Engineering, Environment

 

Evaluation of bearing capacity and settlement of foundations

 

Bunyamin Anigilaje SALAHUDEEN 1* and Ja'afar Abubakar SADEEQ 2

 

1 Samaru College of Agriculture, Ahmadu Bello University, Zaria, Nigeria

2 Department of Civil 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 settlement characteristics and bearing capacity in the North Central zone of Nigeria. Based on the corrected N-values, some geotechnical design parameters including the allowable bearing pressure and elastic settlement of foundations were predicted at varying applied foundation pressures of 50, 100, 200, 300 and 500 kN/m2 using conventional analytical models and numerical modelling. The numerical analysis results using Plaxis 2D, a finite element code, shows that Meyerhof’s and Peck’s et al. analytical/empirical methods of estimating the allowable bearing pressure of shallow foundations provide acceptable results. Results obtained show that an average bearing capacity value of 150 – 350 kN/m2 can be used for shallow foundations at embedment depth of 0.6 to 3.6 m in the North Central zone. Based on recommendation of Eurocode 7 which allows a maximum total settlement of 25 mm for serviceability limit state, it is recommended that raft or deep foundations to be considered for applied foundation pressures exceeding 300 kN/m2 in the North-Central zone to avoid excessive settlement.

Keywords

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

 

Introduction

One of the most significant components of any structure is its foundation. Foundations are integral to overall structural performance. They help in bearing and transmitting the structural loads to the soil, reducing settlements (total and differential), preventing possible movement of structures due to periodic shrinkage and swelling of subsoils, allow building over water or water-logged grounds, resist uplifting or overturning forces due to wind, and resist lateral forces due to soil movement and control water penetration and dampness. To perform satisfactorily, foundations must have two main characteristics: they have to be safe against overall shear failure in the soil that supports them and they must not undergo excessive settlement [1].

Probably the most difficult of the problems that a soil engineer is asked to solve is the accurate prediction of the settlement 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 this value will be achieved. The design of shallow foundations is generally controlled by settlement rather than bearing capacity [3]. As a consequence, settlement prediction is a major concern and is an essential criterion in the design process of foundations. Consistent and accurate prediction of settlement is yet to be achieved by the use of a variety of analytical methods [4].

Comparative studies of the available methods by engineers/researchers [5-8] indicate inconsistent prediction of the magnitude of the calculated settlements. This may be attributed to the fact that most of these methods are model driven, in which the form of the model has to be selected in advance and the unknown model parameters are determined by minimising an error function between model predictions and known historical values. Consequently, prior knowledge regarding the relationship between model inputs and corresponding outputs is needed. In case of settlement of shallow foundations on granular soils, such knowledge is not yet entirely understood [3].

The finite element method can be particularly useful for identifying the patterns of deformations and stress distribution during deformation and at the ultimate state. Because of these capabilities of the finite element method, it is possible to model the construction method and investigate the behaviour of shallow footings and the surrounding soil throughout the construction process, not just at the limit equilibrium conditions [9]. The finite element method (FEM) allows modelling complicated non linear soil behaviour through a constitutive model, various geometrics with different boundary conditions and interfaces. It can predict the stresses, deformations and pore pressures of a specified soil profile [10].

The high level of demands for housing in Nigeria due to the growing population and migration of people to urban areas require alternative construction methods that provide fast, safe and affordable quality housing for the citizens [11-13]. The aim of this study is to explore numerical modelling method that better represents soil constitutive behaviour to develop an improved approximation of foundation soil bearing capacity and settlement and compare the results with those of empirical methods. Also, there is a need to investigate and determine the most appropriate methods to Nigerian soil peculiarities and distinctions based on SPT results, being the most common and economical geotechnical field test used in Nigeria. The study focused on the prediction of foundation soil bearing capacity and settlement 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, Niger and Plateau States) of the Federal Republic of Nigeria.

The objectives of this research were to estimate the bearing capacity and settlement of foundation soils from measured penetration resistance in terms of the SPT corrected N-values at varying depths, to evaluate design equations for foundation soil bearing capacity and settlements using different constitutive models based on SPT results, to model foundation settlement numerically using PLAXIS 2D software and to compare the results of empirical/analytical methods with those of numerical analysis.

 

 

Research Methodology

 

The research made use of standard penetration test (SPT) data (using Donut hammer type) collected from 592 test holes (5328 data set) distributed over the study area. Computations were done based on the average that reliably represents each State and the average of the States was used for the North-Central zone. Bearing capacity and foundation 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 applied foundation pressures of 50, 100, 200, 300 and 500 kN/m2.

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

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

Figure 1. Chart depicting the steps involved in developing the numerical models

 

 

Results and Discussion

 

The results of this study were computed using the most common and conventional empirical methods in the literature based on the average values of input data obtained from the available field information at the time of the study. It is pertinent to state that result presented herein can approximately represent soil conditions in the North-Central zone of Nigeria considered. The elastic settlement and allowable bearing capacity results of the empirical/analytical methods were compared with those 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 SPT N-values because of the greater confinement caused by the increasing overburden pressure. 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 driving energy and its dissipation around the sampler into the surrounding soil. The variation of N60 with depth of test is shown in Figure 2.

