Predicting the bearing capacity of pile installed into cohesive soil concerning the spatial variability of SPT data (A case study)
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
45
Predicting the bearing capacity of pile installed into cohesive soil
concerning the spatial variability of SPT data (A case study)
Duong Hong Tham1*, Truong Nhu Manh1
1Ho Chi Minh City Open University, Vietnam
*Corresponding author: [email protected]
ARTICLE INFO
ABSTRACT
DOI:10.46223/HCMCOUJS.
tech.en.11.1.1405.2021
Nowadays, in situ tests have played a viable role in
geotechnical engineering and construction technology. Besides lab
tests conducted on undisturbed soil samples, many different kinds of
in-situ tests were used and proved to be more efficient in foundation
design such as pressuremeter PMT, cone penetration test CPT,
standard SPT, etc. Among them, a standard penetration test (SPT for
short) is easy to carry out at the site. For decades, it has proved
reliable to sandy soil, but many viewpoints and opinions argued that
the test was not appropriately applicable to cohesive soil because of
scattered and dispersed data of SPT blow counts through different
layers. This paper firstly studies how reliable the SPT data can
predict the physical and mechanical properties; secondly, the soil
strength is determined in terms of corrected N-SPT values, and
finally the bearing capacity of a pile penetrating cohesion soil. By
analyzing data from 40 boreholes located in 18 projects in Ho Chi
Minh City, South VietNam, coefficients of determination between
SPT numbers and physical and mechanical properties of different
soil kinds are not the same: R2 = 0.623 for sand, =0.363 for sandy
clay and =0.189 for clay. The spatial variability of soil properties is
taken into account by calculating the scale of fluctuation θ=4.65m
beside the statistically-based data in horizontal directions. Finally,
the results from two theoretical approaches of predicting pile bearing
capacity were compared to those of finite element program Plaxis
3D and static load test at site. Correlation between the capacity
computed by using corrected N-values instead of soil strength and
results of static load test has proved to be well suitable in evaluating
Received: February 25th, 2021
Revised: March 4th, 2021
Accepted: March 5th, 2021
Keywords:
Standard Penetration Test
(SPT), cohesive soil, spatial
variability, variance reduction
factor, the scale of fluctuation, the bearing capacity of driven and jack-in piles, particularly
bearing capacity of pile
installing in the cohesive soil using the SPT blows.
1. Introduction
The bearing capacity of a pile installed in a soil foundation can be predicted by several
different methods. Some methods used directly soil properties, i.e., shear strength parameters
(cohesion and internal friction angle) obtained by a lab test on undisturbed soil samples; other
indirect methods used data from in situ tests to characterize the soil strength as converted
properties, then apply them to analytical formulas to estimate bearing capacity of the pile. SPT is
an in-situ test that in decades hitherto was proposed to be reliable to sandy soil.
For sandy soil, there is a real significant correlation between internal friction angle and N
46
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
value (Hatanaka & Uchida, 1996). SPT can be used for predicting the bearing capacity of shallow
footings in which, bearing capacity factor for the depth of footings Nq, for friction Nγ were
calculated from regression equations founded by different authors. In the research, the energy ratio
is 60 percent, corrected SPT value N60 can be used for estimating the allowable contact pressure
concerning a 30% probability of exceeding a settlement of 25 mm.
For clayey and cohesive soil, it is rather complicated to ensure the practicability of SPT for
predicting soil properties. Due to scattered data in the correlation between SPT values and the
increase of pore water pressure as the rod plunged into clay layers. Moreover, low permeability of
soil may lead to appear a temporary resistance for driving, higher number of blows will be
obtained. It might have generally been proposed that SPT is rather unreliable to this kind of fine-
grained soil. Nevertheless, SPT has still been a main in-situ test in soil investigation reports, even
for large scale projects. Mahmoud (2013) studied the reliability of using SPT in predicting
geoengineering properties of silty clay and sandy soil. The results indicated not only physical
properties but shear strength parameters such as cohesion and internal friction angle had a
significant correlation to corrected N SPT number, even silty clay.
Variability of soil can be described clearly by the coefficient of variation (COV). This
coefficient varied to a very wide range, depending on soil type. Samples from large data set at the
different locations had the COV (ratio of standard deviation divided by mean) from more than
40% to 150% for some conventional properties (Phoon & Kulhawy, 1999).
Table 1
Wide range of coefficient of variation for clay soil
Depths (m)
parallel to
surface
Depths (m) Horizonal
Clay Layer
Statistics
N-SPT
plans
Mean
St. Dev
2.6
3.9
150
Layer 1
2 - 4
9 - 11
28 - 42
1 - 3
COV (%)
Mean
St. Dev
8.2
10.4
127
Layer 2
Layer 3
8 - 10
COV (%)
Mean
St. Dev
8.9
4.1
47
28 - 42
COV (%)
Source: The researcher’s data analysis
On the other hand, the soil has inherent uncertainties due to spatial variability and its
response to load and effects. The response of sand is quite different as compared to that of clay.
