7.2 Analysis of 4-pile caps and comparison with
7.2.1 Description of the experimental setup
The experiments reported here were originally carried out by of Blévot and Frémy (1967), Clarke (1973), Sabnis and Gogate (1984) and Suzuki (1998, 2000). As can be seen in Figure 7.1, different reinforcement layouts were used; 11 pile caps had grid reinforcement, 9 had bunched reinforcement placed in square over the piles, 8 had a combination of bunched and grid reinforcement. This last category is referred as combined in the following.
Figure 7.1 Some of the reinforcement layouts used in Blévot and Frémy experiments (Blévot 1967)
cross bunched reinforcement
square bunched reinforcement
grid reinforcement
The pile caps tested by Clarke (1973), Sabnis and Gogate (1984) and Suzuki (1998, 2000) were square and had a constant height, as shown in Figure 7.2.
Figure 7.2 Definition of the characteristic dimensions of the pile caps in the test series from Clarke (1973), Sabnis and Gogate (1984) and Suzuki (1998, 2000)
The pile caps tested by Blévot and Frémy were deep with a height of 0,75m and 1m.
In addition the top face was sloping so that the pile had a conical shape as can be seen in Figure 7.3 and Figure 7.4:
Figure 7.3 Definition of the characteristic dimensions of the pile caps from Blévot and Frémy (1967) experiments
L, length of the pile cap
e, spacing between piles h, height of the
pile cap
wc, width of the column
wp, width of the pile
h’
wp, width of the pile L, length of the pile cap
e, spacing between piles
h, height of the pile cap wc, width of the
column
wp, width of the pile wp, width of
the pile
Figure 7.4 Deep pile caps tested by Blévot and Frémy, (a) diagonal cracking, (b) central cracking, (c) strut splitting, (d) complex failure.
No precise information could be found about the exact ratio between h and h’ in the pile caps. Hence, it was assumed that h’/h= considering the pictures taken from the experiments, see Figure 7.4.
Some measures were taken to include the influence of the variable height of the pile caps in the predictions by building codes and the strut-and-tie models:
For the analysis using the codes, the variable height of the pile caps makes the assessment of the shear and punching shear capacities difficult. A simplification was made to consider a pyramidal shape. The shear capacity was calculated at the pile face, were the shear depth as defined in the codes is the smallest. The punching shear capacity was measured on control perimeters at various distances from the column and piles faces; depending on the position of the control perimeter an average shear depth was considered.
For the strut-and-tie model, the fact that the top face has a slope is considered by the reduction in confinement provided to the inclined struts. The assumption that the stresses are carried by direct arch action through a cylinder with dimensions shown in Figure 5.18 is not relevant in that case. Therefore, the width of the cylinder considered
(a) (b)
(c) (d)
was reduced to 60% of the width calculated for pile caps with constant height. This assumption almost always leads to kconfinement=1, meaning that there was very little positive effect from confinement on the splitting/crushing capacity of the main strut in the pile caps tested by Blévot and Frémy.
The complete data about the geometry and the materials used in different pile caps is found in Table 7.1. When the piles or the columns are circular they have been transformed to equivalent square assuming the same cross sectional area. The characteristic yield strength of steel and the characteristic compressive strength of concrete are given. Note that the concrete strength reported is the characteristic fck. Indeed, some authors reported the characteristic strength in their papers, others reported the mean strength. We decided to transform all the concrete’s strength into characteristic strength. Calculations are found in Appendix D.
