7.2 Analysis of 4-pile caps and comparison with
7.2.3.2 Comparison between design codes and the 3-D strut-and-tie model
Table 7.4 Comparison of mean and design resistance predictions to experimental failure loads with EC2, BBK04 and the strut-and-tie model.
bunched combined grid general
EC2 Average Standard deviation Average Standard deviation Average deviation standard Average deviation standard
ULTIMATE
CAPACITY 1,11 0,15 2,09 0,42 1,32 0,32 1,47 0,51
DESIGN
CAPACITY 1,35 0,20 2,26 0,45 1,44 0,31 1,64 0,51
bunched combined grid general
BBK04 Average Standard deviation Average Standard deviation Average Standard deviation Average deviation standard
ULTIMATE
CAPACITY 1,10 0,17 2,09 0,42 1,26 0,29 1,43 0,51
DESIGN
CAPACITY 1,99 0,36 2,38 0,55 1,98 0,66 2,10 0,56
bunched combined grid general
Strut-and-
tie model Average
Standard
deviation Average Standard
deviation Average Standard
deviation Average standard deviation ULTIMATE
CAPACITY 1,23 0,17 1,09 0,06 1,03 0,18 1,11 0,17
DESIGN
CAPACITY 1,76 0,19 1,56 0,16 1,51 0,18 1,61 0,21
The classification in bunched, combined and grid reinforcement layouts was made in order to evaluate the possible resistance variation induced by them. According to previous authors on the subject, grid reinforcement are said to be between 15% and 20% less resistant than bunched and composite ones, that are said to have somehow the same strength. It can be seen in Table 7.4 that only the strut-and-tie model predictions follow this trend. This is interpreted in two points:
Firstly it means that the codes were more sensitive to other parameters like the slenderness or the depth of the pile caps, than to the reinforcement layout, which
means that the number of experiments were not high enough to prevent the codes prediction to be distracted by those factors.
Secondly, it may mean that the 3-D strut-and-tie model is consistent enough not to be distracted by the non uniformity of the samples tested and still be able to capture the real trend.
Table 7.5 shows the ratios between experimental and design failure loads as well the ratios between experimental and mean predicted failure loads according to Eurocode, BBK and the strut-and-tie method. The predicted failure modes for each pile cap tested are also recalled.
Table 7.5 Observed failure load to predicted failure load ratios and failure modes for Eurocode, BBK and the strut-and-tie model
EC2 BBK04 3-D strut-and-tie model
Qfe
[Mpa]
Reported failure mode
Qfe/Qfm Qfe/Qfd
Predicted failure
mode
Qfe/Qfm Qfe/Qfd
Predicted failure mode
Qfe/Qfm Qfe/Qfd
Predicted failure
mode Bunched reinforcement
layout
[Clarke73]
A2 1420 s 1,05 1,30 f 1,02 1,90 p 1,24 1,63 f+s
A8 1510 s 1,12 1,38 f 1,08 2,02 p 1,32 1,73 f+s
A5 1400 s 1,06 1,28 f 1,00 1,90 p 1,16 1,62 f+s
A3 1340 s 1,36 1,73 f 1,36 1,73 f 1,54 2,06 f
A6 1230 s 1,25 1,59 f 1,25 1,75 p 1,43 1,93 f
[Suzuki98]
BPC-20-30-1 495 f 0,89 1,14 f 0,89 1,69 p 1,10 1,54 f+s
BPC-20-30-2 500 f 0,90 1,15 f 0,90 1,71 p 1,11 1,56 f+s
BPC-20-1 519 f+p 1,13 1,26 p 1,16 2,48 p 1,05 1,81 s
BPC-20-2 529 f+p 1,20 1,32 p 1,26 2,70 p 1,13 1,98 s
AVERAGE 1,11 1,35 44% 1,10 1,99 67% 1,23 1,76 75%
STANDARD
DEVIATION 0,15 0,20 0,17 0,36 0,17 0,19
Combined
reinforcement layout
[Blévot67]
4N1 6865 s 2,14 2,30 p 2,14 2,61 p 1,07 1,65 s
4N1b 6571 s 2,36 2,53 p 2,36 2,63 p 1,03 1,48 s
4N2 6453 s 2,18 2,34 p 2,18 2,63 p 1,07 1,59 s
4N2b 7247 s 2,88 3,10 p 2,88 3,36 p 1,19 1,84 s
4N3 6375 s 1,48 1,59 s 1,48 1,59 s 1,04 1,26 s
4N3b 8826 s 1,94 2,13 s 1,94 2,13 s 1,16 1,59 s
4N4 7385 s 1,72 1,85 s 1,72 1,85 s 1,06 1,51 s
4N4b 8581 s 2,03 2,24 s 2,03 2,24 s 1,13 1,58 s
AVERAGE 2,09 2,26 100% 2,09 2,38 100% 1,09 1,56 100%
STANDARD.