Kulhawy et al. (1983) pointed out 4 categories of uncertainties, relating to soil type; they are
saturation status, devices, and techniques of testing, and other uncontrollable factors (borehole
diameter, efficient energy delivered to hammer, robs and type of drilling equipment…etc.). There
are more than 27 sources of uncertainties relating to soil characteristics (5 factors), water table (2
factors), equipment (7 or more factors), and more than 10 factors of the working condition at sites
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
47
(Zekkos, Bray, & Der Kiureghian, 2004). Therefore, regarding SPT, it should take into account
uncertainties in the performance of the test. There were many research works for this content
(Kulhawy & Mayne, 1990). Both ASTM D-1586, ASTM D6066-96 prescribed recommendations
for this feature as well.
In sandy soil, N is largely affected by overburden pressure. The more value of this pressure
is, the correction factors will be higher, approximately proportioning to square of relative density
Dr (Meyerhoff, 1976) as expressed in the following formula:
푁 = 퐷푟2(푎 + 푏. 푝′)
(1)
where a and b are factors of material dependence and p’ is the mean effective stress (Kudmetha &
Dey, 2012). Then the correction factor due to overburden pressure, namely CN, is
푎
2
+100
+푝′
⁄
퐷 (푎+푏.100)
푎+푏.100
푎+푏.푝′
퐶푁 = 푁
=
=
=
(2)
(3)
푐표푟푟푒푐푡
푟
푏
2
푎
푁
퐷 (푎+푏.푝′)
⁄
푟
푏
The correction factor CN by Skempton (1986) defined in Eq. (2) is
푛
퐶푁 ==
/
1+0.01휎
푣표
where σ’vo is overburden pressure in kPa, n = 2 for loose sand and n = 3 for dense sand.
For decades, numerous research works tried to determine the reliability of SPT data in
predicting bearing capacity of pile installed into cohesive soil. For analysis of reliability, it is
necessary to quantify uncertainties by statistical parameters (i.e., standard deviation, mean, and
the law of distribution). Some authors proposed a scheme of reliability-based design in
geotechnical engineering (Honjo, 2011).
For examining correlations between properties in soil foundation, the scale of fluctuation
should be determined. That is a distance in the soil foundation within which there is an
autocorrelation for a specific property (Vanmarcke, 1977). According to Duong (2017),
Vanmarcke‘s theories can be used to quantify the spatial variability of soil properties in estimating
the allowable bearing capacity of the bored pile. The result is a regression formula as below:
푄푎 = 4346.3 − 5202.1휌12 + 34.9휃 + 353.3퐶푂푉 + 357.7퐶푂푉휙
푐
(4)
−565.1퐶푂푉퐸 − 2.9훽 + 0.14푃
푢
where ρ12 is the coefficient of correlation between the two zones 1 and 2 along the pile shaft and
θ is scale of fluctuation in vertical direction. COV(c) COV(φ) is coefficient of variation of cohesion
and internal friction angle, respectively; β is reliability index and Pu is the ultimate bearing capacity
of single pile.
In this paper, SPT data are corrected to use indirectly in predicting the bearing capacity of
a driven pile. By using regression analysis over a large amount of data, correlation between SPT
and soil properties such as water content, depth of testing, modulus of elasticity, Atterberg limit,
etc. of samples taking from 40 boreholes of 18 projects in Ho Chi Minh City were found, soil
strength parameters converted from corrected SPT numbers together with physical properties of
soil was also determined. At least three approaches of computing bearing capacity of pile installed
into foundation are used in which layer of cohesive soil was dominant. Results obtained were
compared to that of a static load test.
48
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
2. Method
2.1. Literature reviews on N-SPT data
Undisturbed soil samples were brought to the laboratory to identify physical and
mechanical properties. Conventional tests, e.g. Atterberg Limits test, direct shear test, unconfined
compression test, etc. were sufficient for supplying materials for computing bearing capacity of
footings and single pile; N data were in-situ test and they were raw data recorded at a site without
any correction. Depths of in situ testing were noted together with N-blow counts.
Bazaraa’s formula can be chosen to correct the raw N numbers (Civilblog, 2013). The first
correction is due to the overburden pressure and the second is only for silty and fine-grained soil.
There was no other correction for borehole diameter or for energy delivered to the rod penetrating
soil layers. Therefore, the first uncertainty was the energy percentage delivered to the penetrator.
