although the rate is lower than that adopted in the standard field test, i.e., 20 mm/s, Kim et al. [9] reported that for a saturated clayey soil and when the penetration rates are about 0.1–20 mm/s, there is no obvious effect on the measured penetration tip resistance and the generated pore water pressure. Three piezometers with a diameter of 20 mm and length of 25 mm were placed in the model ground at different radial distances from the centreline of the cone, but on the same level, in order to monitor the pore water pressure distribution and its variation during the piezocone penetration and dissipation tests (Fig. 1(b)). For the configuration adopted, the ratio of the diameter of the model ground and the cone is about 16. This ratio is relatively small and the pore water pressures measured by the piezometer near the periphery of the cylindrical chamber may be influenced by the boundary (wall of the chamber). This point will be further discussed in presenting the measured and calculated results. The settlement of the model ground was measured by a dial gauge. During piezocone penetration and the subsequent dissipation process, the tip resistance and pore water pressures at the shoulder of the cone and at the locations of the three piezometers installed in the model ground were monitored using a computer through a data logger. 2.2. Test procedure
(a)
(b) Fig. 1. Schematic diagram of laboratory model test. (a) Illustration of the set-up of the test and (b) plane view of the locations of piezometers (P1, P2 and P3).
2.2.1. Preparing model ground Three layers of non-woven geotextile (about 138 g/m2) were first placed at the bottom of the cylindrical chamber to act as a drainage layer. Then six 0.1 m wide geotextile strips were lined vertically along the inner periphery of the chamber to facilitate drainage by outward radial flow of the pore water. In the field condition, the radial boundary is neither drained nor undrained, and so the laboratory set-up is an approximation of the field situation. Thoroughly remoulded clay soil with a water content about 1.2 times its liquid limit was placed in the chamber, layer by layer. To avoid possible air-bubbles being trapped in the sample, each soil layer was thoroughly stirred by a stainless rod. When the soil deposit was about 0.5 m thick, the three piezometers were installed. Then further soil was added until the layer was about 0.8 m thick. Finally, three layers of non-woven geotextile were placed on top of the cylindrical soil specimen to act as a drainage layer, and the piston and air-pressure system were setup. A pre-determined air pressure was applied to pre-consolidate the model ground. Once the degree of pre-consolidation was more than 90%, the air-pressure was adjusted to result in a specimen with the desired over-consolidation ratio (OCR). For cases where OCR > 1.0, there may have been some negative pore water pressure in the ground at this stage. A piezocone penetration and dissipation test was conducted once the unloading-induced negative pore pressures had the opportunity to dissipate (which generally took a few days). 2.2.2. Piezocone penetration and dissipation test After pre-consolidation, the thickness of the model ground was about 0.60 m, and it is estimated that the three piezometers were
107
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
then located about 0.225 m below the surface of the sample. The piezocone was then pushed into the sample so that the pore pressure filter at the shoulder of the cone was located at a depth of 0.225 m from the surface of the model ground. A dissipation test was then conducted by holding the cone stationary. 2.3. Materials used and cases tested The soil used was remoulded Ariake clay [12]. The physical properties of this clay are listed in Table 1. The initial water content of the soil was adjusted to about 133.0% and the sample was thoroughly mixed before putting it into the chamber. Three tests were conducted, as listed in Table 2. The air pressure applied during pre-consolidation was 100 kPa, but there was a shaft installed on the top of the piston, and so the area on which the air pressure could be applied is annular. After correcting for the area of the shaft, the effective consolidation stress transmitted to the soil was estimated to be about 96 kPa. Samples with relatively low values of OCR were tested because most natural soft clayey deposits are found in such conditions. For all cases, after the penetration and dissipation test, soil samples from the model ground were taken for oedometer testing and laboratory mini vane shear tests. The mini vane used has a diameter of 20 mm and height of 40 mm and the shearing speed adopted was 3 degrees/min. 2.4. Test results The test results presented here are: (1) initial distributions of u before starting the dissipation tests, (2) u2 dissipation curves, and (3) dissipation curves recorded by the three piezometers embedded in the model ground. (1) Initial distributions of u The initial distributions of u for samples with OCR = 1, 2 and 4 are shown in Fig. 2. Generally the initial values of u reduced with an increase of OCR. The measurements also show that u reduces with radial distance. It is not possible to discern whether the values of u are actually higher in a zone adjacent to the shoulder of the cone than right on the shoulder (r = r0), since the location of P1 (r1) is not close enough to the cone face to allow such a determination. Locating P1 closer to the centre of the model ground was not attempted as it was thought that the piezometer may be damaged during the cone penetration process or it may influence the outcome of the piezocone dissipation test. As shown in Fig. 2(c) for
Table 1 Physical properties of the Ariake clay used.
