{"id":525,"date":"2025-03-31T04:10:00","date_gmt":"2025-03-31T04:10:00","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/example-6-6-estimation-of-the-ultimate-geotechnical-strength-of-a-pile-subjected-to-axial-compressive-load-based-on-cpt-test-results\/"},"modified":"2026-03-16T14:11:15","modified_gmt":"2026-03-16T14:11:15","slug":"example-6-6-estimation-of-the-ultimate-geotechnical-strength-of-a-pile-subjected-to-axial-compressive-load-based-on-cpt-test-results","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/example-6-6-estimation-of-the-ultimate-geotechnical-strength-of-a-pile-subjected-to-axial-compressive-load-based-on-cpt-test-results\/","title":{"raw":"Example 6.6","rendered":"Example 6.6"},"content":{"raw":"Estimate the ultimate geotechnical strength Qf<\/sub><\/em> of the driven concrete pile shown below. The pile is subjected to axial compressive load and is embedded in a layered profile comprising both fine-grained and coarse-grained layers. Use CPT-based methods of Schmertmann (1978) and Bustamante and Gianeselli (1982) (Chapter 6.12<\/a>) together with the CPT results provided below. Ignore the weight of the pile in the calculations.\n\n[caption id=\"attachment_524\" align=\"aligncenter\" width=\"900\"]\"The Example 6.6. Problem description and input parameters.[\/caption]\n

Answer:<\/h2>\nAs discussed in Chapter 6.12<\/a>, the correction factor \u03b1<\/em>\u2032<\/em> used in Schmertmann\u2019s method in the determination of the skin friction resistance Qsf<\/sub><\/em> of the pile depends on the nature of the surrounding soil (coarse-grained or fine grained). Thus, before proceeding with the estimation of the skin friction resistance, the soil behavior types SBT encountered along the length of the pile must be determined, according to the mentioned in Chapter 1.7<\/a>.\n\n1. Calculation of skin friction resistance Qf<\/sub><\/em> using the method proposed by Schmertmann (1978):\n

1.1\u00a0Skin friction resistance along pile shaft embedded in sand (SBT 5\/6):<\/p>\nFor the part of the concrete pile that is embedded into sand, the variation of the correction factor \u03b1\u2032<\/em>\u00a0<\/em>with depth z<\/em> is determined with the aid of Eq. 6.24 (Figure 6.55<\/a>):\n\n[latex]\\alpha ' = 1.85 - 0.1\\left( {\\dfrac{z}{D}} \\right) + 0.0025{\\left( {\\dfrac{z}{D}} \\right)^2} - 0.259 \\times {10^{ - 4}}{\\left( {\\dfrac{z}{D}} \\right)^3}[\/latex]\n\nThe sand layer is divided into sublayers, the thickness \u0394L<\/em> of which depends on the frequency of sleeve friction resistance fs<\/sub><\/em> measurements from the CPT test.\n\nThe unit friction resistance of each sublayer \u0394Qf <\/sub><\/em>is then estimated with Eq. 6.23 (Figure 6.55<\/a>):\n\n[latex]\\Delta {Q_{sf}} = {f_{sf}}\\left( {\\pi D} \\right)\\Delta L = \\left( {\\alpha '{f_s}} \\right)\\left( {\\pi D} \\right)dL[\/latex]\n\nand summed to find the skin friction resistance of the pile that develops along the part of the shaft embedded in the sand layer, Qsf,sand<\/sub><\/em>.\n\nAlternatively, we can use the Bustamante and Gianeselli\u2019s method to estimate Qsf,sand<\/sub><\/em>. In that case the skin friction resistance along each sublayer is calculated as fsf<\/sub><\/em> = qc<\/sub><\/em>\/\u03b1<\/em> where the coefficient \u03b1<\/em> is provided by Table 6.6 for sand with qc<\/sub><\/em> > 12 MPa (generally qc<\/sub><\/em>\/pa<\/sub><\/em> > 120 in the provided data indicating dense sand) and driven precast concrete piles (Category IIA) to be \u03b1<\/em> = 150. The limiting value of fsf<\/sub><\/em> is from Table 6.6 fsf<\/sub><\/em> < 120 kPa. Using the provided qc<\/sub><\/em> values we calculate Qsf,sand<\/sub><\/em> = 823 kN. There is significant difference between the results of the two methods, and is attributed only partly to the Bustamante and Gianeselli\u2019s method imposing a limiting value to fsf<\/sub><\/em>, as the fsf<\/sub><\/em> is exceeded in merely two sublayers.\n

