Geotechnical and Geological Engineering 22: 245–267, 2004. # 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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Evaluating accuracy for two empirical methods in predicting settlement of drilled shafts AZM S. AL-HOMOUD1, T. FOUAD2 and AHMED MOKHTAR1 1 American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates. e-mail:
[email protected] 2 Al-Azhar University, Egypt
(Received 15 July 2002; revised 31 March 2003; accepted 29 April 2003) Abstract. Several theoretical, empirical and semi-empirical methods are available in the literature to predict settlement of drilled shafts in sandy soils. In the Arabian Gulf countries, specifically in the United Arab Emirates, equations and procedure from the rest of the world are being used in analysis and design of drilled shafts without proper validation. It is the aim of this study to assess the applicability and evaluate the accuracy of two well known, and commonly used methods for pile prediction in the United Arab Emirates (UAE), namely Vesic (1977) and Poulos (1979), via comparison with data from field pile load tests conducted on shafts drilled in the region. Some of these tests were conducted for the purpose of this study, while others were made available through the courtesy of International Piling Contractors who are active in the region (e.g. Bauer International and Swiss Borings). Pile load test data were analyzed to back-calculate the model parameters related to settlement under different loading stages. Geological data and soil properties were obtained from studies conducted at the relevant sites. An effort is made to correlate soil properties with the prediction models. Statistical analysis is conducted to assess the accuracy of the results obtained from the two methods at different stages of loading via those obtained from pile load tests. Moreover, a detailed parametric study is conducted to assess the effect of the related parameters on the predicted pile settlement and the estimated settlement at different stages of loading. The study concluded with a recommendation of the most appropriate models and procedures to be followed for predicting the settlement of drilled shafts in the UAE, together with useful charts and correlation relations. Results showed that settlement values predicted by Vesic (1977) and Poulos (1979) overestimates the true values. Key words. Arabian gulf, design, drilled shafts, field load test, parametric study, prediction methods, sand, settlement.
1. Introduction Bored concrete piles are frequently used in the area of the Arabian Gulf as a result of the continuous development in the building construction. Theoretical, empirical and semi-empirical methods used by geotechnical engineers in determining the behavior of the piles are based on their experience without a comprehensive assessment of the applicability of these methods in the region. The paper presents the results carried out on forty three field pile load tests conducted on shafts drilled in the sandy soils of the Emirates. In order to generalize the outcome of this study, it was considered
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desirable to compile regional (i.e. Arabian Gulf Countries) pile load tests data reported in the literature. The results obtained from the study are then judged against some of those found in the international literature. Specifically, theoretical methods described by both Vesic (1977) and Poulos (1979) are presented and discussed. The equations used can be referred to in the following section.
2. Settlement Analysis 2.1.
VESIC (1977) APPROACH
The settlement of a pile under a vertical working load Qw is divided into 3 components as the summation of three components s1 ; s2 and s3 . Assuming the pile material to be elastic, the deformation of the pile shaft can be evaluated using the fundamental of mechanics of materials: ! " Qwp þ zQws D s1 ¼ Ap Ep According to Vesic (1977), the magnitude of z depends on the nature of unit skin resistance distribution along the pile shaft. If the distribution of f is uniform or parabolic in nature, z is equal to 0.5. However, for the triangular distribution this value is 0.67. The settlement of a pile caused by the load carried at the pile point is expressd as: s2 ¼ C p
Qwp Bqp
The settlement of the pile caused by the load carried by the pile shaft is as follows: s2 ¼ Cs
Qs Dqult
rffiffiffiffi! D Cs ¼ 0:93 þ 0:16 Cp B In calculating the settlement by the method developed by Vesic (1977), the ultimate skin load, Qsult , is assumed to be mobilized at a load value corresponding to a settlement equal to 0.003 B, where B is the diameter of the pile. Next to this value, the skin resistance is considered constant. The value of skin load, Qsi , at load increments prior to the mobilization of the ultimate skin value, Qsult , could be calculated as a ratio of the ultimate value following a linear relationship as follows, where s refers to the settlement: Qsult s0:003B ¼ Qsi si Vesic parameter z is assumed to equal 0.5. In other words, the distribution of the unit skin friction along the pile shaft is assumed to be uniform. The coefficient Cp is assumed to be equal to 0.09 as recommended for sandy soils. The parameter Cs is
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then calculated. The ratio of the calculated-to-measured settlement is then calculated at different stages of loading using spreadsheets. 2.2.
