Structural Aspects of Pile Foundation Design: A Practical Example

In the design of a pile foundation, the geotechnical engineer is expected to hand over the soil investigation report to the structural engineer, who will proceed to provide the longitudinal reinforcements needed for the piles and also design the pile cap. The structural design of a pile cap is an important aspect of pile foundation design and the method of carrying out the design has been presented in this article.

The soil investigation report handed to the structural engineer for the design of pile foundation purpose should contain the embedment length of the piles, the recommended sizes of the pile, the safe working load of each pile size, and other information that may be necessary for the structural engineer to do his design properly. All aggressive materials in the soil should be stated as well so that adequate protection will be given to the pile material(s) for durability.

The first step in the structural design of a pile cap usually involves obtaining the number of piles required to support each column load. This is usually done using the service loads of the column, and relating them to the safe working load of the piles from the soil investigation report. In this article, we are going to show how the structural design of reinforced concrete pile foundations and pile caps can be done based on practical design and site experience.

Design Example
The frame of a 5 storey building is shown in Figure 1, and it is expected to be supported on piles with an embedment length of 20 m. The allowable working loads of the bored pile (CFA) is shown in Table 1. f_y = 460 Mpa, f_cu = 30 Mpa

Table 1: Pile safe working load

Pile diameter (mm)	300	450	600	750	900
Safe working load (kN)	246.74	370.11	493.48	616.85	740.22

Design for Column A1
Service axial load on column = 647 kN
Ultimate axial load on column = 885 kN
Size of column = 450 x 230 mm

Try 2 No of piles
Service load per pile = 647/2 = 323.5 kN
Let us adopt 600 mm diameter piles for uniformity and to have fewer pile boring points

Safe working load of φ600 mm piles = 493.48 kN > 323.5 kN Okay

Centre to centre spacing of piles = 3φ = 3 x 600 = 1800 mm
Overhang of pile cap edge from the pile = 150 mm

Total length of pile cap = 1800 + 600 + 2(150) = 2700 mm
Width of pile cap = 600 + 150 + 150 = 900 mm
Thickness of pile cap = 2φ + 100 = 2(600) + 100 = 1300 mm

The layout of the pile cap is therefore given as shown in Figure 3.

Let us quickly carry out the structural design of pile cap Type 1 according to BS 8110-1:1997. You can also read Design of Pile Cap According to Eurocode 2.

From Table 3.61 of Reynolds et al. (2008), the tensile force to be resisted within the pile cap is given by;

F_t = N/(12ld)[3l² – a²]

Where;
N = Column axial load at ultimate limit state
l = Centre to centre spacing of the piles
d = Effective depth of the pile cap 
a = dimension of the column side parallel to the length of the pile cap

Self weight of the pile cap (ULS) = 1.4 x Area x depth x 24 kN/m³ = 1.4 x 2.7m x 0.9m x 1.3m x 24 kN/m³ = 106.14 kN

N = 885 kN + 106.14 = 991.142 kN
l = 1.8 m
d = 1300 – 100 = 1200 mm = 1.2 m
a = 0.45 m

F_t = [991.142/(12 x 1.8 x 1.2)] x [3 x 1.8² – 0.45²] = 364 kN
A_st = F_t/0.95f_y = (364 x 1000)/(0.95 x 460) = 833 mm²
As_min = 0.13bh/100 = 1690 mm²
Provide 6T20 @ 175 c/c (As_prov = 1974 mm²)

Check for shear
Critical position for shear on vertical section across full width of pile-cap occurs at distance from face of column given by:
a_v = 0.5(l – c) – 0.3φ = 0.5(1800 – 450) – (0.3 x 600) = 495 mm

The shear force carried by the piles V = 991.142/2 = 495.571 kN

The shear stress ν = V/bd = (495.571 x 1000)/(900 x 1200) = 0.458 MPa
Concrete resistance shear stress v_c = 0.632(100A_s/bd)^1/3(400/d)^1/4

v_c = 0.632 x [(100 x 1974)/(900 x 1200)]^1/3 x (400/1200)^1/4 = 0.632 x 0.557 x 0.759 = 0.275 MPa
For grade 30 concrete, v_c = 0.275 x (30/25)^1/3 = 0.292 Mpa
v_c(2d/a_v) = 0.292 x [(2 x 1200)/495] = 1.415 MPa > 0.458 MPa  This is okay

Shear stress at column perimeter
ν = V/ud = (885 x 1000)/[(2 x 225 + 2 x 450) x 1200] = 0.546 MPa
This is less than 0.8√fcu = 4.38 Mpa. Therefore, this is okay.

Anti-burst bars of T12 @ 200 spacing should be provided
Main bars should be returned at least 900 mm into the sides to satisfy anchorage length requirements. You can take anchorage length to be conservatively 50 x diameter of reinforcement = 50 x 20 = 1000 mm

Design of Pile Cap Type 2
Service axial load on column = 1077 kN
Ultimate axial load on column = 1476 kN
Size of column = 450 x 225 mm
The number of φ600 mm piles required = 1077/493.48 = 2.184

Using 3 No of φ600 piles
Service load per pile = 1077/3 = 359 kN

Safe working load of φ600 mm piles = 493.48 kN > 359 kN This is okay

Let us adopt a triangular pile cap arranged in such a way that the column load will be equally distributed to the piles. This arrangement can be found in Table 3.16 of Reynolds et al (2008), and it is shown in Figure 4.

h_p = φ = diameter of pile = 600 mm
Spacing of piles = 3φ = 3 x 600 = 1800 mm
Overhang of pile cap edge from the pile = 150 mm
(α + 1)φ + 300 = (3 + 1)600 + 300 = 2700 mm
φ + 250 =  600 + 250 = 850 mm
φ + 300 =  600 + 300 = 900 mm
(6α/7 + 1)φ + 300 = 2442.857 mm (say = 2445 mm)
(2α/7 + 0.5)φ + 150 = 964.285 mm (say = 965 mm)
Thickness of pile cap = 2φ + 100 = 2(600) + 100 = 1300 mm

The layout of the pile cap is shown in Figure 5.

