Comparision of Axial Compressive Load Capacity of Piles by Different Methods

Comparision of Axial Compressive Load Capacity of Piles by Different Methods

Thanh Quang Truong(1), Nhu Thi Quynh Nguyen(2), Tuan Van Nguyen(3)

1Associate Professor, 2 Lecturer, 3 Post-Graduate Student Department of Civil Engineering – University of Architecture Ho Chi Minh City

196 Pasteur Street, District 3, Ho Chi Minh City, Viet Nam

Abstract Determining the correct bearing capacity of piles has important technical and economic significance for the construction using the pile foundation. However, this is a complicated problem because the bearing capacity of piles depends on many different factors such as soil conditions, geometrical dimensions of piles, method of pile construction, etc. Pile load static compression test in the field is usually performed to verify and estimate the bearing capacity. Due to time and some other practical conditions, some constructions cannot load on piles until failure. In this article, test data is analyzed to predict the ultimate load of Pre-stressed Concrete spun pile PHC. This analysis is based on the results of the four static compression test, which was carried out at Riverside Apartment construction site in Ho Chi Minh City. Four piles have a diameter of 600mm and a length of about 38m÷41m. The geological survey at the site was conducted to a maximum depth of 80m. The ultimate bearing capacity of piles is determined by different methods including Vietnamese standard TCVN 10304:2014 (2014), formula of Japanese Institute of Architects (1988), graph method of Chin-Kondner (1970), Decourt (1999), Mazurkiewicz (2003). Based on the value of ultimate load capacity of four piles were calculated by five different methods, it is shown that each method can estimate different ultimate load capacity of piles. Within the scope of this study, the number of four test piles, and five methods of calculating pile load capacity selected, it shows that when using the formula Institute of Architecture of Japan – AIJ (1988) calculates the ultimate bearing capacity of piles giving more reliable results than the other four methods. Compared with the obtained value when the static compression failing test TP1, the TCVN and the Mazurkiewicz method give the results that are not much different from each other.

Keywords Pile capacity; Pile load; Pile load test; ultimate bearing capacity

1. INTRODUCTION

   Pile foundation is commonly used in high-rise building because of its load capacity. Pile foundation is used when the ground has the soft soil layer on the surface, which is not able to bear the construction load. In this case, piles transfer load to the deeper hard soil layer.

   Prediction and determination pile bearing capacity have a great influence on the economic technical factors of the construction. Using highly reliable method in calculating the bearing capacity makes the selection of pile bearing capacity, pile cross section, pile length quickly, accurately and cost- effectively.

   The correlation between the pile head displacement caused by the axial compressive load which is shown in the graph of piles static compression test is one of the bases of determining the ultimate compressive load capacity for the design pile

   foundation. Due to some limited conditions, in practice, it is usually to choose the maximum compressive load acting on the pile head pile, about 1,5 to 2 times the design load in the test at the site. Therefore, in some cases, the pile static compressive test has not given the ultimate bearing capacity of piles. Mazurkiewicz, Chin, Kondner and Decourt have proposed graphical methods based on the correlation between compressive load and pile displacement to predict the ultimate bearing capacity of piles.

   The research content of this paper is the synthesis of static of static compression test data of 4 piles of high-rise apartment built in Ho Chi Minh City, accompanied by data of the pressure force when constructing piles into the ground such as analyzing the load-displacement curve of piles, calculating the ultimate compressive capacity of piles by a number of different methods and building the correlations between the ultimate compressive capacity of piles and piling stopping force, maximum pile test load and pile design bearing capacity. From the analysis and comparison, the conclusions of the research can be drawn.

2. LITERATURE REVIEW

   There have been many studies on predicting the bearing capacity of piles from theoretical and experimental results. These are the works of Mirza (1997) [1], Dewaikar and Pallavi [2], Nabil [3], Brinch Hansen [4], Mazurkiewicz [5],

   Abdelrahman [6], Chin-Kondner [7], Hansen [8], Davisson

   [9], Fuller-Hoy [10], De Beer [11].

   Mirza (1997) [1] introduced a simple method for calculating the frictional resistance of driven piles into clay. This method is based on the correlation between the characteristic indicators and strength of soils derived from marine clay. The results show that except for the short piles in the hard to very hard clay, the predictions are agreement with the measure results at the site. This correlation is presented that the skin friction component can be calculated and the importance of liquidity index in calculating static capacity is shown.