POULOS (1979) APPROACH
s¼
Qw I1 R k R n R b B:Es
K ¼ ðEp=EsÞRa In adopting Poulos method (1979), the Young’s modulus of the soil is calculated based on the empirical equation that correlates the soil Young’s modulus to the SPT number ½Es ¼ 500ðN þ 15Þ&. The value of SPT used is the uncorrected SPT number N60 as reported in the soil reports. The factor I1 is assumed to be equal to 1. Moreover, the parameters Rk ; Rn and Rb are obtained from Poulos charts found in the literature with the aid of the depth ratio of the piles. The Poisson ratio, u, of sandy soils is assumed to be equal to 0.3 as recommended by Bowles (1997).
3. Pile Data and Soil Conditions For this study the evaluation of the sand parameters was based on the Standard Penetration Test data in conjunction with soil descriptions. Also, information regarding the location of the ground water table was known. Each set of data such as angle of internal friction f, relative density Dr , lateral earth pressure coefficient K and other parameters used in predicting pile settlement were tabulated in spreadsheets at each 1-meter of pile penetration. They are represented as a function of depth, z. Formulae used in predicting pile settlement are then easily applied. Drilling for most of the piles under study was performed using the method of Continuous Flight Auger (CFA). Table 1 list pile geometry, load test and estimated soil parameters. The pile lengths D range from 8 m to 20 m and pile diameters B from 500 mm to 1000 mm. The ratio D=B ranges from 10.6 to 33. All piles under consideration were bored in sandy soils. In an effort to point out the characteristics of the soil, boreholes profiles are categorized into two typical groups to best describe the strata where the piles were bored (Figure 1). In the first group, the first 5 m of the soil consist of loose to very loose silty sands. This loose layer becomes denser with depth. The next 5 m consist of medium dense to dense silty fine sand. Following this level, the grains of the sand become coarser and remain coarse down to 20 m deep. Cemented pieces are occasionally down. This group best describes around 75% of the borehole logs collected. The second group consists mainly of 2 layers each of them with a depth of about 10 m. The top layer consisting of medium dense to dense silty fine sand turns into a dense to a very dense medium grained sand with cemented pieces observed occasionally. In both groups, the ground water elevation is located at a depth of 2.5 m below the ground surface. The average corrected SPT blows count, Ncor,
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AZM S. AL-HOMOUD ET AL. Table 1 Pile geometry, load test and estimated soil parameters Pile information
S.N. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Soil properties
Length of pile (m)
Diameter of pile (mm)
Area (m2)
Design load (kN)
Test load (kN)
f at tip
Dr at tip
8.0 8.0 9.0 9.0 9.0 9.0 9.0 10.0 10.0 12.0 12.0 12.0 12.0 12.0 13.0 13.0 13.0 13.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 15.0 15.0 15.0 15.0 15.5 15.5 17.0 17.0 17.0 17.0 18.0 18.0 19.0 19.5 19.5 20.0 20.0
750 600 800 800 800 800 800 600 750 750 750 500 600 500 700 800 700 500 700 600 1000 900 700 600 600 700 600 600 750 600 800 800 800 800 800 800 700 600 1000 750 600 750 600
0.44 0.28 0.50 0.50 0.50 0.50 0.50 0.28 0.44 0.44 0.44 0.20 0.28 0.20 0.38 0.50 0.38 0.20 0.38 0.28 0.79 0.64 0.38 0.28 0.28 0.38 0.28 0.28 0.44 0.28 0.50 0.50 0.50 0.50 0.50 0.50 0.38 0.28 0.79 0.44 0.28 0.44 0.28
1435 915 2400 1500 0 0 0 990 1590 2100 2100 1000 900 600 2010.28 2350 1990 1000 1400 1100 3700 3200 2070 1540 847 1154 1400 1400 2224.6 2224.6 2000 2000 0 0 0 0 1900 1400 4500 2100 1400 2200 1400
2159.2 1375 3750 2250 2250 2250 2250 1485 2385 3150 3150 1521.2 1324.2 902.8 2980.76 4700 2944.3 1570.3 2110 1668.4 5594.3 4809.1 3140.7 2355.6 1294.1 1805.7 2100 2100 3336.9 3336.9 3042.5 3042.5 2250 2250 3750 3750 2895.3 2110.1 6750 3194.9 2113.5 3336.9 2159.2
33 49 47 42 36 32 36 33 32 35 34 42 41 41 37 53 36 38 48 38 47 47 42 40 35 37 39 36 46 44 39 39 39 39 39 39 40 40 41 42 39 40 38
0.55 1.00 1.00 0.83 0.61 0.45 0.65 0.48 0.47 0.60 0.68 0.76 0.78 0.78 0.65 1.00 0.57 0.65 0.94 0.66 0.90 0.90 0.78 0.74 0.53 0.60 0.71 0.61 0.86 0.81 0.72 0.72 0.63 0.63 0.63 0.64 0.67 0.67 0.67 0.71 0.69 0.64 0.58
