EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARD PENETRATION TEST RESULTS USING EMPIRICAL MODELS (2022)

Engineering,Environment

Evaluation ofbearing capacity and settlement of foundations

Bunyamin Anigilaje SALAHUDEEN 1* and Ja'afarAbubakar SADEEQ 2

1 Samaru College ofAgriculture, Ahmadu Bello University, Zaria, Nigeria

2 Department ofCivil Engineering, Ahmadu Bello University, Zaria, Nigeria

Emails: * basalahudeen@gmail.com;jaafaras@yahoo.com

*Corresponding Author phone:+2348058565650

Received: February 12, 2016/ Accepted: December 8, 2016 /Published: December 30, 2016

Abstract

The standard penetration test (SPT) results (SPT N-values)used in this study were corrected to the standard average energy of 60% (N60)before using them to correlate soil properties and evaluate foundation settlementcharacteristics and bearing capacity in the North Central zone of Nigeria. Basedon the corrected N-values, some geotechnical design parameters including the allowablebearing pressure and elastic settlement of foundations were predicted atvarying applied foundation pressures of 50, 100, 200, 300 and 500 kN/m2using conventional analytical models and numerical modelling. The numericalanalysis results using Plaxis 2D, a finite element code, shows that Meyerhof’sand Peck’s et al. analytical/empirical methods of estimating the allowablebearing pressure of shallow foundations provide acceptable results. Resultsobtained show that an average bearing capacity value of 150– 350 kN/m2 can be used for shallowfoundations at embedment depth of 0.6 to 3.6 m in the North Central zone. Basedon recommendation of Eurocode 7 which allows a maximum total settlement of 25mm for serviceability limit state, it is recommended that raft or deepfoundations to be considered for applied foundation pressures exceeding 300 kN/m2in the North-Central zone to avoid excessive settlement.

Keywords

Numerical modelling; Plaxis 2D; Finite element method; StandardPenetration Test; Bearing capacity; Elastic settlement

Introduction

One of the mostsignificant components of any structure is its foundation. Foundations areintegral to overall structural performance. They help in bearing andtransmitting the structural loads to the soil, reducing settlements (total anddifferential), preventing possible movement of structures due to periodicshrinkage and swelling of subsoils, allow building over water or water-loggedgrounds, resist uplifting or overturning forces due to wind, and resist lateralforces due to soil movement and control water penetration and dampness. Toperform satisfactorily, foundations must have two main characteristics: theyhave to be safe against overall shear failure in the soil that supports themand they must not undergo excessive settlement [1].

Probably the most difficult of the problemsthat a soil engineer is asked to solve is the accurate prediction of thesettlement of a loaded foundation [2]. The problem is in two distinct parts:the value of the total settlement that will occur and the rate at which thisvalue will be achieved. The design of shallow foundations is generallycontrolled by settlement rather than bearing capacity [3]. As a consequence,settlement prediction is a major concern and is an essential criterion in thedesign process of foundations. Consistent and accurate prediction of settlementis yet to be achieved by the use of a variety of analytical methods [4].

Comparative studies of the availablemethods by engineers/researchers [5-8] indicate inconsistent prediction of themagnitude of the calculated settlements. This may be attributed to the factthat most of these methods are model driven, in which the form of the model hasto be selected in advance and the unknown model parameters are determined byminimising an error function between model predictions and known historicalvalues. Consequently, prior knowledge regarding the relationship between modelinputs and corresponding outputs is needed. In case of settlement of shallowfoundations on granular soils, such knowledge is not yet entirely understood [3].

The finite elementmethod can be particularly useful for identifying the patterns of deformationsand stress distribution during deformation and at the ultimate state. Becauseof these capabilities of the finite element method, it is possible to model theconstruction method and investigate the behaviour of shallow footings and thesurrounding soil throughout the construction process, not just at the limitequilibrium conditions [9]. The finite element method (FEM) allows modellingcomplicated non linear soil behaviour through a constitutive model, variousgeometrics with different boundary conditions and interfaces. It can predictthe stresses, deformations and pore pressures of a specified soil profile [10].

The high level of demandsfor housing in Nigeria due tothe growing population and migration of people to urban areas requirealternative construction methods that provide fast, safe and affordable qualityhousing for the citizens [11-13]. The aim of this study is to explore numericalmodelling method that better represents soil constitutive behaviour to developan improved approximation of foundation soil bearing capacity and settlementand compare the results with those of empirical methods. Also, there is a needto investigate and determine the most appropriate methods to Nigerian soilpeculiarities and distinctions based on SPT results, being the most common andeconomical geotechnical field test used in Nigeria.The study focused on the prediction of foundation soil bearing capacity andsettlement based on Standard Penetration Test (SPT) N-values using empirical/analytical(deterministic) models and numerical modelling in the North-Central zone (i.e. Benue, Federal Capital Territory, Kogi, Kwara, Nassarawa, Nigerand Plateau States)of the Federal Republic of Nigeria.