   Dewaikar and Pallavi (2000) [2] analyzed the load test data at the site to predict the ultimate bearing capacity of piles. This analysis was based on 40 results of pile load test obtained from various civil and infrastructure projects constructed in the Mumbai region of India. This study showed that the collected data were analyzed by different methods such as semi-empirical and graphical methods.

   Nabil [3] studied the group effect of bored piles based on the field test performed at a site in South Surra, Kuwait. The study also includes load testing on single piles in compression

   and tension states. There are two groups of piles made, each group consists of five piles. The spacing of piles in the selected pile group is two and three times the pile diameter. The group coefficient value found is 1.22 and 1.93 in case the distance between the two piles is 2d and 3d respectively, where d is the bored pile diameter.

   In a number of documents and different standards, the results of pile compression test have been explained and been proposed to determine the ultimate load capacity from this test.

   J. Brinch Hansen [4] proposed an estimate for caculating the Ultimate bearing capacity, Qu. Method of Brinch Hansen 80% have a the following simple relation:

   – settlement curve is 1.27 mm/ton. Practically, the ultimate load is determined by finding the point at which the curve at

   1.27 mm/ton slope plotted on the graph is tangent to the curve [10].

   Determine the ultimate load of piles according to the method of De Beer [11], the correlation values between load and settlement of piles are plotted logarithmic chart. When the values fall on two approximately straight lines, the intersection of these defines a limit load that is considered a pile yielding load.

3. SOIL INVESTIGATION AND TEST PILE PARAMETERS

   Qu

   2

   1

   C1C2

   (1)

   1. Soil profile

      The soil investigation consists of 6 bore holes drilled to 80 m depth. The layout of the geological boreholes at the

      where, C1: slope of the straight line, C2: y-intercept of the

      straight line.

      Mazurkiewicz proposed a method of extrapolating load and settlement curves [5] [6]. Accordingly, the proposed method is: The plot of the loading test curve toward the settlement was based on the result of load test in the observed location. Drawing lines from soe selected settlement points until they cross the curve. Vertical line is being drawn until it reaches loading pivot. From the cross of the load, a line with an angle of 450 is being made until it crosses the next line. These points are connected until straight line is formed. The cross of the straight line with loading pivot is its ultimate load. This method gives the assumption that loading curve movement forms the shape of parabola. Therefore, the value of the collapsing loads, obtained by using Mazurkiwicz method, should approach 80% of the standardized criteria.

      Another method that can determined the ultimate bearing capacity of piles proposed by Chin, based on the research results of Kondner [7], allows the extrapolation of the failure load in the static load tests. The method consists of dividing each respective load applied by the settlements and put it in the y-axis. In turn, the x-axis, places the settlements obtained during the static load test. The load limit is given by the inverse of the slope formed by the points plotted on the graph.

      Another chart method is proposed by Decourt, which method is similar to those used in the method of Chin- Kondner [7] and Hansen [8]. To apply this method, divide each load with its corresponding settlement and plot the resulting value against the applied load. The Decourt extrapolation load limit is the value of load at the intercept and the slope of the line as given in the equation below.

      construction site is as shown in Figure 1. The soil profile at the site is reported to consist of clay and sand, and is presented in Figure 2. The water table varies from 3.3 m to 5.0 m below the ground surface.

      Fig. 1. General layout of the site with the locations of boreholes.

      TABLE I. PARAMETERS OF SOIL LAYERS.

      Symbol of Soil layers	Soil description	c (kPa)	(Degree)	SPT N
      A	Fill soil, broken rock and brick	–	–	–
      1	Muddy Clay with organic very soft	6.3	3.97	0÷3
      2A	Hard plastic sandy Clay	26.7	13.50	10÷17
      2B	Stiff plastic clay	31.4	13.23	10÷13
      3	Stiff plastic clayey Sand	9.2	23.26	12÷29
      4A	Hard Clay	61.3	16.45	26÷42
      4B	Stiff plastic sandy Clay	28.7	14.18	16÷29
      5	Plastic clayey Sand	9.1	23.50	32÷50

      u

      u

      Q C2

      C1

      (2)

      A variety of laboratory and field tests were performed at the site for the determination of soil conditions and pile design parameters. The subsurface soil parameters are shown in

      A common and relatively widespread method is the

      Davisson (1972) [9]. It has been suggested by Davisson as the load which is accordance by a movement which exceeds elastic pressure (which is assumed by a column which stands by itself) at the value of 0.15 inches and a factor which is relevant to the measurement of Pile Measurement divided by 120.