the case where OCR = 4, P2 was damaged and only the results of P1 and P3 can be presented. (2) Piezocone dissipation curves The dissipation curves for u2 at the shoulder of the cone are shown in Fig. 3. All measured curves are non-standard, i.e., u2 increased initially and then dissipated with time. From the measured dissipation curves, interpreted values of the time (tmax) for u2 to reach its maximum value (umax), and the time increment (t50) for u2 to reduce to 50% of umax are summarized in Table 3. It can be seen that tmax increased with the increase of OCR. (3) Dissipation curves at P1, P2 and P3 The pore pressure dissipation curves measured at the locations of the three piezometers embedded in the model ground are depicted in Fig. 4. All measured curves show a tendency of initial increase in the value of u followed by dissipation to a value close to zero. The measured maximum value of u also reduced with increasing radial distance from the cone. 3. Predicting the distribution of excess pore pressure 3.1. Proposed method It is generally accepted that during a cone penetration process, values of u generated around the cone consists two parts arising from: (1) the change of mean stress (Dup); and (2) the change of shear stress (Dus) (e.g., [1,10,13]). For a normally consolidated clayey soil or loose sand, Dus is normally positive, while for a heavily over-consolidated clayey soil or dense sand, Dus may be negative. The generation of shear-induced negative values of Dus around the shoulder of the cone is generally considered as the main reason for the existence of non-standard dissipation curves [1,4,15]. However, the numerical results from Chai et al. [4] also show that even for a clayey deposit that is close to normally consolidated, at the very beginning (may be for only the first few seconds) of the dissipation process, the pore water pressure at the shoulder of the cone may increase and then decrease, i.e., producing a non-standard dissipation curve. A possible reason for this phenomenon is the partial unloading effect in the vertical direction when (relatively speaking) a soil element moves from the face to the shoulder of a cone, and during this process, the vertical strain increment in the soil element is indeed tensile [16]. This partial unloading effect tends to reduce the value of u near the shoulder of a cone. Its value arising from this cause alone is designated here as Duul. Hence u can be expressed as:
u ¼ Dup þ Dus þ Duul
Soil properties
Liquid limit, LL (%)
Plastic limit, PL (%)
Finer than 2 lm (%)
Water content, Wn (%)
Values
114.0
60.6
63.5
133.0
ð1Þ
where the various components are explained as follows. Using an elastic-perfectly plastic soil model and based on undrained cylindrical cavity expansion theory, the excess pore water
Table 2 Model test conditions. Case
r0v m a (kPa)
r0v 0 (kPa)
OCR
su (kPa)
Radial locations of piezometer (mm) r1
r2
r3
1 2 3
96 96 96
96 48 24
1 2 4
30 26 23
45 45 54
90 90 107
135 135 161
a r0v m is the maximum vertical consolidation stress, r0v 0 is the initial vertical effective stress in the model ground during piezocone penetration and dissipation tests, and su is the estimated undrained shear strength.
108
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
120
Measured
100
Predicted
80
Excess pore pressure (kPa)
140
Cone
Initial excess pore pressure (kPa)
140
60 40 20 0 0
0.05
0.1
0.15
0.2
80 60 40 20 0.01
0.1
1
Radial distance (m)
Time (h)
(a)
(a)
10
100
1000
100
Excess pore pressure (kPa)
100
Measured
80
Predicted 60
Cone
Initial excess pore pressure (kPa)
Predicted
100
0 0.001
0.25
Measured
120
40
20
0.05
0.1
0.15
0.2
0.25
Predicted
60
40
20
0 0.001
0 0
Measured 80
0.01
0.1
1
10
100
1000
Time (h)
Radial distance (m)
(b)
(b) 80
Excess pore pressure (kPa)
Measured 80
Predicted
60
Cone
Initial excess pore pressure (kPa)
100
40
20
0
Measured
40
20
0 0.001 0
0.05
0.1
0.15
0.2
Predicted
60
0.01
0.25
0.1
1
10
100
1000
Time (h)
Radial distance (m)
(c)
(c)
Fig. 3. Piezocone dissipation curves: (a) OCR = 1, (b) OCR = 2, (c) OCR = 4. Fig. 2. Initial u distribution with radial distance from the cone: (a) OCR = 1, (b) OCR = 2, (c) OCR = 4.