Besides, there was no evidence that the site test had the same efficiency at every size of boreholes;
and how about the rod length effects, etc… In general, the abovementioned issues could be taken
into account by the formula as below:
푁60 = 푁푓푖푒푙푑. 퐶퐸. 퐶퐵. 퐶푆. 퐶푅
(5)
where Nfield is the blow counts recorded at the site; CE is the factor of energy correction, CB _ factor
of boreholes, CS _ factor of soil sample size, and CR is the factor of rod length. Many different
authors had pointed out the different levels of energy ratio ER (that was defined to be a ratio of
measured energy divided by theoretical energy. Aoki and Velloso (1975) accepted ER = 70%;
Shioi and Fukui (1982) suggested ER=55%, Meyerhoff (1976), ER=55%. A number ER= 55%
was proposed to be appropriate to use in pile bearing capacity for projects in Viet Nam (Hoang &
Tam, 2016).
Table 2
Bearing capacity of pile using SPT numbers
Formula by
Skin friction
Point bearing
a.k
Qs =
Ns
Aoki and Velloso
(1975)
k
Qp
=
Nb
3.5
1.75
a =14, k =1 (sand);
a = 60,k = 0.2 (clay)
D
Qp = (1+ 0.04 b )Nb
Shioi and Fukui
(1982)
Qs = 2Ns
B
Sand
Clay
Sand
Qs =10Ns
D
Qp = (1+ 0.06 b )Nb
B
Clay
Qs = nS Ns
ns = 1
Qp = 0.4NbC1C2
Meyerhoff (1976)
Non-displacement pile;
ns = 2
C1 C2 factors dependent to ratio D/B (i.e.,
diameter to pile length)
Displacement pile
Qb = nb Nb
Qs = nS Ns
ns=2~4
Bazaraa and
Kurkur (1986)
nb=0.06~0.2
Nb average of N taken 1B above and 3,75B
below pile tip
Source: Hoang and Tam (2016)
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
49
2.2. Correction factors
Bazaraa (1967) proposed the following corrections to obtain the actual count N, based on
the overburden pressure (N is modified to be N’) (Civilblog, 2013):
For po ≤ 75 kPa
4N
N'=
(1+ 0.04 po )
(5a)
For po > 75 kPa kPa
4N
N'=
(3.25 + 0.01po )
(5b)
where N’ is corrected N value; N is the observed N-value; po is overburden pressure, (kPa) = γD;
D is depth of penetration (m); γ is unit weight of soil at the time of testing.
If the stratum (during testing) consists of fine sand & silt below water table, the corrected
N-value (or N’) has to be further corrected to get the final corrected value N” as below:
1
N"=15 + (N'−15)
2
(6)
As such, there are two steps of correction against N numbers for every usage for all
geotechnical computations.
2.3. Spatial variability – Scale of fluctuation
Pile bearing capacity includes shaft friction along the length uD1 and point bearing within
uD2 as described in Figure 1.
(a)
(b)
Figure 1. Diagram for computation scale of fluctuation
Corrected SPT numbers were assumed to display as in Figure 1b. Correlation between the
two zone uD1 and uD2 was characterized by a correlation factor as follows:
50
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
D2 2 (D ) − D22 (D ) − D222 (D2 )
12
12
1
1
u
=
D1,uD2
2D D (D )(D )
(7)
1
1
1
1
(0 u
1)
D1,uD2
where Γ2(Δz) denoted variance reduction factor for spatial average for interval Δz of pile shaft,
determined by Vanmarcke (1983):
1
2 z
2z
2z
2 (z) = ( )2[
−1+ exp(−
)]
(8)
• The scale of fluctuation θ _ being defined as the distance within which some specific soil
property have significant correlation from point to point (Vanmarcke, 1977, 1983) and variance
reduction factor Γ2(Δz) will be applied simultaneously to calculate:
• Skin friction using the average value of corrected SPT blows within the scale of
fluctuation;
• Point bearing using the average value of corrected SPT number from 1D below pile tip
and 4D above the level of pile tip;
• Reliability using standard deviation, which is the square root of variance multiplied by
Γ2(Δz);
• Regression Formula between bearing capacity and several predictors (i.e., independent
variables and parameters), somewhat like the abovementioned formula (4) studied by Duong
(2017).
2.4. Pile bearing capacity considering the spatial variability
As abovementioned remarks, steps for estimating bearing capacity for pile will consider
two main issues: correction and spatial variability (both vertical and horizontal direction). Suitable
approach will be suggested as below:
-
N-SPT blow counts will be corrected first, two kinds of correction are obligatory:
due to depth (sand) and due to fine grained soil and silty sand (clayey soil);
•
Determine scale of fluctuation of SPT numbers N. According to Vanmarcke (1977),
the scale of fluctuation θ may approximately equals to 0.8( ) where
d
n
1
d =
d
(9)
n
i
i=1
where di as shown in Figure 1 is intersections of fluctuating property and its trend function (layers
d1, d2… di is less than the scale of fluctuation θ). Computation was conducted on sublayers which
are smaller than θ.
