Load-Settlement Characteristics of Tropical Red Soils of Southern Nigeria

This study investigated the relationship between the load-settlement curves obtained from field (in situ) plate load test under static loading conditions to those obtained from finite element (FE) analysis, for tropical red soils. Three test locations were selected within the University of Benin campus in Benin City, Nigeria. Laboratory tests were conducted on samples obtained from these three locations to obtain the index and strength properties of the soil, and these were used as input parameters for the FE analysis. The FE analysis was performed with PLAXIS 2D, using Mohr-Coulomb soil model as the constitutive model. Comparison of load-settlement curves obtained from the field plate load test with those obtained from the FE analysis showed that the FE tool was able to predict the ultimate vertical displacement for all three test locations, with good accuracy. The maximum vertical settlement obtained for Site A from the field plate load test was 8.79 mm, while that obtained from FE analysis was 9.02 mm. For Sites B and C, it was 12.77 mm vs 12.30 mm and 22.85 mm vs 22.30 mm respectively. Parametric studies were also conducted in order to evaluate the effect of variations in soil conditions on the static response of the soils. Results from the water table parametric analysis showed significant increase in vertical displacement as the soil immediately below the footing gets saturated. The results also showed that c and ϕ have significant influence on the load-settlement curves under static loading.


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Abstract-This study investigated the relationship between the load-settlement curves obtained from field (in situ) plate load test under static loading conditions to those obtained from finite element (FE) analysis, for tropical red soils.Three test locations were selected within the University of Benin campus in Benin City, Nigeria.Laboratory tests were conducted on samples obtained from these three locations to obtain the index and strength properties of the soil, and these were used as input parameters for the FE analysis.The FE analysis was performed with PLAXIS 2D, using Mohr-Coulomb soil model as the constitutive model.Comparison of load-settlement curves obtained from the field plate load test with those obtained from the FE analysis showed that the FE tool was able to predict the ultimate vertical displacement for all three test locations, with good accuracy.The maximum vertical settlement obtained for Site A from the field plate load test was 8.79 mm, while that obtained from FE analysis was 9.02 mm.For Sites B and C, it was 12.77 mm vs 12.30 mm and 22.85 mm vs 22.30 mm respectively.Parametric studies were also conducted in order to evaluate the effect of variations in soil conditions on the static response of the soils.Results from the water table parametric analysis showed significant increase in vertical displacement as the soil immediately below the footing gets saturated.The results also showed that c and ϕ have significant influence on the load-settlement curves under static loading.
Index Terms-Tropical Red Soils, Static Plate Load Test, Finite Element Analysis, Load-Settlement Curves.