pressure due to the change of mean stress (Dup) can be expressed as follows:
Dup ¼ 2 su lnðR=rÞ ðr 0 < r < RÞ
ð2Þ
where su = the undrained shear strength of the soil; r0 = the radius p of the cylindrical cavity (cone); r = radial distance; R = r0 Ir is the outer radius of the annular plastic zone surrounding the cylindrical cavity and Ir = G/su is the rigidity index of soil, with G = the elastic shear modulus of the soil. For the magnitude of shear-induced excess pore water pressure, Dus, there is no well-accepted method of prediction. Several researchers (e.g., [10,13]) attempted to use the Modified Cam Clay
Table 3 Summary of the laboratory piezocone dissipation test results. Test No.
OCR
tumax (min)
umax (kPa)
t50 (min)
t50m (min)
Ir
1 2 3
1 2 4
0.35 0.75 1.40
128.9 93.7 73.5
83.65 79.59 107.76
60.48 47.94 59.26
100 100 100
(MCC) model [14] to predict the magnitude of Dus. Randolph et al. [13] proposed the following equation to calculate the value of Dus.
Dus ¼ p0i p0f
ð3Þ
where p0i and p0f = the values of mean effective stresses at the initial and failure states, respectively. Using the MCC model and consider-
109
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
Excess pore pressure (kPa)
120
M¼
80
Measured P1 P2 P3
60
Predicted P1
100
su ¼
P3
20 0 0.001
0.01
0.1
1
10
100
1000
Excess pore pressure (kPa)
100 Measured P1 P2 P3 Predicted P1 P2
40
P3
20
0 0.001
0.01
0.1
1
10
100
1000
Time (h)
(b)
Excess pore pres sure (kPa)
60 Measured P1 P3 40
Predicted P1 P3
20
0 0.001
0.01
0.1
1
10
100
ðTriaxial conditionsÞ
ð6Þ
ðPlane strain conditionsÞ
ð7Þ
It can be observed from Eq. (3) that the component (p0i p0f ) does not change with radial distance, and for this reason Randolph et al. [13] proposed that the pore pressure contribution expressed by Eq. (3) should be added to the value of u generated throughout the plastic zone. It is noted that first yielding and material failure coincide in an elastic-perfectly plastic model. But with a strain hardening elasto-plastic model, like MCC, yielding does not necessarily coincide with material failure. As illustrated in Fig. 5, if a deviator stress qif is considered, Points B and C would be considered to be at failure according to an elastic-perfectly plastic model. However, according to the MCC model Points B and C have not yet failed, although at each of these points the soil is yielding plastically. Path YBA can be considered as an effective stress path for undrained compression. Path YC may occur due to internal pore water movement even if the boundary conditions of the soil sample allow no flow, i.e., undrained conditions overall for the soil body. Therefore within the plastic zone predicted by an elasticperfectly plastic model, shear stress-induced excess pore water pressure may vary with radial distance. Based on the results of laboratory model test, Kim et al. [10] assumed that the shear stress induced excess pore water pressure mainly occurs in a shear zone with a radius, rs = (1.5–2.2)r0 < R. They further assumed that the shear induced excess pore water pressure has a maximum value at r = r0, and linearly reduces to zero at r = rs. Chai et al. [4] conducted numerical simulations of piezocone penetration and the results indicate that a zone within which the excess pore water pressure is significantly influenced by the shear deformation is about 10–15 mm thick from the surface of the cone, which is comparable with that proposed by Burns and Mayne [1] of about 10 mm. It is proposed that the value of rs is a portion of the radius of the plastic zone (R) induced by a cavity expansion and a function of OCR. By further assuming that the minimum value of rs is (r0 + 5) mm, rs can be expressed as:
(a)
60
Mp0f 2
Mp0f su ¼ pffiffiffi 3
Time (h)
80
ð5Þ
The value of the undrained shear strength, su, can also be predicted from knowledge of the value of p0f . Conversely, if the value of su is known, p0f can be estimated, and their relationships are as follows
P2 40
6 sin /0 3 sin /0
1000
Time (h)
rs ¼ a ðOCRÞb R ðrs 6 r 0 þ 5 ðmmÞÞ
(c) Fig. 4. Dissipation curves at P1, P2 and P3 locations: (a) OCR = 1, (b) OCR = 2, (c) OCR = 4.