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Figure 1 Typical borehole logs as suggested
encountered in the zone near the pile tip was reported to be 43 blows. The typical corrected N-values of SPT were ranged from 81 to 20 with an average value equal to 61. The N values were corrected for the effects of overburden pressure using the recommendation of Peck et al (1974). The angle of internal friction in the same zone ranges from 33' to 50' with a range of 17' and an average of 41.5' and was predicted based on the recommendations of Liao and Whitman (1989).
4. Estimated Capacities All of piles were tested up to an average value of 1.5 times the design load. Only one pile was tested up to 2 times the design load. This pile was considered as a failed pile as reported by the consultant engineer since it exerts a large amount of settlement (about 17.0 mm). Under this circumstance several definitions of failure load can be adopted. For the analyses reported herein, failure was defined as recommended by Chin (1978), but tests were not accepted unless the pile diagnosis met the reported assumptions. Chin’s method is based mainly on the stress-strain relationships of the materials of the pile and the materials of the soil. The stress strain relationship under normal working stages is linear for pile materials and hyperbolic for soil materials. Under a compressive load P applied at the pile head, the elastic compression of the pile materials is relatively small as compared to the deformation of the supporting soil. For a pile in which the capacity is provided only by skin friction or by end bearing, a plot of D/ P against D will produce a fairly linear relationship. Similarly, for a pile in which the capacity is provided by both skin friction and end bearing, the same plot will produce two intersecting lines. The slopes of the lines represent the ultimate skin capacity and the ultimate total capacity, respectively, as shown in Figure 2. Generally, two points will determine the line needed and third point on the same line confirms the line. However, it is very easy to arrive at a false Chin’s value for the ultimate load if applied too early in the test. It is worth mentioning that many tests were ignored (not given in Table 1) due to this fact where the Chin’s method seemed to be ‘not applicable’ (Al-Homoud et al., 2003). In some other cases, it was very difficult to judge which points should be joined to form a line. These tests were omitted
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Figure 2 Analysis of load settlement curve from pile loading test for a friction and end bearing pile
from the study, too. To judge the reliability of the method in estimating the pile ultimate load, the factor of safety for all pile data was calculated. The factor of safety was obtained as the quotient of the ultimate load as estimated by Chin (1978) approach and the design load as obtained from the pile soil report. Most of the piles in the study show a safety factor between 2 and 3. The minimum value encountered for the factor of safety was 1.7 while the maximum value was 4.6 except for two piles where the factor of safety exceeds this maximum value (6.5 and 9.1). The mean factor of safety was encountered to be 3.2 with a standard deviation value of 1.3. If compared to the code recommendations, we can find out that the BS 8004 recommends a safety factor between 2 and 3 subject to various qualifications while the Eurocode recommends a safety factor of 2 (Tomlinson, 1995). Moreover, the Chin’s Extrapolation approach was used in predicting the ultimate capacity of the failed pile (Pile No. 16). Table 2 shows a comparison between the values of the pile capacities obtained from different approaches used to predict the ultimate, skin and tip capacities. The approaches in comparison are those of the Chin’s Extrapolation (Chin, 1978), the Davisson Offset Limit (Davisson, 1972) and the SHAFT software. The reasons behind selecting these approaches among the other found in the literature are as follows: (1) The Chin’s Extrapolation approach consists the base of the pile capacity analysis in this study. (2) The Davisson method has gained a widespread use among most of the researchers and the designers (Fellenius, 1999). It is considered as the most recognizable method in predicting pile ultimate load.