I. INTRODUCTION
Tropical soils are different from soils found in the temperate regions and represent soils formed under hot, wet soil-forming conditions [1].This gives it unique geotechnical characteristics that can be attributed to the conditions under which it is formed.They often contain high contents of iron and aluminium oxides, resulting from the rapid disintegration of feldspars and ferromagnesian minerals.It is the high iron content that makes it appear as red in colouration.Tropical soils are of two distinct types in terms of geotechnical properties and engineering behaviour.They are: tropical red soils and tropical black soils [1,2].In Nigeria, tropical red soils are common and are often referred to as laterites.According to Toll [3], the term 'laterite' refer to a soil with a high degree of iron cementing, while tropical red soil refer to a soil that has red coloration but without significant cementing.
Despite some desirable engineering properties, tropical soils can be problematic because they are prone to repeated shrinking and swelling [1].The highly structured nature of tropical soils, combined with the fact that they often exist in an unsaturated state, makes them difficult to deal with as engineering materials [1,2].Geotechnical investigations are needed to characterize these soils to enable understanding of their behaviour.However, due to their heterogeneity, geotechnical testing for tropical soils can be difficult to carry out.Test methods that retain the original structure of these types of soils are therefore necessary to characterize the soils; but this is currently a major challenge, hence, the need for in situ testing methods.
The field plate load test is a standard in situ testing technique for both soils and rocks.It has long been used as a model/prototype footing from which representative soil parameters can be derived and used for the prediction of full scale foundation performance [4 -6].The results of static plate load test are applied in earthworks and foundation engineering to determine the load-settlement characteristics and by this evaluate the deformability and the load capacity of the soil.Foundations are often constructed in various subsoil conditions and subjected to static loads due to the various structures supported by the foundation [7].
Very few studies have been carried out on the characterization of tropical soils in Nigeria, especially southern Nigeria, using the field plate load test.This may be due to the fact that the plate load test equipment is expensive and large parametric studies can hardly be realized in the field without excessive cost.For example, Ehiorobo et al. [8] developed a plate load test equipment, which they used to evaluate the dynamic response of soils in Benin City, southern Nigeria, under repeated loading conditions.Static and cyclic plate load tests were conducted for three different locations.The size of plate used was 600 mm × 600 mm, with a thickness of 25 mm.Load-settlement curves were plotted from the results of the static plate load test, which depicted the extent of vertical downward settlement pervading the area at specific loadings.Though the soils in the three different locations were all tropical red soils, the results they obtained showed wide variability in the static properties of the soil.At test point 1, a load of 60 kN gave a settlement of 25 mm, and the bearing pressure at failure load was 167 kN/m 2 ; whereas at test point 2, a load of 29 kN gave a settlement of 10 mm, and the bearing pressure at failure load was obtained as 80 kN/m².This shows the heterogeneous nature of this type of soil.
In another study, Nwankwoala et al. [9]  In the above studies, numerical modelling was not incorporated.Numerical studies do not only allow large parametric studies to be carried out easily, but also help in reducing the cost, effort and errors involved in carrying out plate load test.This study investigated the load-settlement characteristics of tropical red soils in Southern Nigeria using a combination of experimental method (plate load test) and numerical finite element analysis.Also, as major parts of southern Nigeria are often water logged, the effect of water table on the load-settlement characteristics of the soils were also investigated by means of parametric analysis.Due to the variability in properties of these types of soils, the parametric analysis was extended to study the influence of variation in shear strength properties on the load-settlement characteristics of the soils.

A. Study Area
The study area was the University of Benin, Ugbowo campus, located in Benin City, one of the major cities in southern Nigeria.Benin City is a humid tropical urban settlement which comprises of three Local Government Areas namely: Egor, Ikpoba Okha and Oredo.It is located within Latitudes 06°20'N and 06º58'N and Longitudes 05º35'E and 05º41'E [10].It broadly occupies an area of approximately 112.55 km 2 .This extensive coverage suggests spatial variability of weather, climatic and soil elements.Three sites (Site A, Site B and Site C as shown in Fig. 1) located within the University of Benin campus were considered for the study.Soil samples were obtained from these three test locations, and were taken to the Geotechnical laboratory of the University of Benin for the determination of the geotechnical properties of the soils.

B. Experimental Programme 1) Field plate load test:
A locally fabricated plate load test setup (Fig. 2) was used for the study.The plate load test was carried out in accordance with the specifications given in BS 1377-Part 9:1990 [11].A test pit of depth 0.6 m was dug at the test location with the width of the pit at least five times the width of the plate.An area sufficiently large to receive the loading plate was levelled using suitable tools (e.g.steel straightedge or trowel).All loose materials were removed.The loading plate of size 600 mm x 600 mm with 25 mm thickness was then made to lie on, and be in full contact with the test surface at the depth of testing (0.6 m below ground level).Dry medium-grained sand was used to obtain a level surface.For the static loading, a reaction load was placed over a 20 tons capacity hydraulic jack which laid on the test equipment.After the setup had been arranged the initial readings of the dial gauges were noted and the first increment of static load of 20 kN was applied to the plate.This load increment was maintained constant throughout the test duration and the maximum load applied to the plate was 500 kN.
2) Laboratory Testing: Disturbed soil samples were collected from the various test sites at depth intervals of 2 m, and up to 6 m, using hand auger.Laboratory tests were then conducted on the samples recovered from the test sites.The tests conducted were sieve analysis, consistency limits tests, compaction, triaxial and one-dimensional consolidation tests.These were used for the classification of the soils and also as input data for the finite element modelling.Table I presents a summary of the results obtained from the laboratory tests conducted.In accordance with USSC classification, Site A and Site B were classified as Silty Sandy Soil (SM), while Site C was classified as Clayey Sandy Soil (SC).The plasticity of the soils for Sites A and B ranged from low to intermediate plasticity, while that of Site C was intermediate plasticity.