DEVIATION
0,42 0,45 0,42 0,55 0,06 0,16
Grid Reinforcement
Layout
[Clarke73]
B1 2080 s 1,88 2,15 s 1,88 2,15 s 1,24 1,77 f+s
B3 1770 f 1,44 1,60 s 1,44 1,60 s 1,32 1,73 f
[Suzuki98]
BP-20-2-grid 480 f+s 1,08 1,19 p 1,12 2,41 p 1,15 1,73 s
BP-30-25-2-grid 725 s 0,84 0,97 s 0,84 1,00 p 0,94 1,43 s
[Suzuki00]
BDA-40-25-70-1 1019 s 1,09 1,25 s 1,09 1,25 s 0,77 1,24 s
BDA-40-25-70-2 1068 f+s 1,16 1,34 s 1,16 1,34 s 0,81 1,34 s
BDA-20-25-90-1 333 f 0,91 1,16 f 0,91 1,50 p 1,09 1,44 f+s
[Sabnis84]
SS1 250 s 1,57 1,57 s 1,40 2,66 p 1,10 1,59 s
SS2 245 s 1,54 1,55 s 1,38 2,78 p 1,09 1,58 s
SS3 248 s 1,56 1,58 s 1,40 2,76 p 1,00 1,46 s
SS4 226 s 1,42 1,42 s 1,21 2,33 p 0,80 1,33 s
AVERAGE 1,32 1,44 91% 1,26 1,98 82% 1,03 1,51 100%
STANDARD
DEVIATION 0,32 0,31 0,29 0,66 0,18 0,18
OVERALL
FAILURE MODE 79% 82% 93%
AVERAGE 1,47 1,64 1,43 2,10 1,11 1,61
STANDARD
DEVIATION 0,51 0,51 0,51 0,56 0,17 0,21
Concerning the specificities of the series tested:
In the test series of Suzuki (1998) with the most slender pile caps it can be seen that both codes are rather unreliable. Indeed, Eurocode is rather non conservative with design predictions close to 1.2 and even one prediction below 1. BBK is too
conservative regarding the punching capacity with an average prediction around 2 and rather large variations. The predictions of the 3-D strut-and-tie model are good.
In the test series of Blévot and Frémy (1967) pile caps have an average slenderness which corresponds to the average slenderness of the samples tested. They have two major characteristics: they are way deeper (and carry more load) than the rest of the experiments and they have a conical shape. All these pile caps are predicted to fail by shear or punching by the standard models and actually failed in shear. The predictions from the codes are too conservative while the predictions of the model are very good. This wrong resistance evaluation from the codes is believed to be linked to a combination of the two characteristics of the pile caps: depth and conical shape.
Indeed codes of practice assume that, for deep members loaded in shear, the relative capacity should be reduced in large elements due to size effects. However, size effects were proven to be linked to the concrete softening associated to the more critical cracking pattern in deep elements as explained in Section 5.3.5: Size effect in deep elements and in pile caps. Therefore, knowing that the web of stocky pile caps is rather uncracked before failure, accounting for size effects is not consistent and not done in the 3-D strut-and-tie model.