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PREDICTING SETTLEMENT OF DRILLED SHAFTS Table 2 Analysis of pile load test No. 16 using different approaches Data of pile no. 16 Location: Contractor:
Length of pile: Diameter of pile: Testing Load: Design Load: Ratio of Testing/Design Load: Analysis of pile load test:Chin’s Extrapolation Approach: Davisson Offset Limit Approach: SHAFT software
Sharjah-Al-Nahda region Bauer Spezialtiefbau Gmbh Company – Sharjah Branch 13.0 meters 800.0 mm 4700.0 kN 2350.0 kN 200% Ultimate capacity 6351.6 4350.0 2609.0
Skin capacity 2428.0 N.A. 2166.4
Bearing capacity 3923.6 N.A. 442.6
(3) The SHAFT software presents the computerized method in comparison of the graphical and the analytical methods used. From the results shown in Table 2, the Chin’s Extrapolation ultimate capacity is found to be about 30% greater than the Davisson limit. The ultimate total capacity as obtained from Chin’s method is about 6351.6 kN while the value obtained by Davisson approach does not exceed 4350 kN (less than the testing load). This conclusion is in agreement with the findings of the previous researchers (Fellenius, 1999) who set an approximate rule that the Chin’s Extrapolation load is about
Figure 3 Contribution of the tip and skin resistance in the ultimate capacity of the piles based on the estimated values using Chin approach (1978)
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20% to 40% greater than the Davisson limit. It is worth to mention at this point of comparison that the Offset Limit Load proposed by Davisson is not necessarily the ultimate load of the pile (Fellenius, 1999). Moreover we should notice that the Davisson Offset Limit represents only the total capacity of the pile and is unable to differentiate the contribution of the skin and the tip load in developing the resistances of the pile. Applying Chin’s approach (Al-Homoud et al., 2003), both ultimate and skin pile capacities were determined. The tip capacity was then obtained by subtracting the friction capacity from the total capacity of the pile. The skin resistance represents approximately an average of 25.5% of the ultimate capacity of the pile. The contribution of the tip resistance is about 74.5% of the total capacity (Figure 3).
5. Settlement Analysis 5.1.
MOBILIZATION OF SKIN RESISTANCE
The shear strength is assumed to be mobilized at a certain value of load corresponding to a value of settlement equal to 0.003 B, where B is the diameter of the pile. Prior to this load, the skin resistance is calculated as a ratio of the ultimate skin resistance value following a linear relationship between the settlement and the skin resistance developed. Based on the above assumption and analysis of pile load tests data, it is concluded that for most of the piles, the skin resistance is mobilized when the working load applied during the test reaches a value approximately equal to half
Figure 4 Ratio of working load to ultimate load (Qw/Qult) at which the skin resistance is mobilized
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the ultimate load (around 47% of the ultimate capacity of the pile; this value is considered as an arithmetic mean value.) (Al-Homoud, 2003). In other words and as can be concluded from the graph shown in Figure 4, it could be demonstrated that the mean ratio (Qworking/Qultimate) is 47% when the skin resistance of the pile is mobilized. This statistical conclusion is reached with a minimum value equal to 14% and a maximum value of 74% (for the same ratio) and a standard deviation equal to 0.16 (Al-Homoud, 2003). It is worth mentioning that for some piles, the skin resistance was not mobilized during the pile load test in spite of reaching higher percentages of the ultimate load. The settlement at each increment of load is calculated based on the linear relation ship of the mobilization of the skin friction. In these calculations, Vesic (1977) approach is adopted.
