Prediction of bearing capacity of driven piles for Basrah governatore using SPT and MATLAB

1 Introduction

One of the most prevalent and commonly utilized tests in geotechnical engineering is the standard penetration test. The results of this test are considered a good indicator for soil geotechnical parameters like density, shear strength, and compressibility. For earthquake planning, the SPT can be used to determine the liquefaction risk of saturated granular soils. As a result of its simplicity, low cost, and widespread availability of SPT equipment, SPT results have been accepted for the preliminary design of foundations [1, 2, 3]. Before using the measured N-values to estimate and calculate soil geotechnical parameters, they must undergo a series of adjustments. In order to get more reliable results, the corrected N-value should be taken into account. Several studies have recommended using these corrections to eliminate measurement N-value uncertainty based on their findings, but selecting the correct modifications is critical to avoid the need for additional field measurements or lab calculations [3, 4, 5].

Furthermore, the field conditions, the size and characteristics of test equipment, and the diameter and depth of boreholes all play a role in optimizing selected corrections. All of these corrections should be investigated by the geotechnical engineer. Several studies have found that corrected SPT values are related to the soil geotechnical parameters such as shear strength, density, body wave velocities, and liquefaction potential. However, such parameters are still deemed preliminary and cannot be used in the detailed design of foundations. The statistical tests can be used to demonstrate a correlation between the findings of SPTs and the results of other potential field tests such as cone penetration test and pressure meter test, which approves the findings of SPTs [6, 7, 8, 9, 10, 11, 12].

The main goal of study is to create thematic maps that show the differences in bearing capacity of driven piles concerning their geographic locations and length. MATLAB software was used to perform several regression analyses producing 1^st, 2^nd, 3^rd, and 4^th order polynomials based on the results of SPTs carried out in 135 boreholes drilled to a depth of 10 meters below current ground level and distributed over the entire area of Al-Basrah governorate. The findings of the study provide a simple and rapid test for calculating the bearing capacity of driven piles, which can be used directly in the preliminary design of foundation or even in the detailed design of foundations for small projects or temporary works [13, 14, 15, 16, 17].

2 Corrections of standard penetration test

The standard penetration test (SPT) is one of the common field tests suggested for various soil types, especially when sampling and laboratory testing are problematic. The SPT value (N-value) is the number of blows on a split spoon sampler that penetrates 300 mm in the soil. The measured N-value must be subject to several corrections to comply with the standard testing process before it can be used to interpret SPT results [18]. A variety of factors can influence the measured N-values from SPTs. These factors have the potential to increase or reduce N-values, which will have a substantial impact on the soil's predicted geotechnical properties. The geotechnical properties of soil estimated from the SPT values are mostly underestimation, which means a conservative property of soil will be obtained from SPT results. As a result, many modifications to the SPT values may be done to make them more accurate, resulting in more reliable and widely accepted geotechnical properties of soil estimated using SPT data [19].

The depth and diameter of boreholes, type of hammer, diameter of drilling rod, and field parameters such as confining pressure and groundwater table (GWT) can influence the corrections. According to Fletcher [20], the following factors can influence the measured N-values:

• Variation in the weight of hammer and height of drop;

• Using heavy drill rods with a diameter greater than 1 inch;

• The length of the drilling rod exceeds 50 m;

• Using a damaged split spoon sampler;

• Failure to place the sampler on undisturbed soil;

• Careless in counting the number of blows.

In empirical correlations, the geotechnical and geophysical properties of soil are assessed using corrected SPT values (N₁₍₆₀₎) [21]. Eq. (1) indicates the necessary corrections that must be considered to the measured blow count to produce the corrected SPT values (N₁₍₆₀₎).

Where

• N₁₍₆₀₎ – corrected SPT value for the theoretical free-fall hammer with 60% energy;

• N – SPT value measured in the field;

• C_N – overburden pressure correction factor;

• C_E – correction factor for transmitted energy to the SPT stem;

• C_W – correction factor for the GWT;

• C_B – correction factor for the diameter of the borehole;

• C_R – The length of SPT stem correction factor.

