De Beer Method
This method determines the unit pile base resistance. It is based on the so-called "scale effect" for CPT-cone and pile base.
The method is described by the following steps which are performed in the standard 0,2 m interval along the pile length.
1) The calculation of the angle of internal friction φ according to the formula (1)
where: | qc | - | cone tip resistance |
σeff | - | effective stress | |
φ | - | angle of internal friction |
2) The calculation of the βc and βp angles according to the formulas (2) and (3).
Note: Both angles βc a βp can be maximally 90°.
where: | h | - | measurement depth |
dc | - | diameter of the CPT-cone | |
D | - | pile base diameter | |
δ | - | pile base shape coefficient |
For the circular and square piles:
For the rectangular piles:
where: | B | - | shorter side of the pile base |
L | - | longer side of the pile base |
3) Calculation of homogeneous values qp(1) according to the formula (4).
4) Calculation of downward values qp, j+1 according to the formula (5).
where: | a | - | measurement interval |
hcrit | - | critical depth | |
γ | - | unit weight of soil | |
qp(1), crit | - | homogeneous value in the critical depth hcrit |
The critical depth hcrit depends on the pile base diameter D and angle of internal friction φ:
For piles D < 0,4 m
- hcrit = 0,2 m
For piles 0,4 m ≤ D ≤ 0,6 m
- hcrit = 0,2 m for φ < 32,5°
- hcrit = 0,2 m and 0,4 m for φ ≥ 32,5°
For piles D ≥ 0,6 m
- hcrit = 0,2 m for φ < 32,5°
- hcrit = 0,2 m and 0,4 m for 32,5° ≤ φ < 37,5°
- hcrit = 0,2 m and 0,4 m a 0,6 m for φ ≥ 37,5°
Note: The final downward value is minimum for all relevant critical depths.
Note: The downward value must be smaller or equal to the homogeneous value.
5) Calculation of upward values qp, q+1 according to the formula (6).
Note: The upward value must be smaller or equal to the downward value.
6) Calculation of blended (mixed) qr,b values as an average from n upward values qp, q+1. The unit pile base resistance is the blended value in the pile base level.
Note: The blended value must be smaller or equal to the homogeneous value.
Literature:
Prof. Dr. ir E. DE BEER: METHODES DE DEDUCTION DE LA CAPACITE PORTANTE D´UN PIEU A PARTIR DES RESULTATS DES ESSAIS DE PENETRATION (MEMOIRES - VERHANDELINGEN), online: https://www.bggg-gbms.be/l/library/download/urn:uuid:05c758bb-bf51-4eb7-9dc0-5a03b293f7e0/overige+publicaties.pdf?format=save_to_disk&ext=.pdf