ð8Þ
where a and b = constants. Based on the results of back analysis of limited laboratory model test results (to be discussed in the next
q
M
ing an undrained compression stress path, p0f can be predicted as follows:
p0f
¼
p0i
M2 þ g2i
2K
M2
!K ðOCRÞK
ð4Þ
where K = 1 j/k, while j and k are the slopes of unloading– reloading and virgin loading curves in an e ln(p0 ) plot (e is void ratio and p0 is mean effective stress); gi = qi/p0i (qi is the initial deviator stress); and M = the slope of critical state line in a p0 –q plot. For triaxial compression, M is related to the effective friction angle of soil (/0 ) as follows:
qif
A
B C Y O
p’f
p’i
Fig. 5. Illustration of different effective stress paths.
p’
110
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
vertical effective stress to the (current) initial vertical effective stress (r0v 0 ). The assumed conditions are given in Table 4. Values of the shear modulus in Table 4 are calculated from [13]:
Table 4 Stress and strength conditions for Scenario-1.
r0v 0 (kPa)
K0
OCR
e0
j
Plane strain su (kPa)
G (kPa)
R (m)
50.0 25.0 12.5 3.1
0.50 0.71 1.0 1.0
1 2 4 16
2 2 2 2
0.05 0.05 0.05 0.05
12.5 12.5 12.5 12.5
1000 1000 1000 1000
0.16 0.16 0.16 0.16
G ¼ 0:5
j: slope of unloading–reloading curve in e ln(p0 ) plot (e is void ratio and p0 is consolidation mean stress); K0: at-rest earth pressure coefficient; G: shear modulus.
section), the suggested values are a = 0.15 and b = 0.1. If Ir = 100 (R = 10r0), Eq. (8) will result in a value of rs of 1.5r0 for OCR = 1, and about 2r0 for OCR of about 10. Regarding the variation of Dus with radial distance, it is assumed that Dus has a maximum value at r = r0, and zero at r = rs, but it varies with 1/r. Finally, Dus can be expressed as:
r 0 r s 1 rs r0 r
ð9Þ
In determining the value of Duul, it is considered that the stiffer the soil and the lower the confining pressure, the more significant will be the unloading effect. If the stiffness of a clayey soil is related to the maximum consolidation pressure, then both the effects of stiffness and confining pressure can be considered using the relevant value of OCR. Designating the absolute maximum value of Duul as (Duul)max, and then assuming (Duul)max is a portion of the maximum cavity expansion induced value of u at r = r0, the following empirical equation is proposed for calculating the value of (Duul)max
ðDuul Þmax ¼ m ðDup Þr¼r0 ðOCRÞn
ð10Þ
where m and n = constants. In order to get reasonable agreement between the calculated excess pore water pressure distribution and the limited test data available from this study and in the literature [10], sensitivity analysis indicates that the range of m is 0.15– 0.2, and n of 0.2–0.3. It is suggested that m = 0.2 and n = 0.25 are appropriate. It is further assumed that Duul has a maximum absolute value at the shoulder of a cone and zero at r = rs and varies with 1/r, the same as for Dus.