6. Estimated vs. Predicted Settlement 6.1.
VESIC (1977) APPROACH
Based on the assumptions stated above, concerning the settlement analysis, the following points were concluded with respect to the three components of settlement referred to as s1 ; s2 and s3 : The values of the settlement component s2 (settlement due to tip load) as recommended by Vesic (1977) are calculated based on a Cp factor ¼ 0.09. These values, describing the point displacement occurring at the tip of the pile due to the tip load, are very high in comparison of the total settlement of the pile recorded during the pile load test. This result is considered reasonable since the contribution of the tip resistance in the early stages of the working load is most probably limited. It is highly probable that in the usual range of working loads, the skin resistance is the principal loadcarrying mechanisms in all but the softest soils, (Bowles 1988). No contribution from the point load component is encountered in the settlement in these early stages of loading. Moreover, the ultimate point resistance requires a point displacement on the order of 30% of the base diameter for bored piles as reported by Bowles 1988. Based on the above, the comparison between the estimated and the predicted values of settlements as described by Vesic (1977), is limited to the summation of the other two components (s1 and s3 ) where the contribution of the deformation of the pile shaft material and the skin resistance along the pile shaft is dominant in this range of working load. It is noticed that the values of the summation of (s1 and s3 ) components is relatively close to those of the total settlement as estimated from the pile load test report. These values are compared at different stages of loading as shown later in Figure 5 through Figure 7. Estimated settlement is compared to predicted settlement in each of these figures. Two best fit curves, one linear and another nonlinear are shown in each figure. The correlation coefficient is given for each fitting curve.
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Figure 5 Estimated versus predicted settlement according to Vesic (1977) empirical method (Qw < 12% Qult)
Figure 6 Estimated versus predicted settlement according to Vesic (1977) empirical method (25% < Qw < 30%)
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Figure 7 Estimated versus predicted settlement according to Vesic (1977) empirical method (at Qw ¼ 50% Qult appr.)
6.1.1. Working load ðQwÞ < 12% ultimate load ðQult Þ In Figure 5 it can be concluded that the Vesic approach overestimates the settlements for most of the piles in the early stages of the working load that do not exceed 12% of the ultimate load. In other words, the method is considered to be conservative and at the same time it is considered to be accurate. However, in some cases the method can be ‘unsafe’. These cases represent a percentage of 10% of the total number of piles under study. A mean value of 1.98 is encountered for the ratio (Sp/Se) at this stage of loading with a maximum value of 8.7 and a minimum value of 0.6 for the same ratio. The standard deviation for the ratio is found to be 1.59. Reasonable values of the ratio (Sp/Se) are obtained for most of the piles. Accurate predictions are noticed at higher load stages as described below. 6.1.2. ð25% < Working load ðQwÞ < 30%Þ of the ultimate load ðQult Þ The plot in Figure 6 shows the comparison of the estimated and the predicted values of settlement at a higher range of working load (25% < Qw < 30%) of the ultimate load of the pile. Vesic approach seems to have a relatively good and accurate estimated of the pile load settlement at this critical stage. However the approach is considered unsafe in some cases and conservative in other cases. From a statistical point of view, a mean value of 1.60 is encountered for the ratio (Sp/Se) at this stage of loading with a maximum value of 4.52 and a minimum value of 0.65 for the same ratio. The standard deviation for the ratio is found to be 1.01 which is less than the value
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obtained in the earlier stage of loading. Reasonable values of the ratio (Sp/Se) are obtained for most of the piles. 6.1.3. Working load ðQwÞ > 30% ultimate load ðQult Þ The best estimation is obtained in the later stages where the working load exceeds 30% of the ultimate load but does not exceed half of the ultimate load (refer to Figure 7). It is worth to mention that most of the tests have been stopped at this stage. A mean value of 1.44 is encountered for the ratio (Sp/Se) at this stage of loading with a maximum value of 4.32 and a minimum value of 0.73 for the same ratio. The standard deviation for the ratio is found to be 0.93 (the least value obtained in comparison to the previous stages). However the approach is still considered unsafe in some cases and conservative in others. Therefore, in case of settlement based design for this category, it recommended to design the pile by selecting an appropriate factor of safety for settlement, but to be cross checked through pile load test. 6.2.