Figure 2. Variation of corrected N-values with boring depth

 

N60 increased with depth having the highest value of 89.25 on the average in the North-Central zone. The increase in N60 value with depth is due to increased overburden. This confirms the conclusions of Salahudeen et al. [13] that the soils in the northern part of Nigeria are crystalline in nature (which has higher N60 values compared with sedimentary formations) from the basement complex. N60 values are needed for more accurate design analyses and have less variability or scatter due to the test method.

 

Bearing capacity

Based on field test results, the bearing capacities of shallow foundations are determined in terms of the allowable bearing pressures while those of deep foundations (piles) are given in terms of the ultimate bearing capacity. This is because settlement (service limit) controls the allowable bearing capacity in design of shallow foundations while the ultimate limit (shear failure) usually controls the allowable bearing capacity in deep foundations design [13]. For the allowable bearing pressures of shallow foundations, footing plan dimensions of 2 m by 2 m by 0.4 m for length, breadth and depth, were respectively assumed with a safety factor of 3. Variations of allowable bearing capacity of shallow foundations and bearing capacity of piles with boring depth are shown in Figures 3 and 4, respectively.

Figure 3. Variation of allowable bearing pressure with depth

 

Figure 4. Variation of bearing capacity of pile with depth

 

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

In evaluating the bearing capacity of piles, assumed dimensions of 0.3 m by 0.3 m cross-sectional area with embedment length of 10 m were used. Although the results according to Briaud et al. [21] are high compared to those proposed by Meyerhof [22], based on 60 pile case histories and SPT borehole results comprising 43 full scale 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 7 countries, Shariatmadari et al. [23] reported up to 10,505 kN/m2 pile bearing capacity at 25 m depth. Maximum pile bearing capacity values of 3748.50 and 10006.36 kN/m2 were obtained for the North-Central zone using Meyerhof [22] and Briaud et al. [21] methods respectively, at foundation embedment depth of 12.6 m.

 

Elastic settlement of foundations

For the elastic settlement of shallow foundations, plan dimensions of 2 m by 2 m by 0.4 m for length, breadth and depth were respectively assumed. Variations of elastic settlement of foundations with embedment depth for various applied pressures are shown in Figures 5 - 9.

 

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

 

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

 

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

 

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

 

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

 

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

The numerical analysis results of soil body deformation, stress distribution and settlement respectively at collapse of the soil body for the North-Central zone at 0.6 and 12.6 m depths of embedment are shown in Figures 10 - 15.

Figure 10. Numerical analysis mesh showing deformation of the soil body at collapse at 0.6 m embedment depth in the North-Central zone

 

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

 

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

 

Figure 13. Numerical analysis mesh showing deformation of the soil body at collapse at 12.6 m embedment depth in the North-Central zone

 

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

 

Figure 15. Numerical analysis result of settlement up to the collapse of the soil body at 12.6 m embedment depth in the North-Central zone

 

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

 

Total settlement of piles

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

Figure 16. Variation of total settlement of piles with depth

 

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

 

 

Conclusions

 

The study considered N-values corrected to the standard average energy of 60% (N60) as input data in analytical/empirical and numerical models used to predict foundation settlement and bearing capacity in the North-Central zone of Nigeria for 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 following conclusions can be taken:

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

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

¸        It was observed that settlement increased with increased value of applied foundation pressure. Settlements of footings embedded at depths in the range 0.6-3.6 m and pressures above 300 kN/m2 exceeded the limiting value of 25 mm value of allowable total settlement stipulated by Eurocode 7.

¸        A comparison of the fifteen empirical/analytical methods 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 of foundation settlement.

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

 

 

Recommendations

 

Based on the results of this study, the following are hereby recommended for the North-Central zone of Nigeria:

¸        Foundations should be placed at a minimum depth of 1.0 m.

¸        Deep foundations should be considered for applied foundation loads exceeding 300 kN/m2 to avoid excessive settlement.

¸        Results of the study can be used as first approximation of foundation bearing capacity and settlement but does not preclude the use of site specific data.

 

 

 

Acknowledgements

 

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

 

 

Appendix

 

Table A1. Empirical/analytical models for soil bearing capacity analysis

Property

Model

Reference

Corrected N-value

Seed et al. (1985) and

Skempton (1986)

Allowable bearing pressure

of shallow foundations

 

Teng (1969)

Meyerhof (1974)

Peck etal. (1974)

Bowles (1996)

Terzaghi et al. (1996)

Bearing capacity of piles

Meyerhof (1976)

Briaud et al. (1985)

Total settlement of piles

*Vesic (1977)

**Das (2011)

 

 

Table A2. Empirical/analytical models for elastic settlement analysis

S/N

Model

Reference

1

Janbu et al. (1956)

2

Terzaghi and Peck (1967)

3

Schmertmann (1970)

4

Schultze and Sherif (1973)

5

Meyerhof (1974)

6

Schmertmann et al. (1978)

7

Timoshenko and Goodier (1982)

8

Burland and Burbidge (1985)

9

Bowles (1987)

10

Anagnostropolous et al. (1991)

11

Can. Found. Eng. Man.

(CFEM) (1992)

12

Papadopoulos (1992)

13

Terzaghi et al. (1996)

14

Mayne and Poulos (1999)

15

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 = Net effective 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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