Considering a standard piezocone with a diameter of 35.7 mm (r0 = 17.8 mm), two scenarios are assumed and their distributions of u around the cone in the radial direction are calculated by the method presented above. Scenario-1 is that the soils have the same maximum consolidation pressure (p0max ), but different OCR values of 1, 2, 4 and 16. The OCR is defined as the ratio of the maximum
ð11Þ
where e0 = initial void ratio. Adopting axisymmetric plane strain conditions, the calculated distributions of u around a cone are shown in Fig. 6. In these calculations, in Eq. (8), a = 0.15, b = 0.1; in Eq. (10), m = 0.20 and n = 0.25 are used. If only the excess pore water pressures due to cavity expansion and shearing are considered (Fig. 6(a)), then only for the case with OCR = 16 is the initial value of u at the shoulder of the cone less than the values in the immediately adjacent zone of soil. But if the effect of partial unloading is included (Fig. 6(b)), all other cases, except the case of OCR = 1, show that the value of u at the shoulder location is lower than values in the adjacent area. Scenario-2 assumes that the soils have the same (current) initial vertical effective stress but different maximum pre-consolidation pressures, which results in the different OCR values of 1, 2, 4 and 16. The conditions are listed in Table 5 and the calculated distributions of u are shown in Fig. 7. For Scenario-2, cases with higher OCR have a higher value of su, and therefore, higher values of u. As for Scenario-1, if the effect of partial unloading is considered (Fig. 7(b)), then for OCR P 2 the value of u at the shoulder of the cone is lower than the values at locations slightly away from the shoulder. 4. Comparison of simulated and measured pore pressures 4.1. Analysis of model test results To predict the initial distribution of u around a cone, values of Ir and undrained shear strength (su) of the soil are needed. For the three model tests as listed in Table 2, a value of Ir of 100 was assumed. For the undisturbed soil samples at about 225 mm depth from the surface of the model ground, the average value of su measured by the mini vane shear test was about 19 kPa. Considering the effect of initial effective stress on su, the values given in Table 2 are estimated using Ladd [11]’s equation
ð12Þ
where r0v = vertical effective stress; and S and m are constants. For the sample used in the mini vane shear test, the mechanically applied initial total stress was close to zero, but there was suction pore water pressure in the sample. Assuming the suction (effective) stress is about 10 kPa, then the value of OCR for the vane shear sample would be about 10. Further, referring to Ladd’s suggestion of using m = 0.8, and adopting the measured value of su of 19 kPa, a va-
100
100
Cone
75 50
Δup+Δus+Δuul
Scenario-1 OCR 1 2 4 16
75
u (kPa)
Δup +Δus
u (kPa)
p0max
su ¼ S r0v ðOCRÞm
3.2. Performance of the proposed method
50
Scenario-1 OCR 1 2 4 16
25
25 0
j
Cone
Dus ¼ ðp0i p0f Þ
1 þ e0
0
0.1
0.2
0
0
0.1
Radial distance, r (m)
Radial distance, r (m)
(a)
(b)
0.2
Fig. 6. Calculated excess pore water pressure distributions (Scenario-1): (a) Cavity expansion + shear and (b) cavity expansion + shear + unloading.
111
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113 Table 5 Stress and strength conditions for Scenario-2.
r0v 0 (kPa)
K0
OCR
e0
j
Plane strain su (kPa)
G (kPa)
R (m)
50.0 50.0 50.0 50.0
0.50 0.71 1.0 1.0
1 2 4 16
2 2 2 2
0.05 0.05 0.05 0.05
12.5 25.0 50.0 200.0
1000 2000 4000 16,000
0.16 0.16 0.16 0.16
lue of 0.31 can be estimated for the parameter S. With S = 0.31, and m = 0.8 and the values of r0v 0 shown in Table 2, the corresponding values of su were estimated for each sample. These are also listed in Table 2. The simulated initial distributions of u are compared with the measured values in Fig. 2(a), (b) and (c) for OCR = 1, 2 and 4, respectively. It can be seen that only for OCR = 4 is there good agreement between the predictions and measurements. For OCR = 1, at the locations P1, P2 and P3, and for OCR = 2 at the location P3 the measured values of u are higher than the predicted values. Assuming axisymmetric plane strain conditions (i.e., no vertical heaving), and considering a horizontal slice of the model ground, penetration of the cylindrical rod attached to the cone into this slice should have induced an outward radial displacement and thus displacement of a volume of soil. In a horizontal slice the outward displacement caused by the penetration of the cone is equivalent to 0.38% of the volume of the original sample. However, the cone penetration process is close to undrained, with almost no immediate volume change in the soil, which was confirmed by the measured heaving, i.e., the volume of heaved soil was almost the same as the volume of the penetrating cone and rod. This means that for the geometric conditions adopted there may be a possible boundary effect on the test results, which would result in higher measured values of u. The higher the applied vertical stress (r0v 0 ) (i.e., smaller OCR), the greater the constraint on the sample and the larger the effect of the horizontal boundary (i.e., the wall of the model chamber) is likely to be. Comparison of the predicted and measured distributions of u provided in Fig. 2 shows the same tendency. It is also worth noting that the simulated initial distributions of u for the cases where OCR = 2 and 4 show that the value of u at the shoulder of the cone is lower than values in the nearby area, but due to the limited number of experimental measurement points, this trend cannot be directly confirmed by the measured data. However, it has been checked indirectly by comparing the simulated and measured dissipation curves for u2, as shown in Fig. 3. This simulation was carried out using an uncoupled consolidation analysis and the finite difference technique assuming only outward radial drainage. The coefficient of consolidation in the horizontal direction (ch) used in the numerical simulation was a back-fitted value. A method for directly estimating ch values from the