• Determine characteristic length L (Cherubini & Vessia, 2010) L=D+B in which D is the
embedment depth and B is foundation width (i.e., pile diameter);
• Compute Γ2(L), denoted variance reduction factor, using Vanmarcke’s formula (8);
• Within the scale of fluctuation, the average value of corrected N SPT number was used
to compute friction component of pile bearing capacity;
• Compute friction component of bearing capacity for individual segments (incremental
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
51
length of the pile) and point bearing component of bearing capacity of the pile;
• In the numerical model, layers will be divided into sub-layers that based upon the scale
of fluctuation within which, soil strength is indirectly determined by corrected N- values;
• If reliability index of bearing capacity is required, compute variance reduction factor
(i.e., variance multiplied by variance reduction factor), standard deviation, and the average value
(reliability index was defined as the ratio between average value divided by the standard deviation
for a specified limit function).
• Reliability of SPT numbers will be assessed by comparing indirectly predicted value of
pile bearing capacity using either Meyerhoff’s formulas and finite element modeling software and
that of static load test;
• Compute friction component of bearing capacity for individual segments (incremental
length of pile) and point bearing component of bearing capacity of pile;
• In numerical model, layers will be divided into sub-layers that based upon the scale of
fluctuation within which, soil strength is indirectly determined by corrected N- values;
• If reliability index of bearing capacity is required, compute variance reduction factor
(i.e., variance multiplied by variance reduction factor), standard deviation and average value
(reliability index was defined as ratio between average value divided by standard deviation for a
specified limit function);
• Applicability of SPT numbers will be assessed by comparing indirectly predicted value
of pile bearing capacity using either Meyerhoff’s formulas and finite element modeling software
and that of static load test.
Table 3
Data collection for regression analysis
2
2
2
2
2
4
6
6
0.38
0.39
0.29
0.33
13.02
13.03
14.55
14.19
1.07
1.06
0.84
0.90
0.24
0.25
0.17
0.19
…
35.3
70.8
88.4
78.6
22.61
21.49
24.69
23.26
2
2
5
5
4
3
5
5
10
9
10
10
18
18
18
18
48
50
52
54
0.20
0.19
0.18
0.18
16.68
16.61
16.60
16.74
0.63
0.61
0.62
0.60
0.25
0.18
0.19
0.17
520
539
559
578
45.92
48.68
42.70
45.15
33
34
37
31
16
16
17
14
16
16
16
15
Source: Truong (2017)
52
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
3. Results
3.1. Data collection and soil strength in terms of corrected N blows
To assess the reliability of SPT numbers in predicting the physical properties and strength
of cohesive soil, the procedure is:
• Classify data into 4 groups: medium sand, silty sand, clayey sand, and sandy clay.
• Soil data of 40 boreholes taken from 18 projects were tabulated as in Table 3, in which
soil was again classified into three groups: non-cohesive soil (sand), fine soil (clay), and cohesive
soil (both clayey sand and sandy clay) for clearly physical properties.
• Because SPT data must be corrected by transforming N into N’ for sand and N’ into N”
for clay, depth of sampling was taken into account in all regression equations.
Table 4
Collected Data of 18 projects
Data
Number of samples
Type
Project Number
2,6,10,17, 18
State of soil
Sand
20
Medium density
(BH1)
1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12,
13, 16, 17, 18
Clayey sand,
sandy clay
185
233
Mainly plastic
(BH1)
1,2,3,4,5,6,7
Semi solid to stiff,
low plasticity
Clay
9,10,11,12, 16,17,18 (BH2)
Source: Truong (2017)
In order to find out the correlation between SPT numbers and soil physical properties such
as unit weight γ, moisture ω, void ratio e, modulus of elasticity E, plasiticity index Ip and shear
strength (cu, φ), data were tabulated as described in Table 3 for each soil group.
Figure 2. Data analysis tool in Excel (Truong, 2017)
With level of confidence is 95%, corrected N is chosen to be dependent variable Y and
independent variables Xs.
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
53
Figure 3. Regression analysis window for correlation between SPT and other properties
• N’ will be correction value for sand and N” for both clayey sand and sandy clay
(cohesive soil in general). For predicting indirectly the bearing capacity of the pile, the bearing
component at pile tip, and the friction along the shaft are converted in terms of N’ or N”. With soil
strength parameters (i.e., cohesion and internal friction angle) and physical properties related to
SPT number, a regression equation will be obtained and used in evaluating the bearing capacity of
soil foundation or driven pile
It is necessary to compare three values :
• Parameters of soil properties (physical parameters and soil strength) in terms of SPT
numbers (this study);
• Shear strength of the conventionally obtained lab tests.