The objectives of thisresearch were to estimate the bearing capacity and settlement of foundation soilsfrom measured penetration resistance in terms of the SPT corrected N-values atvarying depths, to evaluate design equations for foundation soil bearingcapacity and settlements using different constitutive models based on SPTresults, to model foundation settlement numerically using PLAXIS 2D software andto compare the results of empirical/analytical methods with those of numericalanalysis.

Research Methodology

The research made use ofstandard penetration test (SPT) data (using Donut hammer type) collected from 592test holes (5328 data set) distributed over the study area. Computations weredone based on the average that reliably represents each State and the averageof the States was used for the North-Central zone. Bearing capacity andfoundation settlement estimations were made at depths of 0.6, 2.1, 3.6, 5.1,6.6, 8.1, 9.6, 11.1 and 12.6 m and settlement was determined at varying appliedfoundation pressures of 50, 100, 200, 300 and 500 kN/m2.

Based on the analyticalmethods, bearing capacity and foundation settlement were evaluated using somecarefully selected models listed in Table A1 and A2, respectively (see Appendix).On the other hand, numerical analysis of foundation settlement and bearingcapacity were performed using a non-linear finite element analysis with a finiteelement code, Plaxis 2D, which is a software for deformation analysis andmodelling of geotechnical problems.

The input data in Plaxisare index, elastic and strength parameters obtained from the processed SPTN-values. The software portfolio includes simulation of soil and soil-structureinteraction. Plaxis 2D is an axisymmetric finite element package used fortwo-dimensional analysis of deformation and stability in geotechnicalengineering. It uses advanced soil constitutive models for the simulation ofthe non-linear, time dependent and anisotropic behaviour of soils and rocks.Plaxis 2D portfolio models the structure, the soil and the interaction betweenthe structure and the soil. Soil layers and foundation structure parameters areinputted into Plaxis and the construction stages, loads and boundary conditionsare defined in an already defined geometry cross-section containing the soilmodel then Plaxis automatically generates the unstructured 2D finite elementmeshes with options of global and local mesh refinements. Using its calculationfacilities, Plaxis 2D undergoes a calculation process and presents thecalculation and model outputs which can be accessed in animation and/ornumerical forms. The input data in numerical modelling are index, elastic andstrength parameters obtained from the processed SPT N-values [14]. The steps involved in developing the numerical model can bedepicted by the chart shown in Figure 1.

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (1)

Figure 1. Chartdepicting the steps involved in developing the numerical models

Results and Discussion

The results of thisstudy were computed using the most common and conventional empirical methods inthe literature based on the average values of input data obtained from theavailable field information at the time of the study. It is pertinent to statethat result presented herein can approximately represent soil conditions in theNorth-Central zone of Nigeria considered. The elastic settlement and allowablebearing capacity results of the empirical/analytical methods were compared withthose of numerical modelling output using Plaxis.

Corrected N-values (N60)

According to Bezgin [15]a correction to average energy ratio of 60% (N60) is required to SPTN-values because of the greater confinement caused by the increasing overburdenpressure. The correction factors used in the study are those proposed by Das [1]to standardize the field penetration number as a function of the input drivingenergy and its dissipation around the sampler into the surrounding soil. Thevariation of N60 with depth of test is shown in Figure 2.

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (2)

Figure 2. Variation of corrected N-values withboring depth

N60 increasedwith depth having the highest value of 89.25 on the average in the North-Centralzone. The increase in N60 value with depth is due to increasedoverburden. This confirms the conclusions of Salahudeen et al. [13] that thesoils in the northern part of Nigeriaare crystalline in nature (which has higher N60 values compared withsedimentary formations) from the basement complex. N60 values areneeded for more accurate design analyses and have less variability or scatterdue to the test method.

Bearing capacity

Based on field testresults, the bearing capacities of shallow foundations are determined in termsof the allowable bearing pressures while those of deep foundations (piles) aregiven in terms of the ultimate bearing capacity. This isbecause settlement (service limit) controls the allowable bearing capacity indesign of shallow foundations while the ultimate limit (shear failure) usuallycontrols the allowable bearing capacity in deep foundations design [13].For the allowable bearing pressures of shallow foundations, footing plandimensions of 2 m by 2 m by 0.4 m for length, breadth and depth, were respectivelyassumed with a safety factor of 3. Variations of allowable bearing capacity ofshallow foundations and bearing capacity of piles with boring depth are shownin Figures 3 and 4, respectively.