C. Finite Element (FE) Modelling
In this study, the finite element modelling was done using Plaxis 2D with Mohr-Coulomb model selected as the constitutive soil model.The Mohr-Coulomb soil model is a simple and well known linear elastic -perfectly plastic soil model, and thus has a fixed yield surface.The linear elastic part of the model is based on Hooke's law of isotropic elasticity, while the perfectly plastic part is based on the Mohr-Coulomb's failure criterion formulated in a nonassociated plasticity framework [5].The advantage of this model is that it estimates a constant average stiffness for each layer.Due to this constant stiffness, computations are quite fast and give a good first impression of the problem.The Mohr-Coulomb failure criterion is a model describing the response of materials subjected to external stresses [12].According to Craig [13], the Mohr-Coulomb failure criterion can be expressed as: This equation determines the critical combination of effective principal stresses that gives rise to a failure condition.
The parameters required for the Mohr-Coulomb soil model were determined, using the results obtained from the laboratory tests.A Poisson's ratio (v) of 0.3 was adopted in this study based on values given in the literature for similar soil types.The elastic modulus used for the model predictions was calculated using the expression below: where: Eoed is obtained from oedometer test in the laboratory, v Poisson's ratio The saturated and unsaturated unit weights were evaluated using Equations 3 and 4 respectively.
where: γw unit weight of water in kN/m², e void ratio w water content The material properties of the soil for the test sites are given in Table II.These were assigned to each layer in the Plaxis 2D program to create the soil profile.
After the soil profile had been created, material properties of the steel plate were inputted into the Plaxis program.The material properties were:  Thickness of the plate (t), 25mm  Weight of the plate (w), measured as 64 kg (0.628 kN/m²)  Normal stiffness (EA), obtained as 7.56+E07 kN/m, with E (elastic modulus of steel) taken as 210+E06 kN/m²  Flexural rigidity (D), obtained from Equation 5below, as 3.0+E02 kN/m²/m.
where: E Elastic modulus for steel taken as 210+E06 kN/m² t Thickness of the plate in mm v Poisson's ratio Thereafter, a distributed load of 500 kN/m² was applied to the steel plate.
For the mesh used in the finite element analysis, an axisymmetry mesh described by Mohr-Coulomb failure model was chosen.A 15-node triangular element (12-gauss points) with a fourth order interpolation for displacement and numerical integration was used to define the finite element mesh as shown in Fig. 3a, 3b and 3c for the three test sites.

A. Results of field plate load test
The results obtained from the static field plate load test conducted on the three test sites are shown in Fig. 4, in the form of a load-settlement curve.
The load-settlement curves shown in Fig. 4, depicts the extent of vertical downward displacement pervading the area at specific loadings.The initial straight line as seen in the graphical plot (at pressures between 0 and 50 kN/m 2 ) indicates the elastic region.Comparing the nature of these curves to those given in literature [14,15] shows that the soil in Site A and Site B corresponds to cohesive soils while that of Site C corresponds to medium cohesionless soils.Settlements were recorded at regular intervals of the applied pressure, up to a maximum of 500 kN/m².The maximum settlement recorded for Site A, B and C was 8.79, 12.77 and 22.85 mm respectively.

B. Comparison of field results to output from FE analysis
Fig. 5a, 5b and 5c shows the results of the static field plate load test compared with those obtained from the FE analysis.Looking at all three plots, it can be seen that the FE tool (PLAXIS 2D) gave fairly accurate predictions of the load-settlement behaviour of the soils in the various test locations.For Site A (Fig. 5a), there were noticeable variations in the load-settlement curves of the field data and the FE analysis, especially at the middle region of the curve.This may have resulted from the sensitivity of some of the soil parameters to environmental sampling, and also to the nature of the soil.Despite this, the maximum settlement predicted by the FE analysis tool, which was 9.02 mm, was very close to that obtained from the field.In contrast to Site A, Site B only had slight variations in the load-settlement curves obtained from the FE analysis and that of the field data.The maximum settlement predicted by FE was 12.30 mm, whereas that obtained from the field was 12.77 mm.Site C showed the best correlation between the loadsettlement curves obtained from FE and those obtained from the field.The maximum settlement from FE was 22.30 mm, as compared to 22.85 mm that was obtained from the field.This might have been as a result of the type of soil at this test location and the conditions of testing both for field and modelling.