Self weight of the pile cap (ULS) = 1.4 x Area x depth x 24 kN/m³ = 1.4 x 5.166 m² x 1.3m x 24 kN/m³ = 225.61 kN

Total load on pile cap at ULS = 1476 kN + 225.61 kN = 1701.61 kN
l = 1.8 m
a = 0.225 m
b = 0.45 m

Tensile force to be resisted by the reinforcement in the direction parallel to X-X;
F_t,x = N/(36ld)[4l² + b² – 3a²]
F_t,x = [1701.61/(36 x 1.8 x 1.2)] x [4 x 1.8² + 0.45² – 3 x 0.225²]  = 284 kN

Tensile force to be resisted by the reinforcement in the direction parallel to Y-Y;
F_t,y = N/(18ld)[2l² – b²]
F_t,y = [1701.61/(18 x 1.8 x 1.2)] x [2 x 1.8² – 0.45²]  = 275 kN

Let us use the highest value for design in anticipation that we will provide the same reinforcement in both directions
A_st = F_t/0.95f_y = (284 x 1000)/(0.95 x 460) = 649 mm²
As_min = 0.13bh/100 = 1690 mm²
Provide T20 @ 175 c/c in both directions (As_prov = 1974 mm²)

Shear resistance
The shear force carried by the piles V = 1701.61/3 = 567.2 kN
The shear stress ν = V/bd = (567.2 x 1000)/(1000 x 1200) = 0.472 MPa
v_c(2d/a_v) = 0.292 x [(2 x 1200)/495] = 1.415 MPa > 0.472 MPa  This is okay
Shear will obviously not be a problem.

Design of Pile Cap Type 3
Service axial load on column = 1825 kN
Ultimate axial load on column = 2545 kN
Size of column = 400 x 400 mm
The number of φ600 mm piles required = 1825/493.48 = 3.69

Use 4 No of φ600 piles
Service load per pile = 1825/4 = 456.25 kN

Safe working load of φ600 mm piles = 493.48 kN > 456.25 kN This is okay

Let us adopt a square pile cap arranged in such a way that the column load will be equally distributed to the piles. This arrangement can be found in Table 3.16 of Reynolds et al (2008), and it is shown in Figure 6.

Self weight of the pile cap (ULS) = 1.4 x Area x depth x 24 kN/m³ = 1.4 x 7.29 m² x 1.3m x 24 kN/m³ = 318.43 kN
Total load on pile cap at ULS = 2545 kN + 318.43 kN = 2863.43 kN

Tensile force to be resisted by the reinforcement in both directions;
F_t = N/(24ld)[3l² – a²]
F_t = [2863.43/(24 x 1.8 x 1.2)] x [3 x 1.8² – 0.40²]  = 528 kN

A_st = F_t/0.95f_y = (528 x 1000)/(0.95 x 460) = 1208 mm²
As_min = 0.13bh/100 = 1690 mm²
Provide T20 @ 175 c/c in both directions (As_prov = 1974 mm²)

Shear resistance
The shear force carried by the piles V = 2863.43/4 = 715.9 kN
The shear stress ν = V/bd = (715.9 x 1000)/(1000 x 1200) = 0.595 MPa
v_c(2d/a_v) = 0.292 x [(2 x 1200)/495] = 1.415 MPa > 0.472 MPa  This is okay

The structural engineer is expected to provide the following drawings;

(1) Setting out drawing showing the piling points and layout with a known reference point
(2) General column/pile cap layout/arrangement
(3) Pile cap/ground beam/ground floor slab layout
(3) Columns, piles and pile cap reinforcement drawings (detailing)
(5) Ground beams and ground floor slab reinforcement detailing
(6) Construction procedure sketches

Construction Considerations
(1) Ground beams are usually provided to chain the pile caps together, and to provide the needed support for the ground floor slab. There are construction scenarios where the ground floor slab is placed directly on the pile caps, but note that this concept is quite different from piled raft foundation. The ground beams are usually embedded into the pile caps, or may be allowed to sit directly on the pile caps depending on the site level. A typical construction drawing showing this interaction is given in Figure 7.

(2) Contractor should maintain a minimum concrete cover of 75 mm

(3) There may be need to be cast the pile cap in two stages to achieve the configuration shown in Figure 7.  The first casting will get to the bottom level of the ground beams (see Figure 8), then the ground beam reinforcements are laid (see Figure 9), before the final casting of the pile cap and ground beams to the required level (see Figure 10). Read about bonding of old and new concrete.

On getting to the stage shown in Figure 10, the bays are filled with sharp sand, and the ground floor slab is cast as appropriate.

Do you need help in design, consultancy, production of construction drawings, supervision, and project management, contact us today at Structville Integrated Services Limited. We are excellent at what we do, and we pride ourselves in professionalism and integrity. Send an e-mail now to info@structville.com copy structville@gmail.com or send a whatsapp message to +2347053638996.

References
[1] Reynolds C.E., Steedman J.C., Threlfall A.J. (2008): Reynolds’ Reinforced Concrete Designer’s Handbook 11th Edition. Taylor and Francis, New York