For rod lengths greater than 6 m, the rod correction factor (C_R) can be taken unity; for rod lengths less than 3 m, C_R = 0.75 is recommended. In this investigation, C_R is set to unity to keep things simple [17]. In boreholes larger than 12 cm in diameter, the borehole diameter adjustment should be considered, but the diameter of the drilling in this study was 10 cm, so the correction factor (C_B) is set to unity. The measured N-value decreases as the confining pressure decreases due to increasing the borehole diameter. It's worth mentioning that many of these considerations are overlooked during site studies [1, 2, 3, 4].

3 Description of study area and field tests

The study area is the governorate of Al-Basrah, which was established in 636 AD and is located in southern Iraq at 30° 30^′ 29.1672^″ N and 47° 47^′ 0.5604^″ E on the Global Positioning System (GPS). This city is home to Iraq's main port, Um Qasar, and numerous oil wells. The prominence of Al-Basrah governorate stems from the city's oil fields and construction one of Al-Faw port on the Arabian Gulf to the south. Boreholes were drilled to a depth of 10 meters below ground level, with a ground surface elevation of approximately 5 meters above sea level. Boreholes were drilled throughout the study area, particularly along the two sides of the Shatt Al-Arab River, which runs northwest to southeast through the city.

The quality and level of groundwater table significantly impact the magnitude of allowable bearing capacity of driven piles. The fieldwork had been conducted over a large area of Al Basrah governorate; the drilled boreholes were mostly conducted in available free lots, which reflected the nonuniform distribution of boreholes in the study area. Also, boreholes must be drilled in undeveloped properties to prevent conflicts with property owners and the restricted space available in the built area. To avoid any issues during drilling, the crew began by locating existing facilities such as sewage pipes, electrical cables, freshwater pipelines, and telephone, and internet connections within the study area. The boreholes were drilled with a flying auger with a diameter of 10 cm and extended to a depth of 10 m below ground level. Several SPTs were performed using an automatic hammer along the depth of boreholes.

On a Google Earth satellite view, Figure 1 shows drilled boreholes’ distribution. In addition, Figure 2 shows the study area and distribution of boreholes. The SPTs data were used to compute the driven pile's permitted bearing capacity. Furthermore, after 24 hours of drilling, the GWT was measured in the field, and the density of the soil was calculated experimentally for each well. Because the groundwater level in some boreholes had not risen after 24 hours, the GWT has no value in Table 1 and has no bearing capacity calculation impact. Table 1 shows the measured N-values from SPTs conducted at depths of 1.5, 6, and 9.5 m below the existing ground surface, as well as the GWT for 135 boreholes. Due to the highly soft soil layers at those depths, conducting successful SPTs in some boreholes and at specific depths, such as boreholes 80 and 84 in Table 1, is difficult.

Figure 1

Distribution of the boreholes (source: Google Maps)

Figure 2

Borehole locations used in the analysis

4 Bearing capacity of driven piles

Predicting the bearing capacity of piles is one of the difficult tasks in geotechnical engineering. Therefore several strategies and approaches have been developed to overcome forecast uncertainty. Certain simplifying assumptions and/or empirical methodologies are used in the procedures for soil stratigraphy, soil-pile structural interaction, and soil resistance distribution along the pile. As a result, they are unable to generate fully quantitative results that may be applied directly to foundation design. Five approaches for determining pile bearing capacity can be used:

• In-situ dynamic testing.

• In-situ static testing.

• In-situ integrity testing.

• Theoretical calculation of bearing capacity of piles based on soil properties and pile type and dimensions.

• Indirect methods based on the results of in-situ investigation tests [3, 23, 24, 25].

In recent years, in-situ testing approaches have grown rapidly in the geotechnical design of piles foundations. This is due to the rapid development of in-situ testing devices, a better understanding of soil behavior, and an awareness of some of the limitations and shortcomings of traditional laboratory testing. There are two methods for estimating or calculating the bearing capacity of a pile: direct and indirect ways. The use of pile-load tests and theoretical computations are examples of direct approaches. The SPT is one of the indirect approaches used to assess the pile bearing capacity in this study. Filtering and averaging data of pile resistance, failure zone around the pile base, total stress approaches, and pile capacity in dense strata with restricted base penetration are all factors that influence the uncertainty of indirect methods. The bearing capacity of driven piles estimatedfrom the results of corrected SPT values is nearly equivalent to those calculated from static testing [26, 27, 28, 29].