1.2 Skin friction resistance along pile shaft embedded in clay (SBT3) and silt (SBT4):<\/p>\nA similar procedure is followed for the part of the pile embedded into the fine-grained clay\/silt layers. In that case, the correction factor \u03b1\u2032<\/em>\u00a0<\/em>depends on the sleeve friction resistance, and is provided from Eq. 6.26 for concrete piles (Figure 6.56<\/a>):\n\n[latex]\\alpha ' = 1.28 - 1.473\\left( {\\dfrac{{{f_s}}}{{{p_a}}}} \\right) + 0.839{\\left( {\\dfrac{{{f_s}}}{{{p_a}}}} \\right)^2} - 0.1634{\\left( {\\dfrac{{{f_s}}}{{{p_a}}}} \\right)^3}[\/latex]\n\n[caption id=\"attachment_524\" align=\"aligncenter\" width=\"900\"]\"The Figure 6.55. Calculation of pile\u2019s skin friction resistance along the sand layer (SBT5\/6).[\/caption]\n\n[caption id=\"attachment_524\" align=\"aligncenter\" width=\"900\"]\"The Figure 6.56. Calculation of the pile\u2019s skin friction resistance along the clay (SBT3) and silt (SBT4) layers.[\/caption]\n\nDividing again into sublayers we can estimate the unit skin friction resistance with Eq. 6.23, and the total friction resistance developing along the part of the pile embedded in fine-grained soil, Qsf,clay<\/sub><\/em> (Figure 6.56<\/a>).\n\nAgain we will use the Bustamante and Gianeselli\u2019s method to estimate Qsf,clay<\/sub><\/em>, for comparison purposes. Skin friction resistance along each sublayer is again calculated as fsf<\/sub><\/em> = qc<\/sub><\/em>\/\u03b1<\/em> where the coefficient \u03b1<\/em> for clay with qc<\/sub><\/em> = 1 to 5 MPa (firm to stiff clay) and driven precast concrete piles (Category IIA) to be \u03b1<\/em> = 40. The limiting value of fsf<\/sub><\/em> is from Table 6.6 fsf<\/sub><\/em> < 35 kPa. Using the provided qc<\/sub><\/em> values we calculate Qsf,clay<\/sub><\/em> = 499 kN. Again, there is a significant difference between the results of the two methods.\n\nWhile this comparison is based on fictitious CPT data, therefore one may argue that the differences between the two methods may have been exaggerated (the total skin friction resistance estimated with Schmertmann\u2019s method is Qsf<\/sub><\/em> = 2700 kN, and the total skin friction resistance estimated with Bustamante and Gianeselli\u2019s method is Qsf<\/sub><\/em> = 1322 kN i.e., less than half) its purpose in not to endorse one method over the other. Instead, its purpose is to inform the reader about the uncertainties associated with estimating the ultimate geotechnical strength with empirical methods. This is the reason why careful selection of risk ratings AS2159 is required, particularly when using legacy methods to estimate the design bearing capacity of piles.\n\n2. End-bearing resistance, Qb<\/sub><\/em>:\n\nIn order to apply the LCPC method and use Eq. 6.29 to estimation the end bearing resistance of the pile, we must first estimate the equivalent average cone resistance qc(eq)<\/sub><\/em>, following the procedure described in Chapter 6.12<\/a>:\n