dissipation curves will be discussed later. For all three cases, the simulated dissipation curves compared very well with the measured data, except for OCR = 1, in which case the simulation does not result in a non-standard dissipation curve, but the measurements do. The simulated and the measured dissipation curves for the piezometers at P1, P2 and P3 are compared in Fig. 4. For OCR = 1 and 2 (Fig. 4(a) and (b)), there are considerable discrepancies between the measured and simulated dissipation curves, while for OCR = 4 (Fig. 4(c)), the comparison can be judged as good or at least fair. The main reason for these discrepancies is considered to be the boundary effect, as discussed previously, and this effect is more profound for lower values of OCR. It is noted that the measurements show an initial increase of u and then dissipation at P1, P2 and P3. But the simulation does not clearly show this phenomenon for P1 and P2. The reason is not very clear, but a possible cause may be a delay in the pore water pressure response. Chai et al. [6] reported similar observations from laboratory oedometer tests conducted with pore water pressure measurement; after applying an incremental load under undrained conditions a time period of about 2 h was needed for the measured pore water pressure to reach more than 90% of the applied load. Furthermore, the process involved in a piezocone dissipation test is not a constant total stress process. As discussed by Fahey and Lee Goh [7] and Chai et al. [4], during the consolidation process the soil immediately around the cone tends to displace toward the cone, and some unloading (or swelling) may also occur in the soil more remote from the cone. None of these factors has been considered in the numerical simulation. The comparisons presented here between the simulated and measured distributions of u and the dissipation in a horizontal plane indicate that generally the proposed method for estimating the initial distribution of u is reasonable. Further validation of the method has been achieved by comparing predicted and measured data [10] reported in the literature, as described in the following section.
4.2. Data of Kim et al. [10] Kim et al. [10] reported measured radial distributions of u obtained from laboratory model tests. The tests were conducted using a mixture of kaolinite and Joomoonjin (Korea) sand (in equal portions), and a standard u2 type cone (1000 mm2 projected cone area and 60° cone apex angle, and the filter for excess pore water pressure measurement was on the shoulder of the cone). The model chamber had a diameter of 1.2 m and a height of 1.0 m. For the conditions adopted, and assuming axisymmetric plane strain conditions, for a horizontal slice of the model ground the cone penetration produced a volumetre displacement less than 0.09% of the original volume of the slice, and so the boundary effect should be
800
200 0
0
400 200
0.1
0.2
0
Scenario-2 OCR 1 2 4 16
Cone
400
Δup+Δus+Δuul
600
Cone
u (kPa)
600
800 Scenario-2 OCR 1 2 4 16
u (kPa)
Δup+Δus
0
0.1
Radial distance, r (m)
Radial distance, r (m)
(a)
(b)
0.2
Fig. 7. Calculated excess pore water pressure distributions (Scenario-2): (a) Cavity expansion + shear and (b) cavity expansion + shear + unloading.
112
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113
Table 6 Stress, strength and stiffness of model ground of Kim et al.’s [10] tests. Case
r0v 0 (kPa)
K0
OCR
Triaxial su (kPa)
Ira (kPa)
Rb (m)
1 2 3 4
200 40 20 10
0.50 1.1 1.6 2.2
1 5 10 20
70 54 48 43
100 100 100 100
0.178 0.178 0.178 0.178
Assumed. Calculated.
much less than that observed in the model tests conducted in this study. The stress conditions adopted and the corresponding strength and stiffness of the soils tested are listed in Table 6. The values of K0, OCR and su are from Kim et al. [10]. Kim et al. also reported the values of shear modulus (G) from which the rigidity index (Ir) could be estimated, but their suggested value of G for the case of OCR = 1 was more than 10 times the value suggested for the other cases with higher OCR values, which seems inconsistent. The measured zones where u > 0 had outer radii about 10 times the radius of the cone, and so a value of Ir of 100 was simply assumed here. The simulated initial distributions of u are compared with measured values in Fig. 8(a)–(d) for OCR = 1, 5, 10 and 20, respectively. From these figures, the following points can be observed: (a) The estimated size of the shear zone (rs) given by Eq. (8) seems quite reasonable. (b) Except for OCR = 1, the cases where both the effects of shear and partial unloading are considered resulted in better simulations.