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (3)

Figure 3. Variation of allowable bearingpressure with depth

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (4)

Figure 4. Variation of bearing capacity of pilewith depth

Based on the methodproposed by Meyerhof [16] and Plaxis, foundation pressures in the range of 150– 350 kN/m2 were proposed for use in the North-Centralzone at shallow depths (depths in the range of 0.6 - 3.6 m).

In evaluating thebearing capacity of piles, assumed dimensions of 0.3 m by 0.3 m cross-sectionalarea with embedment length of 10 m were used. Although the results according toBriaud et al. [21] are high compared to those proposed by Meyerhof [22],based on 60 pile case histories and SPT borehole results comprising 43 fullscale pile load tests and 17 dynamic tests with Case Pile Wave Analysis Program(CAPWAP) collected from 18 sources reporting data from 26 sites and from 7countries, Shariatmadari et al. [23] reported up to 10,505 kN/m2pile bearing capacity at 25 m depth. Maximum pile bearing capacity values of3748.50 and 10006.36 kN/m2were obtained for the North-Central zone using Meyerhof [22] and Briaud etal. [21] methods respectively, at foundation embedment depth of 12.6 m.

Elastic settlement of foundations

For the elasticsettlement of shallow foundations, plan dimensions of 2 m by 2 m by 0.4 m forlength, breadth and depth were respectively assumed. Variations of elasticsettlement of foundations with embedment depth for various applied pressuresare shown in Figures 5 - 9.

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (5)

Figure 5. Variation of elastic settlement withdepth for 50 kN/m2 foundation pressure

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (6)

Figure 6. Variation of elastic settlement withdepth for 100 kN/m2 foundation pressure

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (7)

Figure 7. Variation of elastic settlement withdepth for 200 kN/m2 foundation pressure

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (8)

Figure 8. Variation of elastic settlement withdepth for 300 kN/m2 foundation pressure

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (9)

Figure 9. Variation of elastic settlement withdepth for 500 kN/m2 foundation pressure

The figures show thedifferent empirical/analytical models commonly used in computing elasticsettlement of shallow foundations. The N60 values indicate thatsettlement values will be low due to high N60 values in the regionas confirmed in the elastic settlement results. The recorded trend isconsistent with observations reported by Rasin [24] and Salahudeen et al.[13].

The numerical analysisresults of soil body deformation, stress distribution and settlementrespectively at collapse of the soil body for the North-Central zone at 0.6 and12.6 m depths of embedment are shown in Figures 10 - 15.

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (10)

Figure 10. Numerical analysis mesh showingdeformation of the soil body at collapse at 0.6 m embedment depth in the North-Centralzone

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (11)

Figure 11. Numerical analysis result of stressdistribution up to the collapse of the soil body at 0.6 m embedment depth inthe North-Central zone

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (12)

Figure 12. Numerical analysis result ofsettlement up to the collapse of the soil body at 0.6 m embedment depth in the North-Centralzone

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (13)

Figure 13. Numerical analysis mesh showingdeformation of the soil body at collapse at 12.6 m embedment depth in the North-Centralzone

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (14)

Figure 14. Numerical analysis result of stressdistribution up to the collapse of the soil body at 12.6 m embedment depth inthe North-Central zone

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (15)

Figure 15. Numerical analysis result of settlementup to the collapse of the soil body at 12.6 m embedment depth in the North-Centralzone

A comparison among theanalytical methods used in this study with the results of numerical modellingshow that the methods proposed by Schmertmann et al. [29], Burland andBurbidge [31], Canadian Foundation Engineering Manual (CFEM) [34] as well asthat of Mayne and Poulos [36] gave good estimations of foundation settlement.

Total settlement of piles

Variation of settlementof pile (bored) under a vertical working load with depth based on methodsproposed by Vesic [38] and that of Das [1] is shown in Figure 16.

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (16)

Figure 16. Variation of total settlement ofpiles with depth

The total settlement isthe sum of elastic settlement of pile, settlement of pile caused by the load atthe pile tip and settlement of pile caused by the load transmitted along thepile shaft. The wide margin between the methods used is an indication that thesettlements need to be modelled in order to come up with an appropriate methodthat will be more suitable for Nigerian soils. However, it is pertinent tostate that numerical modelling of piles was not included in the scope of thestudy carried out.

