Predicting the bearing capacity of pile installed into cohesive soil concerning the spatial variability of SPT data (A case study)

No. Soil layers γ Ϭ’ ϕ c a Cu,i k fi Axq Qsi 
 ness vo SPT p 2
 m kN/m3 kN/m2 (o) kPa kPa kN/m2 m2 (kN) 
 Firmly 
 1 plastic clay 2 19.8 19.8 16.8 2.4 7.75 1 8.39 2 8.4 2.8 23.5 
 Firmly 
 2 plastic clay 2 19.8 59.4 16.8 2.4 13.9 1 20.31 2 20.3 2.8 56.9 
 Firmly 
 3 plastic clay 1.7 19.8 96.0 16.8 2.4 13.4 1 31.33 2 31.3 2.4 74.6 
 Granular 
 4 soil, dense 1.9 2.02 13.21 31.3 0 13.6 0.63 80.29 2 50.5 2.7 134.2 
 Plastic 
 4 clayey sand 0.8 1.05 15.54 25.2 1.1 12.9 0.68 74.24 2 50.2 1.1 56.2 
 Friction component (kN) 345.3 
 Np k1 qb Ab Qb 
 Point bearing component kPa m2 kN 
 13.2 400 5260 0.12 644.4 644.4 
 Total bearing capacity (kN) 989.7 
Source: Truong (2017) 
 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 
 th
by formulas (15) and (17) where Ns.i is average number of SPT in the i 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 m 
 8.4 BH-1 0.35 m (D=0.35m) 
 No Soil layers thickness γ Ϭ’vo SPT aP fL Cu,i fi Axq Qsi 
 m kN/m3 kN/m2 KPa kN/m2 m2 kN 
 1 Firmly plastic clay 2 19.8 19.8 7.8 0.5 1 48.44 24.2 2.8 67.8 
 2 Firmly plastic clay 2 19.8 59.4 14.0 0.5 1 87.29 43.6 2.8 122.2 
 3 Firmly plastic clay 1.7 19.8 96.03 13.4 0.5 1 83.99 42.0 2.38 100 
 Granular soil, 
 4 1.9 20.2 132.1 13.6 0.7 1 85.26 04.5 2.66 12.1 
 dense 
 5 Plastic clayey sand 0.8 10.5 155.4 13.0 0.8 1 81.21 65.6 1.12 73.5 
 Friction component (kN) 375.6 
 Np k1 qb Ab Qb 
 Point bearing 
 kPa m2 kN 
 component 
 13.2 400 5260 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 = .S gh (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: 
 C = (C )2 + (C )2 + (C )2
 design labtest convert mod 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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