• Shear strength of previous studies about correlations between soil properties (physical,
mechanical properties and compressibility).
Then the most appropriate values to use in foundation engineering are selected.
3.2. Correlation equations
Some results were described in Tables 4, 5 and equations of multivariable regression are
shown in Figure 4:
Figure 4. Regression statistics and variance analysis ANOVA (Truong, 2017)
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Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
Results of multivariable linear regression for different kinds of soil (Sand, Clay, Sandy
Clay and Clayed Sand) are tabulated in Table 5.
Table 5
Significance of the Analysis of Variance (ANOVA) for sand, sandy clay/clayey sand, clay
Regression Statistics
Analysis of variance (ANOVA)
Type
R2
Adjusted R2
F
Significance F
0.003
Sand (20 samples)
Clayey sand,
0.623
0.456
6.194
0.363
0.189
0.341
0.171
16.905
10.571
2.07E-15
3.86E-9
Sandy clay (185
samples)
Clay
(233 samples)
Source: Regression equation for sandy soil
N'= 224.9 - 0.13 Z + 0.022 - 7.89 d -139.67e + 0.02E
(10)
where Z is the depth of sampling, other symbols are given in Table 3.
In multivariable linear regression analysis, R2 adjusted is used instead of (R Squared). R2
adjusted = 0.456 (or R = 67.5%) indicated that the predictors or a few independent variables as
prescribed only explained nearly 46% dependent variables N’. It meant that more than 54% was
due to other uncertainties in measurement, errors in lab tests etc.
These properties of sand were rather reliable in predicting N’.
As for silty sand, results from observed 70 samples showed no correlation found.
Regression formula for clayey sand and sandy clay
N"= 9.955+ 0.036Z -0.026 + 0.813d + 0.098(Ip ) + 0.009E
(11)
R2 (R Squared adjusted) = 0.341 (slightly smaller as that of Sand with R Squared adjusted
= 0.456) indicated that the predictors or a few independent variables as prescribed only explained
nearly 34% dependent variables N‘. It meant that more than 66% was due to other uncertainties in
measurement, errors in lab tests, etc. These properties were relatively reliable in predicting N”.
Regression formula for clay
N"= 78.629-0.044Z-82.65 - 2.81d + 7.31(Ip ) + 0.048E
(12)
R2 (R Squared adjusted) = 0.171 indicated that the predictors or a few independent
variables as prescribed only explained nearly 17% dependent variables N’. It meant that more than
83% was due to other uncertainties in measurement, errors in lab tests, etc.
These properties were weakly reliable in predicting N”. Based on soil data and corrected
numbers of SPT data, by conducting multivariable regression analysis, some results are:
• Sand: relatively usable
• Sandy Clay/ Clayey Sand: tentatively usable
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
55
• Clay: tentatively usable with remarkable caution.
• Based on R2 adjusted (R2 adjusted = 0.456 for sand and = 0.341 for clayey sand and
sandy clay; for clay, R2 adjusted = 0.171) SPT is reliable for sand and clayey sand, and weakly
reliable for clay in a multi variable regression model.
• Although the R squared was relatively small, but strongly related to each other,
expressed in very small value Significant F in the most right column of Table 6
Table 6
Regression statistics and variance analysis ANOVA (Truong, 2017)
Source: Truong (2017)
• For sand moisture, dried density, initial void ratio and overburden pressure (depth of
samplings) affected most to corrected SPT numbers instead of recording data without correction.
• For clay, depth of sampling, plasticity index did not affect SPT both N’ and N”.
Cohesion and modulus of deformation E had a slight effect on N”. This might be unclear.
• For cohesive soil, depth of sampling affected most significant the corrected SPT
numbers. Hence, a correction was obviously necessary.
• Corrected SPT numbers were applicable for both sand (N’) and clay (N”), with different
coefficients of determination.
3.3. Single-variable regression analysis for shear strength parameters of cohesive soil
At 95% confidence level: there was a weak correlation between corrected SPT number N”
and many different soil parameters altogether but it was a significant correlation between N” (or
N’) and E, c, φ. Regression formulas for the main parameters of soil strength and compressibility
for different soils are in Table 7.