The conical shape of the pile caps, as can be seen in Figure 7.4, is taken into account both in the code and the 3-D strut-and-tie model approaches:
In the strut-and-tie model, the conical shape is considered to have no influence on the node region but reduces the splitting crushing capacity of the web due to the reduction of confinement of the strut. The simplified approach with an equivalent cylinder, as shown in Figure 5.18, is still relevant but the width of the cylinder needs to be reduced. The width of the cylinder was actually reduced by 60% which ended up in a ratio between the cylinder width and the size of the hexagonal node faces size to be equal or less than 1 (except one where the ratio was slightly over 1). This resulted in confinement factors equal to one (i.e. no positive confinement).
The effect of the conical shape in the codes was the consideration of a reduced effective depth for the calculation of the shear and punching capacities (the procedure is briefly explained at the beginning of this chapter and the calculations are found in Appendix D). The corresponding decrease of the nominal shear capacity induced is believed to be too conservative and reveals the inconsistency of a sectional approach for stocky pile caps. Indeed, a slight change in the shape of the element resulted in a wrong assessment of the resistance associated to an incorrect mechanical approach that might lead the designer to mistakes.
Table 7.5 shows that the 3D strut-and-tie model is able to predict correctly 93% of the failure modes, against 79% and 82% for Eurocode and BBK. However, failure mode prediction is a bit tricky as it is not always easy to specify the nature of a failure in pile caps. In fact, a combination of flexural, shear and punching failure is often occurring without a possibility to clearly separate them, for example some complex cracking patterns at failure are shown in Figure 7.4 For instance the model developed only predicts two types of failure: flexural and shear failures. Indeed punching failures are very seldom in stocky pile caps where a combination of splitting and cracking of the compressive strut seems to be the most common shear failure mechanism. Shear and punching failures were both considered as shear failure types for the counting in order to keep equity between the models.
The most important information in Table 7.4 and in Table 7.5 is the standard deviation. Indeed, the model developed has, out of a base of 28 experiments, showed a standard deviation in the design resistance predictions of 0.21 compared to 0.51 and 0.56 for Eurocode and BBK respectively. If a 4 pile cap without shear reinforcement was to be designed using the 3D strut-and-tie model, it would, in average, resist 1.61 times the load it was designed for and there is 5% chance that is fails below 1.26 times this load and less than 1% chance that it fails below 1.12 times this load. On the other hand, if the pile cap was designed, aiming at the same resistance, by the Eurocode, it would have resisted, in average, 1.64 times the design load but the 5%
and 1% failure safety proof are reached for loads equal to 0.8 times and 0.45 times the design load (respectively 2.10, 1.18, 0.8 with BBK) Therefore, if a designer is conscious of these variations and wants to guarantee a 1% failure safety for the structure (without taking into account partial safety factors on loads, which will greatly improve the safety) it means that he would have to aim at a load 2.5 times higher when designing with Eurocode compared to using the 3D strut-and-tie model.
Another way to express this is that, if a pile cap is designed, aiming at resisting a given load there is a risk of 10,5% that is fails before this load if designed with EC2, 2,5% if designed with BBK and 0,18% if it is designed with the strut-and-tie model.
If the average resistance and standard deviations evaluated from the 28 pile caps reported are considered as true, it means that tremendous improvement in design can be made using the 3-D strut-and-tie model. Although the database tested is too small to guarantee these conclusions, the trend is clearly shown that design with the 3D strut-and-tie model is more consistent, and thus more effective than sectional approaches.
The feeling of Skanska’s designers that design according to BBK for punching was very drastic is confirmed by the high numbers of too conservative predictions of punching to EC2. Indeed, in some cases where the geometry is specific the BBK control perimeter definition is not good and slightly better results can be obtained applying the Eurocode procedure.
However, it should be pointed out that both design methods are of poor quality as shown by the high standard deviations. Indeed, even if the definition of control perimeters in EC2 is more advanced than the one in BBK, it remains a sectional approach, a method that is questionable for the analysis of pile caps and disturbed regions in general.
Swedish pile caps designers have to be aware of that the forthcoming change from BBK to EC2 design code will not solve their pile caps design issues. The improvement of the pile cap design relies on the acceptance that design procedures based on sectional approaches are not adapted to pile caps. The use of a design approach based on the well established strut-and-tie method, like the model presented in this thesis, is the most accessible way to greatly improve the design of pile caps.