POULOS (1979) APPROACH
Based on the theoretical approach derived by Poulos (1979) that assumes no slip occurring between the pile and the soil, the settlements of all the piles under study are calculated and then compared to the values estimated during the pile load test at different stages of loading. From the plots shown in Figure 8 through Figure 10 the following points can be concluded.
Figure 8 Estimated versus predicted settlements according to Poulos approach (1979) at working load < 12% ultimate load
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6.2.1. Working load ðQwÞ < 12% ultimate load ðQult Þ The plot in Figure 8 shows the estimated versus the predicted settlements at a load stage less than 12% of the ultimate load. It can be concluded that the Poulos approach, like the empirical method adopted by Vesic (1977), overestimates the settlements for most of the piles in the early stages of the working load that do not exceed 12% of the ultimate load. A mean value of 2.50 is encountered for the ratio (sp/se) at this stage of loading. The standard deviation for the ratio is found to be 1.61. 6.2.2. ð25% < Working load ðQwÞ < 30%Þ of the ultimate load ðQult Þ Accurate predictions are noticed at higher load stages. The plot in Figure 9 shows the comparison of the estimated and the predicted values of settlement at a higher range of working load (25% < Qw < 30%) of the ultimate load of the pile. Poulos approach may be considered unsafe in some cases and conservative in other cases. From a statistical point of view, a mean value of 1.63 is encountered for the ratio (sp/se) at this stage of loading with a maximum value of 5.55 and a minimum value of 0.28 for the same ratio. The standard deviation for the ratio is found to be 1.27 which is less than the value obtained in the earlier stage of loading. Reasonable values of the ratio (sp/se) are obtained for most of the piles. 6.2.3. Working load ðQwÞ > 30% ultimate load ðQult Þ As predicted by Vesic (1977), the best estimation is obtained in the later stages where the working load exceeds 30% of the ultimate load but does not exceed
Figure 9 Estimated versus predicted settlement according to Poulos (1979) empirical method (25% < Qw < 30%)
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Figure 10 Estimated versus predicted settlement according to Poulos (1979) empirical method (at Qw ¼ 50% Qult appr.)
half of the ultimate load using Poulos (1979) method. As mentioned previously, most of the tests have been stopped at this stage. A mean value of 1.56 is encountered for the ratio (sp/se) at this stage of loading with a maximum value of 5.65 and a minimum value of 0.38 for the same ratio. The standard deviation for the ratio is found to be 1.07 (the least value obtained in comparison to the previous stages).
7. Discussion Two empirical methods are adopted to predict the settlement of the piles at different stages of loading. A focus on the statistical comparison of the results obtained from both methods is adopted. Hence from the plots shown in Figure 11 through 13 it can be concluded that in the early stage of loading where the working load does not exceed 12% of the ultimate load, the values obtained by the empirical approach of Poulos (1979) are relatively higher than those obtained by Vesic (1977) theoretical method given that both methods are considered conservative while estimating the settlement in this early stages of loading. In some cases both methods gave similar values for the predicted settlements. This is interpreted from the plot in Figure 11. In Figure 12, the values of settlement obtained by both methods at higher stage of loading (25% < Qw < 30% of ultimate load) are compared. Symmetry can be proved from the plot. Adopting the same procedure in comparison, the values of settlements obtained by both methods at a load stage about 50% of the ultimate load are compared in Figure 13.
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Figure 11 Comparison of the estimated settlements by Vesic (1977) and Poulos (1979) at working load