C. Parametric Analysis
Further studies were done by carrying out parametric analysis in order to evaluate the effect of variation of soil conditions on the static response of the soil.Three parameters were varied, which were the depth of water table, cohesion and angle of internal friction.

1) Effect of Change in Depth of Water Table:
The depth of water table was varied at the various depths as shown in Tables III to V, for Site A, B and C respectively.This was done in order to determine how the results will differ due to the presence of water.
The normalized depth of water table or depth of water table from the footing level was obtained using: where: The percentage of additional displacement due to water table was obtained using: where: y Vertical displacement,  0 Final vertical displacement assuming no water table From the results in Tables III to V, it can be seen that the percentage of additional displacement due to water table is highest when the water table is close to the footing.Similar trends were observed by Shahriar [16].At depth of 1 m, the percentage of additional displacement was 76.27% for Site A; while for Site B and C, it was 38.21% and 50.22% respectively.This shows that the position of water table with respect to a footing has significant impact on the deformation properties of the soil.For water table at greater depths below the footing, the effect is negligible; whereas for depths close to the footing, the effect is more pronounced.Results obtained from the parametric analysis after varying the c and ɸ values, are presented in Figures 6 to 8, for Site A, B and C respectively.It was observed that these two strength parameters have significant influence on loadsettlement characteristics under static loading and soil behaviour.A higher vertical displacement was observed for Site C for all cohesion and angle of internal friction values, than those of Sites A and B, suggesting that load-settlement characteristics of clayey tropical red soils are more sensitive to changes in shear strength parameters.This indicate that randomness, due to inherent soil variability, in shear strength properties of tropical red soils (especially those with more clayey fractions) will have significant impact on foundation designs and should be taken into consideration.This study examined the static soil properties of tropical red soils in Southern Nigeria using the static plate load test, and compared the results to that obtained by FE analysis using Plaxis 2D.
The FE tool was able to predict almost accurately the ultimate displacement for all the three test locations used for the study.For site A, where a total vertical displacement of 8.79 mm was obtained from the field, the FE model predicted a total settlement of 9.02 mm.For site B, it was 12.30 mm vs 12.77 mm; while for Site C, it was 22.30 mm vs 22.85 mm.The load-settlement curves plotted using data from the field and FE tool compared reasonably well, especially for Site C. The results show that for tropical red soils, given the basic properties of the soilindex and strength properties, FE analysis can be used to predict the load-deformation characteristics of the soils.This is significant, especially in locations where it might be very difficult to carry out the static plate load test.For such areas, this study has shown that for tropical red soils, FE analysis can be used to obtain the load-deformation characteristics of the soil.
Parametric studies carried out to determine the effect of varying the depth of water table on the load-settlement behaviour of the soils in the three test locations, revealed that lower water tables were detrimental to the settlement characteristics of the soils.Also, varying the shear parameters (c and ϕ) were seen to have significant effect on the load-settlement curves under static loading.

Fig. 1 .
Fig. 1.GIS imagery of the study area within University of Benin

Fig. 2 .
Fig. 2. Schematic of the plate load test setup

Fig. 3a .
Fig. 3a.Finite Element Mesh for Site A

Fig. 4 .Fig. 5 .
Fig. 4. Field load-settlement curves for the three test sites (Site A, Site B and Site C)

TABLE III :
PARAMETRIC ANALYSIS ON EFFECT OF CHANGE IN DEPTH OF WATER TABLE FOR SITE A

TABLE IV :
PARAMETRIC ANALYSIS ON EFFECT OF CHANGE IN DEPTH OF WATER TABLE FOR SITE B Depth of water table from surface, dw' (m) The typical values of cohesion and frictional angle for the soil types investigated were varied.The selected values are presented in Table VI.The selected values were obtained from properties of similar class of soils as obtained from literature (see Table VII).

TABLE VI :
VALUES OF COHESION AND FRICTIONAL ANGLE FOR