Table 7
Regression formulas for converting N-values to soil properties (units in SI, i.e., kPa and degree)
Confidence level
Soil type
85%
95%
E
φ
E
C
φ
E=111.5+1.826N’
φ =32.6°-0.01N’
E=57.67+2.38N’’
C=0.134+0.001N’’
φ =19.81+0.52N’’
E=118.8+2.431N’
φ =32.93°-.02°N’
E=61.63+2.37N’’
C=0.141+0.002N’’
φ =20.33+0.56N’’
Sand
Clayey
sand/ Sandy
56
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
Confidence level
Soil type
85%
95%
Clay
E
C
φ
E
E=52.6+1.7N’’
C=0.367+0.02N’’
φ =15.89+0.36N’’
E=52.6+1.7N’’
E=56.7+1.939 N’’
C=0.407+0.022N’’
φ =16.5+0.39N’’
E=56.7+1.939N’’
Clay
Source: Truong (2017)
Results obtained from the abovementioned regression analysis can be compared to those
of previous works conducted by Mahmoud (2013) in which shear strength of silty clay with sand
soil can be calculated as following equations:
φ (in degree) = 0.209N” + 19,68
c (in kG force/cm2) = 0.014 N” – 0.18
where N” is the corrected SPT numbers, E in kPa.
4. Prediction of the bearing capacity of pile as per TCVN 10304: 2014 (Ministry of
Sciences and Technology, Vietnamese Government, 2014) concerning the spatial variability
Mean values of corrected SPT N-values will be estimated in sub-layers which should be
smaller than scale of fluctuation θ (Figure 5). Soil properties within scale of fluctuation are
chosen by using converted values from corrected SPT numbers.
4.1. Soil profile
Soil profile are shown in Figure 5. A designed pile will be installed through 5 soil layers.
Clayey soil is dominant. Average depth is from formula (9), or
5.7 +1.9 + 7.5 + 6 + 8
d =
= 5.82m`
5
Scale of fluctuation was taken θ = 0.8
d
=4.65 m. Pile bearing capacity can be calculated
appropriately by using soil properties within a distance di < θ.
(a)
(b)
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
57
(c)
Figure 5. Corrected numbers SPT. a) Borehole BH1 (all are N”); b) Borehole BH1 (some N’,
other N”); c) Borehole BH2, all corrected N” (Truong, 2017)
In general, ultimate bearing capacity is calculated by formula as below:
Q = q A + u ( f l + f l )
(13)
s
b
b
c,i c,i
s,i s,i
where, qb is point bearing resistance in kPa, Ab and u are cross section of pile tip and perimeter
of pile section, respectively. fc.i and lc.i are skin friction and length of ith pile segment penetrating
in clay, respectiveley; and the second term in paratheses of the formula (13) is for sand ith layers.
All the resistance of soil at pile tip qb or shaft friction fc.i along the pile mantle are calculated by
the modified N-SPT numbers, especially within the scale of fluctuation θ (i.e., black vertical
line).
4.2. Bearing capacity suggested by the Meyerhoff’s formula
This formula has still been used popularly in Vietnam as an alternative for comparison
purpose (TCVN 10304: 2014, Ministry of Sciences and Technology, Vietnamese Government,
2014). Soil strength will be used to compute shaft pile friction and point bearing.
For pile installing into sandy soil,
fs,i = Ks .vo '.tan
qb = v 'Nq + c.Nc
(14)
(15)
where Nq Nc are bearing capacity factor, dependent on friction angle of soil; Ks is coefficient
of lateral pressure, Ks =(1~1.2)(1-sinφ’) for driven pile; tan(δ) is coefficient of external friction
between soil and pile shaft.
Appendix G of TCVN 10304:2014 (Ministry of Sciences and Technology, Vietnamese
Government, 2014) also recom-mended a Meyerhoff’s formula of skin friction and point
bearing resistance using SPT N-values, as below:
10.Ns,i
fs,i =
(16)
3
58
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
(17)
qb = 300.Np
For pile installing into cohesive soil
(18)
(19)
fc,i =p .fL.cu,i
qb = 9.cu
where αp is factor applied for driven pile, depended on the ratio of undrained strength to average
effective stress (in spreadsheet denoted ap); fL is a factor relating to the slenderness length h/D
(D= diameter) of pile.
These abovementioned formulas were applied to driven or jacked-in pile. For
considering spatial variability, each soil layer will be chosen as di as in Figure 2. In case the
scale of fluctuation is taken into account, friction and point bearing will be computed within
that scale of fluctuation θ.