Conclusions

The study consideredN-values corrected to the standard average energy of 60% (N60) asinput data in analytical/empirical and numerical models used to predictfoundation settlement and bearing capacity in the North-Central zone of Nigeriafor footing of 2 m by 2 m by 0.4 m size and varying pressures of 50, 100, 200,300 and 500 kN/m2. Based on the results of this study, the followingconclusions can be taken:

¸Allowable bearing pressures of 150-350kN/m2 at depths between 0.6 and 3.6 m obtained using the Meyerhof methodare adequate for North-Central soils. The values are very close with those ofnumerical analysis using Plaxis 2D.

¸The maximum elastic settlement valuesrespectively for all the applied foundation pressures show that the soils inthe North-Central zone are on the average, less susceptibility to compression.

¸It was observed that settlement increased withincreased value of applied foundation pressure. Settlements of footingsembedded at depths in the range 0.6-3.6 m and pressures above 300 kN/m2exceeded the limiting value of 25 mm value of allowable total settlement stipulatedby Eurocode 7.

¸A comparison of the fifteen empirical/analyticalmethods considered in this study, showed that the Schmertmann et al.[29], Burland and Burbidge [31], Canadian Foundation Engineering Manual (CFEM) [34]as well as the Mayne and Poulos [36] methods gave good estimations offoundation settlement.

¸Plaxis 2D tend to overestimate the elasticsettlement of footings for embedment depths up to 2 m and at applied foundationpressure greater than 300 kN/m2.

Recommendations

Based on the results ofthis study, the following are hereby recommended for the North-Central zone ofNigeria:

¸Foundations should be placed at a minimum depthof 1.0 m.

¸Deep foundations should be considered forapplied foundation loads exceeding 300 kN/m2 to avoid excessivesettlement.

¸Results of the study can be used as firstapproximation of foundation bearing capacity and settlement but does notpreclude the use of site specific data.

Acknowledgements

The authors wish toacknowledge the assistance of the Management of In-depth Engineering Limited, Kaduna, Nigeria that provided all standardpenetration test data used for the study. For the assistance of Dr. M. Jaliliof Islamic Azad University, Semnan, Iran with respect to training on the use ofPlaxis software.

Appendix

Table A1. Empirical/analyticalmodels for soil bearing capacity analysis

Property

Model

Reference

Corrected N-value

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (17)

Seed et al. (1985) and

Skempton (1986)

Allowable bearing pressure

of shallow foundations

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (18)

Teng (1969)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (19)

Meyerhof (1974)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (20)

Peck etal. (1974)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (21)

Bowles (1996)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (22)

Terzaghi et al. (1996)

Bearing capacity of piles

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (23)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (24)

Meyerhof (1976)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (25)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (26)

Briaud et al. (1985)

Total settlement of piles

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (27)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (28)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (29)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (30)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (31)

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (32)

*Vesic (1977)

**Das (2011)

Table A2. Empirical/analyticalmodels for elastic settlement analysis

S/N

Model

Reference

1

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (33)

Janbu et al. (1956)

2

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (34)

Terzaghi and Peck (1967)

3

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (35)

Schmertmann (1970)

4

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (36)

Schultze and Sherif (1973)

5

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (37)

Meyerhof (1974)

6

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (38)

Schmertmann et al. (1978)

7

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (39)

Timoshenko and Goodier (1982)

8

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (40)

Burland and Burbidge (1985)

9

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (41)

Bowles (1987)

10

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (42)

Anagnostropolous et al. (1991)

11

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (43)

Can. Found. Eng. Man.

(CFEM) (1992)

12

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (44)

Papadopoulos (1992)

13

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (45)

Terzaghi et al. (1996)

14

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (46)

Mayne and Poulos (1999)

15

EVALUATION OF FOUNDATION SETTLEMENT CHARACTERISTICS FROM STANDARDPENETRATION TEST RESULTS USING EMPIRICAL MODELS (47)

Anderson et al. (2007)

Abbreviations

(N1)60= N60 correction for overburden pressure

B =Width of foundation (m)

BR= Reference width = 0.3 m

Df= Depth of embedment (m)

Es =Appropriate value of elastic modulus of soil (kN/m2)

Es= Elastic modulus of soil

H =Thickness of the compressible layer (m)

L =Length of foundation (m)

N =Measured penetration number (N-value)

N60= Corrected standard penetration number for field conditions

N60(a)= Adjusted N60 value

Pa= Atmospheric pressure = 100 kN/m2

q =Applied foundation pressure (kN/m2)

q = Neteffective pressure applied at the level of the foundation (kN/m2)

qn=Net pressure on the foundation (kN/m2)

Se= Elastic settlement (mm)

Se(1)= Elastic settlement of piles

Se(2)= Settlement of pile caused by the load at the pile tip

Se(3)= Settlement of pile caused by the load transmitted along the pile shaft

μS= Poisson’s ratio of soil

σ10= Effective overburden pressure in kN/m2

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