The results presented in the previous section show that the pore water pressure distribution in the radial direction from the shoulder of the cone can be reliably predicted. It is suggested that the coefficient of consolidation of the soil in the horizontal direction (ch) can also be estimated by back analysis of the dissipation curve for the pore pressure measured at the shoulder of the cone, u2. The back fitted value should be a reliable estimate of the ‘‘true’’ value of ch of the soil. As such, it proves a convenient reference for evaluating other proposed methods for directly estimating values of ch from measured dissipation curves. For example, for a non-standard dissipation curve, Chai et al. [4] proposed a method for estimating the value of ch. The basic idea of this method is to correct the measured time taken for the excess pore water pressure to dissipate from its maximum value to 50% of the maximum value, t50. The correct time is defined as t50c, and then this value of t50c is used in the equation proposed by Teh and Houlsby [16] for standard dissipation curves to calculate directly the value of ch. The equation proposed by Chai et al. for evaluating t50c is as follows:
t50c ¼ 1 þ 18:5
pffiffiffiffi Ir
ð14Þ
OCR = 5 Measured Δup +Δus+Δuul Δup +Δus Δup
Cone
200
u (kPa)
Cone
u (kPa)
0:245 r 20 t 50c
300 200 100
100
0
0.1
0
0.2
0
0.1
0.2
Radial distance, r (m)
Radial distance, r (m)
(a)
(b)
400
400
OCR = 10 Measured Δup +Δus+Δuul Δup +Δus Δup
200
OCR = 20 Measured Δup +Δus+Δu ul Δup +Δus Δup
300
u (kPa)
Cone
300
u (kPa)
ð13Þ
Ir 0:3 200
400
OCR = 1 Measured Δup+Δus+Δuul Δup+Δus Δup
300
100 0
0:67
Applying Eqs. (13) and (14) to the three model dissipation test results (Fig. 3), values of ch have been estimated, and in Table 7 these are compared with: (a) values of the coefficient of consolidation of the soil in the vertical direction, cv, measured directly in
400
0
t50
t u max t 50
For a piezocone with a filter element for pore water pressure measurement located at the shoulder of the cone, the equation for calculating the value of ch is as follows [16]:
ch ¼ The reasonable comparisons between the predicted and measured distributions of u for Kim et al.’s model tests further reinforces the statement that the proposed method is capable of predicting the piezocone penetration-induced excess pore water pressure distributions in the radial direction.
Cone
a b
5. Estimating ch from non-standard dissipation curves
200 100
0
0.1
0.2
0
0
0.1
Radial distance, r (m)
Radial distance, r (m)
(c)
(d)
0.2
Fig. 8. Simulated distributions of u for Kim et al.’s model tests: (a) OCR = 1, (b) OCR = 5, (c) OCR = 10, (d) OCR = 20.
113
J.-C. Chai et al. / Computers and Geotechnics 57 (2014) 105–113 Table 7 Comparison of ch and cv values of the model tests. Case
OCR
cv (m2/min)
Estimated ch (m2/min)
Back fitted ch (m2/min)
(ch)back/(ch)estimated
1 2 3
1 2 4
2.28E06 3.60E06 6.00E06
9.11E06 1.15E05 9.30E06
1.4E05 1.5E05 1.6E05
1.5 1.3 1.7
laboratory oedometer tests conducted at the appropriate initial vertical effective stress r0v 0 ); and (b) numerically back fitted values of ch. It can be seen that the values of ch estimated by Eqs. (13) and (14) are smaller but close to the back fitted ch values obtained from the dissipation simulations. It can be observed from Fig. 3 that although the simulated curves compared well with the measured ones, for OCR = 2 and 4, the simulated values of tumax are larger than the corresponding measurements. As can be seen from Eq. (13), the larger the value of tumax, the smaller t50c will be, and consequently a larger value of ch will be interpreted. This comparison suggests that Eqs. (13) and (14) can be used to interpret values of ch from measured non-standard dissipation curves. The estimated ch values are about 1.5–4 times the corresponding laboratory values of cv. The behaviour of a remoulded clayey soil may be initially isotropic, but after consolidation under onedimensional (1D) conditions with a pressure of 96 kPa, it is very likely to exhibit stress-induced anisotropic consolidation behaviour. The stress-induced anisotropy is stronger for a remoulded soil than an undisturbed soil sample because the remoulded soil has a weak or even no inter-aggregate bonding [8]. For undisturbed Ariake clay samples, the ratio of ch/cv is known to be about 1.5 [5], and for a remoulded Ariake clay sample consolidated under 1D condition and a pressure of 96 kPa, a ratio ch/cv of about 1.5–4 may be reasonable. 6. Conclusion The distribution of piezocone penetration-induced excess pore water pressure (u), as well as its dissipation behaviour, have been investigated by laboratory model tests, theoretical analysis and numerical simulation. Based on the test and analysis results, the following conclusions can be drawn. (1) A semi-theoretical method has been proposed to predict the radial distribution of excess pore pressure, u, induced at the level of the shoulder of a cone. In the method, the effects of the undrained shear strength (su), over-consolidation ratio (OCR) and rigidity index (Ir) of the soil have been considered. The validity of the method has been checked by using the model test results from this study and other experimental data available in the literature. (2) With a reliably predicted initial distribution of u and the measured dissipation curve of pore water pressure at the shoulder of the cone (u2), the coefficient of consolidation of the soil in the horizontal direction (ch) can be back fitted by dissipation analysis. Comparing the back fitted values of
ch with values estimated from the dissipation curve by a previously proposed method indicates that the previously proposed method can result in a good estimation of ch from non-standard dissipation curves (in which u2 initially increases and then dissipates with time).
