Pile cap is a very basic structure in construction design. This article would like to share the basic points to do in the process of calculating and choosing the size of pile cap, especially for those who are new to design work.
When designing a pile cap structure, the important parameters that need to be selected initially are the depth of the base and the height of the pile cap.
1. Selecting the depth of pile cap
The depth of the base is selected based on many factors similar to the depth of the foundation when designing a shallow foundation structure. The depth h from the natural ground surface to the foundation bottom is called the foundation depth. If before construction, the land must be leveled according to the plan, then the foundation depth is calculated from the planned ground surface. If before construction, according to the plan, the land must be filled, then only when the filled soil is old enough (3 years for sand soil, 5 years for clay soil) is the foundation depth calculated from the planned ground surface. If the filled soil is not old enough, the foundation depth is still calculated from the natural ground surface. This is because at greater depths, the soil is more compacted, the load on both sides is greater, so the bearing capacity of the soil is also greater. The larger the h value, the larger the standard pressure of the ground. Therefore, to be on the safe side, in the calculation, use a small value of h (when leveling the ground, count from the planned ground surface, when filling the ground, count from the natural ground surface). In both cases, it must be understood that if leveling or filling the ground over a very large area, the calculation of the foundation depth from the planned ground surface is completely correct, if only leveling or filling over a small area, the calculation is approximate.
A condition for the design engineer to choose the depth of the foundation base is to ensure that the passive soil pressure of the soil on the side of the pile foundation is balanced with the horizontal pressure transmitted to the foundation surface from the column foot. This condition applies to low pile foundations (piles only bear vertical forces transmitted from the foundation):
$$H_{min}=0,7tg\left(45^o-\frac{\varphi}{2}\right)\sqrt{\frac{2Q}{\gamma{b}}}$$
$H_{min}$: depth of the foundation bottom from the ground or basement surface to ensure the above minimum conditions
φ: internal friction angle of the soil on the foundation bottom
Q: horizontal load calculated at the foundation level transmitted by the column foot
γ: unit weight of the soil on the foundation bottom (with buoyancy)
b: Expected width of the foundation perpendicular to the horizontal load direction
2. Select height of the pile cap
The minimum pile cap height must be selected to ensure the shear resistance conditions: on the inclined cross-section and puncture resistance according to the requirements of the reinforced concrete structure design standard TCVN 5574:2012.
Calculate the shear strength on the inclined cross-section of the pile foundation
According to clause 6.2.3.2 of TCVN 5574:2012, the test formula according to this condition is:
$$Q\leqslant{Q}_{max}=0,3\varphi_{w1}\varphi_{b1}R_bbh_o$$
$Q_{max}$: strength on the inclined section of the pile cap
$\varphi_{w1}$: coefficient considering the influence of horizontal reinforcement placed according to the height of the cap $\varphi_{w1}=1+5\alpha\mu_w$
$$\alpha=\frac{E_s}{E_b}$$
$\mu_w=\frac{A_{sw}}{sb}$ calculated based on the arrangement of horizontal reinforcement in the cap: the area of horizontal reinforcement distributed over 1 unit length of 1 cap direction $\frac{A_{sw}}{s}$
$\varphi_{b1}=1-\beta{R}_b$. For normal concrete β=0,01
$Q$: total reaction force of piles located outside the inclined section closest to the column (section C1 as shown in the drawing)
Punching design of column on Pile cap
According to clause 6.2.5.4 of TCVN 5574:2012, Conditions for pile cap resistance to perforation caused by columns:
$$F\leqslant{F}_b+0,8F_{sw}$$
$F_b=\alpha{R}_{bt}u_mh_o\frac{h_o}{C}$ and taken not greater than the value corresponding to the perforation tower with $C=0,4h_o$
α=1 for normal concrete
$u_m$: average value of the upper and lower bottom circumferences of the perforation tower formed when perforated, within the working height $h_o$ of the pile cap $u_m=\frac{1}{2}\left[2(h_c+b_c)+2(h_c+2C_1+b_c+2C_2)\right]$
$F_{sw}$: total shear force due to the horizontal reinforcement cutting the side faces of the perforation tower $F_{sw}=R_{sw}\sum{A_{sw}}$
$\sum{A_{sw}}$: total area of the horizontal reinforcement cutting the side faces of the perforation tower
F: punching force, equal to the total pile reaction outside the bottom range of the punching tower.
Pile punching calculation:
The calculation is similar to the calculation of column puncture, with:
$D$: side of square pile or of square inscribed with round pile
In case the punctured compression tower face is inclined at an angle of $45^o$:
$$u_m=4(D+h_o)$$
In case the punctured compression tower face is inclined at an angle greater than $45^o$:
$$u_m=\frac{1}{2}\left[4D+b_1+C_1+b_2+C_2\right]$$
$F$: reaction force of the pile under consideration causes punching.
To facilitate structural engineering practice, we have created a spreadsheet here