The total number of drilled boreholes was 135; however, only 95 boreholes were chosen in this investigation to reduce numerical dispersion caused by significant changes in SPT values in certain places, which affected the reliability of the MATLAB software results. The bearing capacity of driven piles was evaluated for 95 boreholes drilled to a depth of 10 m below ground level and spread across the entire study area of Al-Basrah governorate. The bearing capacity of driven piles with lengths 6, 7, 8, 9, and 10 m estimated from polynomials generated using MATLAB were compared with those obtained from empirical equations based on corrected SPT values. When calculating the allowable bearing capacity of driven piles, a high safety factor of 3 is considered due to the soil's heterogeneity, high variation in GWT, and high quantities of organic matter and garbage.

The main changes to the SPT values were the overburden correction factor (C_N), as mentioned in Eq. (4), the energy correction factor (C_E), which is equivalent to 0.7, and the groundwater correction factor (C_W), as defined in Eq. (2). The corrected N-values can be used to compute the allowable bearing capacity of driven piles [26, 27]. Table 2 shows the borehole coordinates and the computed allowed bearing capacity of driven piles using Eqs. (4) to (7) with a safety factor of 3. Due to a large amount of space required to show such data, the enormous amount of data used in calculating the ultimate bearing capacity for different depths in 95 boreholes will not be shown in this study.

Where

• Q_b – end bearing resistance;

• Q_s – skin friction resistance;

• P_a – atmospheric pressure (≈ 100 kN);

• A_b – cross-sectional area of pile;

• P – pile perimeter;

• L – pile length;

• Q_utl – ultimate bearing capacity;

• Q_all – allowable bearing capacity;

• FS – factor of safety = 3

5 MATLAB Modeling of SPT Data

To produce a surface indicating the variance in the allowable bearing capacity of driven piles of several depths in the research region, MATLAB was used to process the data of SPTs conducted in 135 boreholes. Because of the high variance and may be singularities in the results of SPTs conducted at several depths in 135 boreholes, it's important to avoid using extreme SPT values when calculating the allowable bearing capacity of driven piles with MATLAB. These extremes could be the consequence of a small number of boreholes being drilled in particular sections of the study area or a large difference in the geotechnical properties of soil in some locations of the study area.

Several trials were conducted using the 1^st order surface, 2^nd order surface, 3^rd order surface, and 4^th order surface to develop an acceptable surface representative for the fluctuation of bearing capacity of driven piles having several lengths with spatial coordinates. The bearing capacity of driven piles from produced surfaces can be calculated using Eqs. (8) to (11). Tables 3 and 4 contain the corresponding parameters for each equation. More accurate findings are obtained by increasing the order of the polynomial representing the surface depicting the fluctuation of the bearing capacity of driven piles. However, such a surface will increase the number of parameters required to compute the bearing capacity, making the procedure more difficult. The number of parameters increases from three to fifteen when the polynomial order is changed from first to fourth, as shown in Table 3, while the root means square error (RMSE) remains unchanged. Figures 3 to 6 illustrate the surfaces created using 1^st, 2^nd, 3^rd, and 4^th order polynomials for variation in bearing capacity of a driven pile of 6 m length for 95 boreholes.

Figure 3

Variation of the allowable bearing capacity of driven piles (6 m length) using 1^st order polynomial

Figure 4

Variation of the allowable bearing capacity of driven piles (6 m length) using 2^nd order polynomial

Figure 5

Variation the allowable bearing capacity of driven pile (6 m length) using 3^rd order polynomial

Figure 6

Variation the allowable bearing capacity of driven pile (6 m length) using 4^th order polynomial

The first- and second-order interpolation polynomials almost invariably result in flat surfaces, which essentially reflect variations in the allowable bearing capacity as a function of coordinates and length. Furthermore, while applying the equation with less parameters is simple, employing third- and fourth-order interpolations will result in surfaces with several folds, resulting in extremely sensitive estimates of the allowable bearing capacity of driven piles, especially around inflection point surfaces. As a result, adopting 1st-order interpolation, where the surface polynomial has just three parameters and an acceptable root mean squared error (RMSE) when predicting the allowed bearing capacity of driven piles, is advised to save time and effort. R² is also the fraction of the dependent variable's variation that can be predicted by the independent variable(s), and it ranges from 0.6379 to 0.7565. As the order of the polynomial used to represent experimental data increased, the value of R² increased. This was due to a closer match between the pile's projected allowed bearing capacity and determined SPT values. The adjusted R² is a type of R² that has been adjusted to account for the model's number of predictors.