      According to the Fuller-Hoy method, the ultimate bearing capacity of piles corresponds to where the slope of the load

      Table I and Table II.

      TABLE II. PHYSICAL PROPERTIES OF SOIL LAYERS.

      Symbol of Soil layers	Water content (%)	Plasticity index IP (%)	Liquidity index IL	Unit weight (kN/m3)	Void ratio eo
      A	–	–	–	–	–
      1	73.16	28.3	1.2	15.2	1.975
      2A	21.2	14.5	0.33	19.8	0.659
      2B	24.92	18.5	0.20	19.6	0.732
      3	18.89	6.4	0.35	20.1	0.582
      4A	20.05	22.5	< 0	20.7	0.581
      4B	21.55	14.9	0.24	20	0.638
      5	19.24	6.3	0.36	20.1	0.591

      Fig. 2. Geological section at the site.

      BH1 BH2

      Fig. 3. Variation of SPT – N with depth for borehole BH1 and BH2.

      BH3 BH4

      Fig. 4. Variation of SPT – N with depth for borehole BH3 and BH4.

      The SPT profile along with soil parameters with depth for each borehole are shown in Figure 1, 2, 3, 4.

      BH5 BH6

      Fig. 5. Variation of SPT – N with depth for borehole BH5 and BH6.

   2. Test Pile Parameters

      Piles selected in this study is Pre-stressed Concrete spun pile PHC with d = 600 mm with the design load capacity Qd = 250 ton (the working load).

      Fig. 6. Pre-stressed Concrete spun pile PHC at the site.

      At the site, four test piles labeled as TP1, TP2, TP3 and TP4 respectively are compressed into the ground to the design depth and ensure not to exceed the maximum pile pressure value Fpmax. Method of compressing the pile by using the load from the counterweight to create the force to push the pile to the ground. Correlation between Pile pressing force (Fp) and Depth of embedment z for each pile are shown in Figure 7.

      Fig. 7. Relationship between pile pressure value and pile tip depth.

      With each pile we have found that pile pressing force tends to increases proportionally to the pile tip depth and reaches the maximum value of Fp max = 503.2 tons when the pile is stopped.

4. DETERMINE PILE CAPACITY

   The objective of research was to calculate the amount of bearing capacity of single pile, based on several conventional methods. It is obtained based on soil investigation in the field; they were value of SPT, liquidity index (boring log) data for one location from some points of observation and the analysis of the bearing capacity of the single pile and its settlement, based on loading test data.

   In the research scope of this paper, it is calculating the ultimate bearing capacity of the piles by using the formula based on Vietnamese standards (Pile Foundation Design Standard: TCVN 10304: 2014) [12] and from the pile test results.

   1. Prediction of Pile Load Capacity Using Vietnamese Code

      First, based on the geological cross-section in Figure 2 and the location of the pile, establish the actual geological column that the experimental pile is placed in. The stratigraphic column and the thickness of each soil layer that the four piles in the survey placed in are shown on the Figures 8 and the Figures 9 .

      Fig. 8. Soil profile of test piles (TP1 and TP2).

      Fig. 9. Soil profile of test piles (TP3 and TP4).

      The pile diameter is taken as 600 mm and the lengths of experimental piles TP1, TP2, TP3 and TP4 are 37.9 m, 38.6 m, 41.8 m and 41.8 m, respectively.

      Then, the formulas for determining the ultimate bearing capacity of piles in Vietnamese standards are applied to calculate the pile bearing capacity. The ultimate bearing capacity of piles according to this standard uses the symbol Rc,u.

      Case 1: The pile capacities are calculated using the provisions of the TCVN 10304: 2014 code (2014) [12].

      Rc,u = c (cq qbAb + ucf fili) (3)

      The parameters in this formula strictly comply with the provisions of the standard, its value depends on the geometrical characteristics of the pile, the physical and mechanical parameters of the soil obtained from laboratory experiments such as liquidity index, physical state, soil type and tip depth.