Table 8
Illustrated spreadsheet for computing abutment B pile bearing capacity using Meyerhoff’s formula
and corrected N’, borehole BH-1
WITH CORRECTED N VALUES
8.4
M
M
(D=
0.35)
8.4 BH-1 0.35
Thick-
ness
N-
SPT
No. Soil layers
γ
Ϭ’vo
ϕ
c
ap
Cu,i
kPa
k2
fi
Axq
Qsi
m
kN/m3 kN/m2 (o)
kPa
kN/m2 m2
(kN)
Firmly
1 plastic clay
2
19.8
19.8
19.8
2.02
1.05
19.8 16.8 2.4 7.75
59.4 16.8 2.4 13.9
96.0 16.8 2.4 13.4
1
1
1
8.39
20.31
31.33
2
2
2
2
2
8.4 2.8
23.5
56.9
74.6
Firmly
2 plastic clay
2
20.3 2.8
31.3 2.4
Firmly
3 plastic clay
1.7
1.9
0.8
Granular
4 soil, dense
13.21 31.3
0
13.6 0.63 80.29
50.5 2.7 134.2
Plastic
4 clayey sand
15.54 25.2 1.1 12.9 0.68 74.24
50.2 1.1 56.2
Friction component (kN) 345.3
Np
k1
qb
Ab
Qb
Point bearing component
Source: Truong (2017)
kPa
m2
kN
13.2
400 5260
0.12 644.4
644.4
Total bearing capacity (kN) 989.7
If the uncorrected N values are used, bearing capacity equals approximately to 85.86 tons
with:
• Friction component: 282.6 kN (-18.1% as compared to that of using corrected N);
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
59
• Point bearing component: 572.8 kN (-11.1% as compared to that of using corrected N).
4.3. Bearing capacity suggested by Architectural Institute of Japan (item G.3.2 of the
TCVN 10304: 2014) (Ministry of Sciences and Technology, Vietnamese Government, 2014)
Appendix G of National Standard (TCVN 10304: 2014, Ministry of Sciences and
Technology, Vietnamese Government, 2014) described steps to apply the main contents of
Recommendations for Design of Building Foundation (Architectural Institute of Japan issued in
1988, hereinafter denoted AIJ for short) in predicting the bearing capacity of pile, both driven and
bored piles. SPT data were used to indirectly compute friction fs,i and point bearing resistance qb
by formulas (15) and (17) where Ns.i is average number of SPT in the ith soil layer; Np is average
value of SPT blow counts taken within a zone 1D below the pile tip level and 4D above level of
the pile tip. An Excel spreadsheet for computing bearing capacity was displayed as in Table 9
below:
Table 9
Illustrated spreadsheet for computing abutment B pile bearing capacity using recommendation of
AIJ and corrected N’, borehole BH-1
WITH CORRECTED N VALUES
8.4
0.35
fi
m
m
8.4 BH-1
(D=0.35m)
Qsi
No
Soil layers
thickness
γ
Ϭ’vo
SPT
7.8
aP
fL
Cu,i
Axq
m
2
kN/m3 kN/m2
KPa kN/m2 m2
kN
1
2
3
Firmly plastic clay
Firmly plastic clay
Firmly plastic clay
19.8
19.8
19.8
59.4
0.5
1
1
1
48.44
87.29
83.99
24.2
43.6
2.8
2.8
67.8
2
14.0 0.5
13.4 0.5
122.2
100
1.7
19.8 96.03
20.2 132.1
10.5 155.4
42.0 2.38
04.5 2.66
65.6 1.12
Granular soil,
dense
4
5
1.9
0.8
13.6 0.7
13.0 0.8
1
1
85.26
81.21
12.1
Plastic clayey sand
73.5
Friction component (kN)
375.6
Np
k1
qb
Ab
Qb
Point bearing
component
kPa
5260
m2
kN
13.2
400
0.12 88.2
88.2
Total bearing capacity (kN)
463.8
Source: Truong (2017)
For uncorrected N blow counts, total bearing capacity equals approximately to 378 kN
with:
• Friction component: 305 kN (-18.8% as compared to that of using corrected N).
• Point bearing component: 73 kN (-17.2% as compared to that of using corrected N).
4.4. Bearing capacity determined by numerical method
For comparison purposes, a Plaxis 3D model was used in Figure 6. Mohr-Coulomb (MC)
soil behavior model was chosen because of its relevancy to the bearing capacity problem, partly
because of limited data from soil reports (without results from triaxial compression tests). Data of
60
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
soil properties input into software were converted from corrected SPT N-values, as
abovementioned regression equations of Table 7. Calibration for the model was disregarded in
case accepting a linear proportion factor between measured bearing capacity and computed one.
Figure 6. Plaxis model for determining bearing capacity of pile
At-site determination of the ultimate bearing capacity of a pile has complied with item
7.3.2 of TCVN 10304: 2014 (Ministry of Sciences and Technology, Vietnamese Government,
2014) “Pile Foundation - Code for design building foundation and construction works” that
admitted a settlement at failure as below:
S = .Sgh
(20)
where, Sgh is settlement at ultimate condition, taken as 40mm (item 7.3.2); ξ = 0.2. As such,
ultimate bearing capacity will be the load at which the pile settlement equals to 8 mm:
Figure 7. Ultimate bearing capacity of 35cm square pile from static load test and Plaxis model
(Truong, 2017)
Ultimate bearing capacity by static load test is 676.8 kN, while this value is determined by
yield point (big displacement at a constantly kept load) at P=473.7 kN (solid circle line in Figure
7).