The 1^st order polynomial with 95% confidence bounds is:

The 2^nd order polynomial with 95% confidence bounds is:

The 3^rd order polynomial with 95% confidence bounds is:

The 4^th order polynomial with 95% confidence bounds is:

6 Results and discussion

Using the coordinates of 95 boreholes and the corrected N-values obtained from SPTs, the first-order interpolation outlined in the preceding section will be used to estimate the allowable bearing capacity of driven piles with lengths of 6, 7, 8, 9, and 10 m. The first-order polynomial in Eq. (8) will be used to determine the allowable bearing capacity of driven piles having several depths. The parameters defining the polynomial for all investigated lengths of driven piles are given in Table 5. Because of the large range of recorded SPT values, there was no uniformity in the values of a parameter defining the 1^st order polynomials [3]. The SPT values generally increased with depth; however, the soft layer stratification caused the SPT values to decrease in some boreholes. To avoid the uncertainty caused by SPT values and seasonal oscillations in the GWT, the overburden pressure is calculated using the effective unit weight in this study. The surfaces representing the change in allowable bearing capacity of several lengths of driven piles are planes, as shown in Figures 7 to 10. The disparity revealed that the northern study area authorized bearing capacity of driven piles is higher than the southern parts of the study area. Table 6 shows comparison between the results of bearing capacity of driven piles calculated from SPTs and proposed 1^st order polynomial.

Figure 7

Surface defining the variation of the allowable bearing capacity of the driven pile having 7 m length

Figure 8

Surface defining the variation of the allowable bearing capacity of the driven pile having 8 m length

Figure 9

Surface defining the variation of the allowable bearing capacity of the driven pile having 9 m length

Figure 10

Surface defining the variation of the allowable bearing capacity of the driven pile having 10 m length

Additionally, as soil depth increases, its allowable bearing capacity increases. The five depths studied all followed the same pattern. According to the allowable bearing capacity of driven piles, the weak zone is in the southeast corner of the city.

Where X = E−47.5 and Y = N−30.2; E is longitude (easting) in degrees; N is latitude (northing) in degrees, and Q_all is the allowable bearing capacity of the driven pile (kPa).

7 Conclusions

Production of thematic surfaces showing the variation of bearing capacity of driven piles in Al-Basrah governorate is the main objective of this study. The thematic surfaces produced by MATLAB software depending on the results of SPTs conducted in the study area. The SPTs conducted at depth 1.5, 6, and 9.5 m in 135 boreholes drilled to a depth of 10 m. Based on the results of study, a preliminary estimation of bearing capacity of driven piles can be easily estimated from the proposed equations. The following points can be concluded from the results of this study:

• The results of SPTs conducted in the study area give a comprehensive idea about the geotechnical properties of soil in the study area and can be used safely to estimate the allowable bearing capacity of driven piles across Al-Basrah's governorate.

• In the preliminary design of piles, geotechnical parameters of the soil can be used.

• One of the promising techniques using MATLAB software to create a three-dimensional surface that illustrates the change in allowable bearing capacity of driven piles as a function of geographic coordinates and length.

• The first-order polynomial, with only three parameters and an RMSE of 28.4993 kN, was the simplest and easiest to calculate the allowable bearing capacity of driven piles.

• The allowable bearing capacity of driven piles obtained from the proposed Eq. (12) were in good agreement with those calculated from the SPT data. The difference in the allowable bearing capacity of driven piles calculated from proposed equation and those calculated from SPTs ranged from (−3%) to (+38%).

• Calculating the allowable bearing capacity of driven piles using the suggested equation will save time and money, especially for small projects.