      Case 2: Based on the formula Standard Institute of Architecture of Japan – AIJ (1988) – Also shown in the Appendix of Vietnamese standard TCVN 10304:2014, section G3.2:

      compressive loading and unloading are shown in Figures 11, 12, 13 and 14 respectively. The value of pile head displacement corresponding to each level of compressive load with the maximum at each stage of the piles is summarized in Table IV.

      Stage	Recorded maximum head settlement (mm)
      	TP1	TP2	TP3	TP4
      1	9.35	7.56	8.00	5.99
      2	24.15	23.33	20.03	19.53
      3	51.01	29.16	24.10	24.22

      Stage	Recorded maximum head settlement (mm)
      	TP1	TP2	TP3	TP4
      1	9.35	7.56	8.00	5.99
      2	24.15	23.33	20.03	19.53
      3	51.01	29.16	24.10	24.22

      TABLE IV. RECORDED HEAD SETTLEMENT.

      Rc,u = qb Ab + u(fc,ilc,i + fs,ils,i) (4)

      Different from case 1, the parameters in formula (3) are determined mainly based on soil properties obtained from field soil testing such as SPT (N) value.

      Calculating the ultimate compressive strength of piles for the four survey piles, applying the formulas for the two formulas mentioned above. Summary of the Ultimate load capacity values are presented in Table III.

      TABLE III. THEORETICAL PILE CAPACITIES.

      Test Pile	Pile dimensions		Ultimate Pile Capacity Rc,u (Tons)
      	Length (m)	Diameter (mm)	Case 1: TCVN 10304:2014	Case 2: AIJ (1988)
      TP1	37.9	600	495	590
      TP2	38.6	600	503	594
      TP3	41.8	600	529	622
      TP4	41.8	600	567	687

      The values of the bearing capacity of the piles calculated according to the formula will be compared with the pile load capacity obtained from the static compression test of the piles themselves.

   2. Estimating the ultimate compressive strength of the pile from the field pile static compression test

      The four test piles TP1, TP2, TP3 and TP4 have a diameter of 600 mm and a length of 38.8 m, 39.5 m, 41.0 m and 41.0 m respectively and have a working load of 250 tons.

      Fig. 10. Pile head displacement meter.

      The pile static compression test at the site in 3 stages. Stage 1 with a pile head compression load value of 100% of the working load (the value is 250 tons). Stage 2 with pile head compression load value 200% working load (value is 500 tons) and stage 3 with maximum compressive load (Qmax) 220% working load (value is 550 tons) .

      The load-displacement relationship of the static compression test piles TP1, TP2, TP3 and TP4 at the stages of

      Fig. 11. Load settlement relationship for pile TP1.

      Fig. 12. Load settlement relationship for pile TP2.

      Fig. 13. Load settlement relationship for pile TP3.

      Fig. 14. Load settlement relationship for pile TP4.

      In this section, we use the method of estimating the ultimate bearing capacity of the pile by the graphical method based on the Load – displacement curve in the first stage in the pile static compression test at the site. The graphical methods of Mazurkiewicz [5], [6], Chin-Kondner [7] and Decourt [8] have chosen to apply in this study.

      Details of the relationship of Load (Q) and pile head settlement () of the pile static compression test curves in phase 1 of the test piles are redrawn with a larger scale shown in Figures 15, Figure 16, Figure 17 and Figure 18.

      Fig. 15. Load settlement relationship for pile TP1 (Stage 1).

      Fig. 16. Load settlement relationship for pile TP2 (Stage 1).

      Fig. 18. Load settlement relationship for pile TP4 (Stage 1).

   3. Graphical method used to determine Ultimate Capacity of Piles

      1. For TP1 pile

         1. Method of Mazurkiewicz

            Fig. 19. The graph of determining Qu of the pile TP1 using Mazurkiewicz method.

            Estimated ultimate compressive capacity of piles by this method is Qu = 440 ton.

         2. Method of Chin-Kondner

            Fig. 20. The graph of determining Qu of the pile TP1 using Chin-Kondner method.

            1

            Fig. 17. Load settlement relationship for pile TP3 (Stage 1).

            Qu =

            = 323 ton

            C1

            Estimated ultimate compressive capacity of piles by this method is Qu = 323 ton.

            Fig. 21. The graph of determining Qu of the pile TP1 using Decourt method. Fig. 24. The graph of determining Qu of the pile TP2 using Decourt method.