Three piles with different configuration were considered: For borehole BH1 with 5 layers:
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
61
abutment B pile (square 35cm, L=8.4 m) and pile P58 (square 25cm pile, L=8.6 m). For borehole
BH2, with 7 layers: pile P61 (square 30cm, L=12.2 m). Calculating spreadsheets are established
as in Table 8, Table 9. Results are compared as shown in Figure 8:
Figure 8. Comparisons between ultimate bearing capacity of pile using Meyerhoff’s formula,
AIJ, Plaxis and Static Load Test (Truong, 2017)
4.5. Discussion
• Correlation equations in Table 5 should be studied within the scale of fluctuation for
higher R2 (adj.) instead of the entire soil profile. But since the thickness of soil layers was smaller
than the scale of fluctuation θ, and R2 (adj.) was very high, therefore, the calculation for bearing
capacity would be implemented with sufficient and reasonable accuracy in practice. By applying
the scale of fluctuation, the spatial variability is taken into account, so the bearing capacity for the
pile is calculated with a more rigorous procedure.
• Regression equations for converting N-values into soil strength might have some errors.
The most likely value may be computed by the square root of the sum of squares (or SRSS) law
as follows:
2
Cdesign = (Clabtest )2 + (Cconvert)2 + (Cmod el
)
(21)
in which, the first term belongs to soil properties obtained by conventional lab tests; the second
term refers to measurement or correlation with corrected N-values, and the third term relates to
formula of shaft friction and tip resistance (Cherubini & Vessia, 2010).
• Back analysis to calibrate the numerical model is necessarily conducted for obtaining
the proper set of soil strength properties unless a linear correlation in the elastic domain is found.
• Load - displacement curve obtained by Plaxis indicated that soil foundation for the pile
was still workable in the elastic domain. Meanwhile, results from the static load test showed a
sharper trend in curvature, indicating a yielding point in the bearing capacity of the soil foundation.
• Bearing capacity computed by AIJ using directly corrected N-values proved to be close
to that of the static load test (Figure 8). Furthermore, comparison on results of bearing capacity
obtained by two approaches, (one from numerical finite element model _ Plaxis 3D, using
converting data of soil properties from N-values_, and the other from static load test) pointed out
62
Duong H. Tham, Truong N. Manh. Ho Chi Minh City Open University Journal of Science, 11(1), 45-64
that there was a linear correlation between them as in Figure 9 as following:
Figure 9. Results of bearing capacity obtained by Plaxis, A.I.J v/s by Static Load Test
This may come to a suggestion that corrected N-values can be used tentatively in predicting
the bearing capacity of pile installing into cohesive soil at a specific site, and AIJ formula using
directly corrected N-values will be more predictable than other analytical approaches.
Single variable linear regression analysis at a level of confidence of 95% provides a set of
converted parameters of soil strength_friction angle and cohesion_ which is possible to predict
bearing capacity in a numerical model.
4. Conclusion
The bearing capacity of a pile installing into cohesion soil can be assessed by comparing
the results obtained by theoretical formulas using converting corrected N-values, numerical model,
and static load tests. Multivariable linear regression analysis showed a weak correlation between
N-values and physical properties of the cohesive soil and depth of testing, but single variable linear
regression model showed a significant correlation of corrected N values to cohesive soil strength
(i.e., friction angle and cohesion) with a level of confidence 95%. The spatial variability is taken
into account with the scale of fluctuation, θ, postulated by Vanmarcke (1977). The soil profile
characterized by the numbers of SPT blows is divided into segments of which its length is smaller
than θ. Two locally used approaches including the Meyerhoff’s formula, and recommendation
suggested by the Architectural Institute of Japan, Appendix G, item G.3.2 (TCVN 10304: 2014,
Ministry of Sciences and Technology, Vietnamese Government, 2014) were used in which the soil
strength were indirectly converted from corrected N-values and assigned as input data into models;
the results were compared to those of numerical model Plaxis 3D and static load test. Results
indicated that the approach of AIJ using directly SPT data predicted a closer value of bearing
capacity as compared to that of the static load test. Besides, the numerical model Plaxis 3D using
indirect SPT data (i.e., model converted SPT data to soil strength and compressibility) pointed out
a value of bearing capacity which was a highly linear correlation to the reliable result of the static
load test. These results could help practitioners in estimating bearing capacity with SPT data with
a satisfactory accuracy.
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