Acknowledgement Mr. A. Saito, technician at Saga University, Japan, assisted the laboratory tests reported in this article. References [1] Burns SE, Mayne PW. Monotonic and dilatory pore pressure decay during piezocone tests in clay. Can Geotech J 1998;35(6):1063–73. [2] Campanella RG, Robertson PK. Current status of the piezocone test. In: Ruiter J, editor. Penetration testing. Rotterdam: Balkema; 1988. p. 93–116. [3] Chai J-C, Agung PMA, Hino T, Igaya Y, Carter JP. Estimating hydraulic conductivity from piezocone soundings. Geotechnique 2011;61(8):699–708. http://dx.doi.org/10.1680/ geot.10.P.009. [4] Chai J-C, Sheng D-C, Carter JP, Zhu H-H. Coefficient of consolidation from nonstandard piezocone dissipation curves. Comput Geotech 2012;41:13–22. http://dx.doi.org/10.1016/j.compgeo.2011.11.005. [5] Chai J-C, Jia R, Hino T. Anisotropic consolidation behavior of Ariake clay from three different CRS tests. Geotech Test J ASTM 2012;35(6):1–9. http:// dx.doi.org/10.1520/GTJ103848. [6] Chai J-C, Carter JP, Saito A, Hino T. Behaviour of clay subjecting to vacuum and surcharge loading in an oedometer. Geotech Eng J, SEAGS AGSSEA 2013;44(4):1–8. [7] Fahey, M, Lee Goh, A. A comparison of pressuremeter and piezocone methods of determining the coefficient of consolidation. In: Proceedings 4th international symposium on pressuremeters, Sherbrooke, Quebec, Canada, Balkema, Rotterdam; 1995. p. 153–60. [8] Hattab M, Hammad T, Fleureau J-M, Hicher P-Y. Behaviour of a sensitive marine sediment: microstructural investigation. Geotechnique 2013;63(1):71–84. http://dx.doi.org/10.1680/geot.10.P.10. [9] Kim K, Prezzi M, Salgado R, Lee W. Effect of penetration rate on cone penetration resistance in saturated clayey soils. J Geotech Geoenviron Eng 2008;134(8):1142–53. [10] Kim T, Kim N, Tumay MT, Lee W. Spatial distribution of excess pore-water pressure due to piezocone penetration in overconsolidated clay. J Geotech Geoenviron Eng 2007;133(6):674–83. [11] Ladd CC. Stability evaluation during staged construction. J Geotech Geoenviron Eng ASCE 1991;117(4):540–615. [12] Miura N, Chai J-C, Hino T, Shimoyama S. Depositional environment and geotechnical properties of Ariake clay. Indian Geotech J 1998;28(2):121–46. [13] Randolph MF, Carter JP, Wroth CP. Driven piles in clay – the effects of installation and subsequent consolidation. Geotechnique 1979;29(4):361–93. [14] Roscoe KH, Burland JB. On the generalized stress-strain behavior of wet clay. In: Heyman J, Leckie FA, editors. Engineering plasticity. Cambridge University Press; 1968. p. 535–609. [15] Sully JP, Robertson PK, Campanella RG, Woeller DJ. An approach to evaluation of field CPTU dissipation data in overconsolidated fine-grained soils. Can Geotech J 1999;36:369–81. [16] Teh CI, Houlsby GT. An analytical study of the cone penetration test in clay. Geotechnique 1991;41:17–34.