            Qu =

            C2 = 308 ton

            C1

            C

            Qu = 2 = 357 ton

            C1

            Estimated ultimate compressive capacity of piles by this method is Qu = 308 ton.

      2. For TP2 pile

         1. Method of Mazurkiewicz

            Fig. 22. The graph of determining Qu of the pile TP2 using Mazurkiewicz method.

            Estimated ultimate compressive capacity of piles by this method is Qu = 510 ton.

         2. Method of Chin-Kondner

            Fig. 23. The graph of determining Qu of the pile TP2 using Chin-Kondner

      3. For TP3 pile

         1. Method of Mazurkiewicz

            Fig. 25. The graph of determining Qu of the pile TP3 using Mazurkiewicz method.

            Estimated ultimate compressive capacity of piles by this method is Qu = 350 ton.

         2. Method of Chin-Kondner

            Fig. 26. The graph of determining Qu of the pile TP3 using Chin-Kondner method.

            1

            method.

            1

            Qu =

            = 500 ton

            C1

            Qu = = 371 ton

            C1

            Estimated ultimate compressive capacity of piles by this method is Qu = 371 ton.

            Estimated ultimate compressive capacity of piles by this method is Qu = 500 ton.

            Fig. 30. The graph of determining Qu of the pile TP4 using Decourt method.

            Fig. 27. The graph of determining Qu of the pile TP3 using Decourt method.

            C

            Qu = 2 = 506 ton

            C

            Qu = 2 = 356 ton

            C1

            C1

            Estimated ultimate compressive capacity of piles by this method is Qu = 506 ton.

      4. For TP4 pile

         1. Method of Mazurkiewicz

            Fig. 28. The graph of determining Qu of the pile TP4 using Mazurkiewicz method.

            Estimated ultimate compressive capacity of piles by this method is Qu = 460 ton.

         2. Method of Chin-Kondner

            Fig. 29. The graph of determining Qu of the pile TP4 using Chin-Kondner method.

            1

            Estimated ultimate compressive capacity of piles by this method is Qu = 356 ton.

   4. Results and Discussions

   Fig. 31. Qu of TP1 pile is calculated by 5 different methods.

   Fig. 32. Qu of TP2 pile is calculated by 5 different methods.

   Qu =

   = 371 ton

   C1

   Estimaed ultimate compressive capacity of piles by this method is Qu = 371 ton.

   Fig. 33. Qu of TP3 pile is calculated by 5 different methods.

   Fig. 34. Qu of TP4 pile is calculated by 5 different methods.

   The Ultimate load capacity of four piles are shown on the Figures from Figure 5 to Figure 7 when calculated by 5 different methods.

   Let the symbol Qmax be the maximum load of the static compression test at the site and Qu is the estimate of the ultimate load capacity of the pile by different methods. Calculate the ratio between Qu and Qmax and those value are compared between test piles as well as between different calculation methods. The results are presented in Figure 35 and Figure 36.

   Fig. 35. Valuae of Qu/Qmax for TP1 pile and TP2 pile.

   Fig. 36. Valuae of Qu/Qmax for TP3 pile and TP4 pile.

   Set the symbol Qd to be the working load of the pile. Calculate the ratio between Qu and Qd and those value are compared between test piles as well as between different calculation methods. The results are presented in Figure 37 and Figure 38.

   Some of the comments made are as follows:

   With one pile, different calculation methods result in the ultimate bearing capacity of piles having different values. The method of calculation by the formula has greater results than the method based on the graph of the load relationship and the pile settlement in the pile static compression test. The pile load capacity calculated according to the AIJ formula gives the maximum value.

   With 4 static compression test piles in the field, TP1 pile has reached the failure value, which means that the value of the ultimate load capacity of this pile has been determined as Qu = 500 tons. Therefore, it can be seen that the calculation method according to TCVN and AIJ formulas as well as Mazurkiewicz's graphical method gives relatively consistent results compared to the other two methods.

   For piles TP2, TP3 and TP4, the pile compression test at the site reached the value of Qmax = 550 tons, however, these piles have not reached the pile failure limit. Therefore, it can be commented that the calculation of the bearing capacity according to the formula of the Japanese Institute of Architects – AIJ (1988) is relatively more reliable than the other four methods.