Table 7.1 Properties and failure load of the experiments specimens
28 Pile caps L (m) h (m) Pitch between piles e(m)
Width of columns wc(m)
Diameter of round piles (m)
Equivalent square width of piles wp(m)
Reinforcement layout
As (one direction) (cm^2)
Steel yielding strength fyk
(Mpa)
Concrete cylinder strength fck (Mpa)
d (m) Failure load (kN)
Clarke73
A2
0,95 0,45 0,6 0,2 0,2 0.177 bunched square 7.85 410 27.2 0,4
1420
A8 1510
A5 0,95 0,45 0,6 0,2 0,2 0.177 bunched square 7.85 410 26.6 0,4 1400
A3 0,95 0,45 0,6 0 2 0,2 0.177 bunched square 5.50 410 30.4 0,4 1340
A6 0,95 0,45 0,6 0,2 0,2 0.177 bunched square 5.50 410 25.8 0,4 1230
B1 0,75 0,45 0,4 0,2 0,2 0,177 grid 6,28 410 26.7 0,4 2080
B3 0,75 0,45 0,4 0,2 0,2 0,177 grid 4,71 410 35 0,4 1770
Suzuki98
BP-20-2-grid 0,9 0,2 0,54 0,3 0,15 0,133 grid 5,67 413 20.4 0,15 480
BP-30-25-2-
grid 0,8 0,3 0,5 0,25 0,15 0,133 grid 5,67 413 26,3 0,25 725
BPC-20-30-
1 0,8 0,2 0,5 0,3 0,15 0,133 bunched 4,25 405 29,8 0,15 495
BPC-20-30-
2 0,8 0,2 0,5 0,3 0,15 0,133 bunched 4,25 405 29,8 0,15 500
BPC-20-1 0,9 0,2 0,54 0,3 0,15 0,133 bunched 5,67 413 21,9 0,15 519
BPC-20-2 0,9 0,2 0,54 0,3 0,15 0,133 bunched 5,67 413 19,9 0,15 529
Blévot &
Frémy67
4N1 1,59 0,75 1,2 0,5 0,35 combined 78,37 277,8 36,5 0,674 6865
4N1b 1,59 0,75 1,2 0,5 0,35 combined 47,16 479,6 40 0,681 6571
4N2 1,59 0,75 1,2 0,5 0,35 combined 67,86 289,4 36,4 0,66 6453
4N2b 1,59 0,75 1,2 0,5 0,35 combined 42 486,3 33,5 0,67 7247
4N3 1,59 1 1,2 0,5 0,35 combined 60,82 275 33,5 0,925 6375
4N3b 1,59 1 1,2 0,5 0,35 combined 38,47 453,3 48,3 0,931 8826
4N4 1,59 1 1,2 0,5 0,35 combined 58,88 291,4 34,7 0,92 7385
4N4b 1,59 1 1,2 0,5 0,35 combined 37,68 486,4 41,5 0,926 8581
Suzuki00
BDA-40-25-
70-1 0,7 0,4 0,45 0,25 0,15 0,133 grid 6,28 358 25,9 0,35 1019
BDA-40-25-
70-2 0,7 0,4 0,45 0,25 0,15 0,133 grid 6,28 358 24,8 0,35 1068
BDA-20-25-
90-1 0,9 0,2 0,45 0,25 0,15 0,133 grid 3,14 358 25,8 0,15 333
Sabnis and Gogate84
SS1 0,325 0,15 0,2 0,0673
(equivalent) 0,076 0,067 grid 1,491 499,4 31,27 0,11 250
SS2 0,325 0,15 0,2 0,0673
(equivalent) 0,076 0,067 grid 0,974 743,2 31,27 0,11 245
SS3 0,325 0,15 0,2 0,0673
(equivalent) 0,076 0,067 grid 1,252 886 31,27 0,109 248
SS4 0,325 0,15 0,2 0,0673
(equivalent) 0,076 0,067 grid 1,819 599,8 31,27 0,11 226
For each pile cap, for both the design codes (EC2 and BBK) and the strut-and-tie model, predictions were made concerning both the mean and the design resistance:
The mean resistance prediction is based on the mean strength of materials. The mean concrete fcm and steel fym strengths were used. It was assumed that the mean yield strength of steel was equal to 1.1fyk, indeed in deep elements like pile caps, large deformations cannot occur and it is very unlikely that steel will reach the ultimate strain. The mean resistance prediction considers no partial safety factor for the load and no partial safety factor for the materials. The design predictions are based on the design strength of materials, namely fcd for concrete and fyd for the steel. The design strength of materials was obtained by using γc and γs reduction factors that are stated in EC2 and BBK. The design strength prediction considers partial safety factor for material but here no partial safety factor for the load.
The procedure for determining the material strengths and the code predictions can be found in Appendix D.
The predictions for flexural capacity and one-way shear capacity are identical for Eurocode and BBK in sectional approaches, indeed, BBK recently adopted design approaches from Eurocode.
On the other hand, the methods for shear design differ between the two design codes.
Predictions according to the Swedish design practice only concern BBK in the comparative tables presenting results hereafter, although it is common in Sweden to use the “Concrete handbook – structural design”, which is said to predict higher punching capacities. However, in the case of pile caps, the flexural reinforcement ratio is usually very low, in which case BBK and the “Concrete handbook – structural design” predict almost the same punching capacity.