A "pile formula" generally refers to an equation used in geotechnical engineering to calculate the capacity, settlement, or other design parameters of a pile foundation. Based on the provided reference, a specific pile formula is given for calculating the unit toe resistance of a close-end pile using the NGI approach and CPT data.
Understanding Pile Capacity
Pile foundations are designed to transfer loads from a structure through weak soil layers to stronger soil or rock. Their capacity is determined by the resistance mobilised at the pile tip (toe resistance) and along the pile shaft (shaft friction).
According to the reference, the pile capacity itself is specifically defined as:
- The load mobilized at the pile head displacement equal to 10% of the pile base diameter (10%B).
Pile formulas, like the one detailed below, help engineers estimate these resistances and, consequently, the overall pile capacity.
NGI Approach Formula for Unit Toe Resistance
The reference provides a specific formula (Eq. 7.22) used in the NGI (Norwegian Geotechnical Institute) approach for determining the unit toe resistance of close-end piles. This method utilizes data from Cone Penetration Tests (CPT), specifically the cone resistance measured at the pile toe. The reference notes that no averaging procedure is done for the cone resistance ($q_{c,tip}$) used in the formulas.
The formula for the unit toe resistance at 10%B displacement ($q{b0.1}$), as presented in the reference (Eq. 7.22), is related to the cone resistance at the pile tip ($q{c,tip}$).
Formula Breakdown
The reference states: "(7.22) q b 0.1 q c , t i p = 0.8 1 + D r 2"
Interpreting this notation as a standard geotechnical formula where unit toe resistance ($q{b0.1}$) is calculated using cone resistance ($q{c,tip}$), the formula for unit toe resistance is:
$q_{b0.1} = 0.8 \cdot \left(1 + \frac{Dr}{2}\right) \cdot q{c,tip}$
Where:
- $q_{b0.1}$: The unit toe resistance mobilized at a pile head displacement of 10%B. This is the value being calculated.
- $q_{c,tip}$: The cone resistance measured at the pile toe using a CPT. This value is used directly from the test results without averaging.
- $0.8$: A coefficient used in this specific NGI approach formula.
- $(1 + D_r/2)$: A term included in this formula. The reference does not explicitly define $D_r$, but it is a factor within this specific calculation method.
This formula calculates the resistance per unit area at the pile toe ($q_{b0.1}$). To find the total toe resistance, this unit resistance would typically be multiplied by the base area of the pile. This total toe resistance, along with the shaft friction, contributes to the overall pile capacity.
Practical Application
Formulas like Eq. (7.22) are crucial in geotechnical design for:
- Predicting Pile Bearing Capacity: Estimating the maximum load a pile can support at its base.
- Designing Pile Foundations: Determining the required pile length and diameter based on expected loads and soil conditions.
- CPT Data Utilization: Directly applying site-specific CPT results to foundation design.
Understanding and correctly applying these "pile formulas," such as the NGI approach for unit toe resistance, is fundamental for ensuring the safety and performance of pile foundations.