   It is difficult to comment on which calculation method gives more reliable results. With this pile condition, it is found that this method gives more reliable results, but this method gives unreliable results compared to other pile conditions. The results of calculating the ultimate bearing capacity of each pile are different, depending on each geological form as well as on the value of compressive load and pile displacement when testing piles statically and using different calculation methods. If we compare the working load of the pile with the ultimate load capacity calculated by five different methods,

   we find that the factor of safety FS for the piles:

   Pile TP1: FS = (1.23÷2.36); Pile TP2: FS = (1.43÷2.38); Pile TP3: FS = (1.40÷2.49); Pile TP4: FS = (1.42÷2.75);

   Fig. 37. Valuae of Qu/Qd for TP3 pile and TP4 pile.

   Fig. 38. Valuae of Qu/Qd for TP3 pile and TP4 pile.

5. CONCLUSIONS

The ultimate capacity Qu for each test pile was predicted using five methods stated above including two methods using theory formula and three graphical methods based on static load test that are used in the evaluation of the pile load test. It is difficult to comment on which calculation method gives more reliable results. With this pile condition, it is found that this method gives more reliable results, but this method gives unreliable results compared to other pile conditions. The results of calculating the ultimate bearing capacity of each pile are different, depending on each geological form as well as on the value of compressive load and pile displacement when testing piles statically and using different calculation methods. Each method can estimate different ultimate load capacity of piles. Within the scope of this study, the number of 4 test piles, and 5 methods of calculating pile load capacity selected, it shows that when using the formula Institute of Architecture of Japan – AIJ (1988) calculates the ultimate bearing capacity of piles giving more reliable results than the other four methods. Compared with the obtained value when the static compression failing test TP1, the TCVN and the Mazurkiewicz method give the results that are not much different from each other.

ACKNOWLEDGMENT

The authors would like to acknowledge the Coteccons construction joint stock company and ICP International Construction Project & Consultancy JSC for their valuable assistance.

REFERENCES

1. U. A. A. Mirza, Pile Skin Friction in Clays, International Journal of Offshore and Polar Engineering, Vol. 7, No. 1, 1997, pp. 538-540.

2. D. M. Dewaikar and M. J. Pallavi, Analysis of Pile Load Tests Data, Journal of Southeast Asian Geotechnical Society, Vol. 6, No. 4, 2000, pp. 27-39.

3. Nabil F. I., Axial Load Tests on Bored Piles and Pile Groups in Cemented Sands, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127, No. 9, 2001, pp. 766- 733.

4. Brinch Hansen, J., 1963, Discussion, Hyperbolic Stress-Strain Response of Cohesive Soils, Journal of Soil Mechanics, Foundation Division ASCE, V. 89 No.SM4, pp. 241-242.

5. Mazurkiewicz, B.K., 1972, Test Loading of Piles According to Pollish Regulations, Royal Sweedish Academy of Engineering Sciences, Commission on Pile Research, Report No.35, pp20, Stocholm.

6. Abdelrahman G. E., Shaarawi E. M., and Abouzaid K. S. (2003). Interpretation of Axial Pile Load Test Results for Continuous Flight Auger Piles, Proceedings of the 9th Arab Structural Engineering Conference, 2003, Abu Dhabi, UAE, pp. 791-801.

7. Chin, F.K., 1970, Estimation of Pile Not Carried to Failure, Proceedings 2nd Souteast Asian Conference on Soil Engineering, Singapore, pp. 81-90.

8. Decourt, L., 1999, Behaviour of Foundations Under Working Load Conditions, Proc. of the 11th Pan-American Conf. on Soil Mechanics and Geotechnical Engineering, Dolguassu, Brasil, V. 4, pp. 453-488.

9. M.T.Davisson, High Capacity Piles, In Innovations in Foundation Construction, Soil Mechanics Division, Illinois, ASCE, Chicago, USA, pp.81-112, 1972.

10. Fuller, F.M. and Hoy, H.E., 1970, Pile Load Tests Including Quick Load Test Method Conventional Methods and Interpretations, Highway Research Record No.333, pp. 78-89, Transportation Research Board, USA.

11. De Beer, E.E. and Wallays, M., 1989, Franki Piles with Overexpanded Bases, La Technique des Travaux, No:333, pp. 48.

12. The Vietnam Construction Standard, Pile Foundation Design Standard: TCVN 10304:2014.