Chapter 6 Experimental results
6.3 Soil stress field
6.3.3 Calculated static stress field: soil-cell model assumption
In Chapter 5 it is shown that the linear assumption for the interpretation of the pressure cells output in terms of soil stresses, as was assumed in the above section, is not correct. Thus to obtain a correct picture of the stress field, we need to investigate closely the soil dynamics and then the stress history during driving. The model described in Chapter 5 is a history-dependent model; that means that, in order to calculate the stress at a given point, at a particular instant in time during the pile driving history, it is necessary to know the full past stress history before that point.
The incremental state of stress in the soil after each impact of the hammer on the pile is the result of the transient stress history. This in turn implies that for a given transducer the final static stress field can be calculated using the model only by going through the full dynamic time history of stress at each blow. This has been done for selected transducers, and permits the same presentation of results to be made, as in the case of the linear assumption.
6.3.3.1 Implications of the soil-cell model assumption
Before presenting the results obtained using the soil-cell interaction model, it is necessary to say how the complete stress history throughout the driving, needed as input to the model, is obtained.
Recreating the missing blow histories
The dynamic data for each transducer are available only for every tenth blow.
To record the complete history for each blow of every transducer for every test would have required equipment not available physically or financially. However, the procedure to be described can be justified by the fact that over 10 blows, the increase in depth of the pile is sufficiently small that the sensor sees practically the same waves coming from the pile.
In the previous discussion it was pointed out that a stress interpretation by the nonlinear transducer calibration model requires a complete stress history. As the transient stress record for a transducer is available for every tenth blow only, this history is lacking for the previous 9 blows of each recorded blow. In order to get the complete history, it is necessary to recreate the effects of these 9 blows. The following reasoning to recreate the missing dynamic histories of the blows was used.
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Figure 6.3.3.1.a shows values of stress directly evaluated from the output voltage values of the transducer from dynamic and static records. For all the measurements obtained from the dynamic records there is only one value every 10 blows; in between we link the points by a straight line (i.e., linear interpolation). The following is presented:
1. the measured stress at the beginning of the dynamic record for each recorded tenth blow ( axis shows "calibrated" line);
2. the measured stress at the end of the dynamic record ( dashed line);
3. the measured static stress at each blow from the static record of the second ATD (solid line);
4. the peak transient stress during a blow ( dotted line);
5. the minimum transient stress during a blow ( dotted line);
The correlation between 1, 2, and 3 confirms that the use of the linear interpolation does not bring significant modifications of the measured static stress history. Therefore, to recreate the missing blows we could use a linear interpolation of the recorded ones.
Now, from Figure 6.3.3.1.b which shows the history of incremental (1st order deriva- tive) measured stress, we see that the peak and minimum stress incremental histories are very different. It can be seen that the peak transient value can increase while the min- imum value decreases. If a linear interpolation of a record is done, it is not possible to obtain simultaneously an increase of the peak and a decrease of the minimum, but only an increase or a decrease of both the peak and the minimum. Therefore, the use of the linear interpolation to create the missing blow histories would then have unwanted consequences such as the distortion of the expected signal.
The choice was made to repeat each blow 10 times, which replaces the linear inter- polation by a step approximation. This, in turn, implies that the same final static output will be found 10 times, which will not correlate well with the static data. Thus, the final output values for each blow will be given by the static data.
To calculate the stress field at a given time the following steps have to be followed:
1. reconstruct the blow history by using the method described above ( i.e., repeating the effect of blow 20 for blows 16 through 25);
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2. implement the correction given by the static stress field (which corresponds to adding an extra point to each blow);
3. run the complete blow history through the model;
4. write on file for each blow the static stress and output, the peak and minimum transient stresses and output, and the absolute maximum stress and output encountered.
Implication of soil-cell model assumption for one blow
Figure 6.3.3.1.c shows the transient records of a transducer located at Z/ A
=
26.67, R/ A
=
2.67 obtained using the linear assumption and the soil-cell model. There are shown on the figure are several characteristic points on the records such as initial, peak, minimum, and final points. The points are also shown in Figure 6.3.3.1.d where the calculated stress is plotted versus the measured stress. In the case of the linear assumption, the calculated stress is equal to the measured stress, so the points lie on the diagonal. For the use of the model, the logarithmic decay and the asymptotic reloading can be followed.The points are not on the diagonal anymore, and lower values of stress compared to the linear values are observed.
Figures 6.3.3.1 e and f present the same sequence as Figures 6.3.3.1.c and d, for the same transducer, with the pile at a depth of D / A
=
26.8, instead of 22.6. The transient record then shows tensile stress instead of compression stress. The stress level is far below the past maximum stress, and there is then no contact between the hysteresis behavior of the stress signal and the diagonal line of the linear assumption.Comparison in the dynamic history between the linear and soil-cell model assumptions
To illustrate the difference between the linear assumption and the model as- sumption, we first compare the stress history (min, max, and static), measured (linear assumption), and calculated (model assumption), for one particular transducer in a given test.
The results are given in figures 6.3.3.1.g to 6.3.3.1.k. The derived results from the model were obtained by running the model through the complete dynamic data. The following can be said about the resulting static values:
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a. It should first be said that globally the behaviors in the linear and model assumptions are the same with differences of amplitude but not of physical representativeness.
b. The smoothed steps that can be seen on the plots are due to repeating each blow 10 times.
c. Figures 6.3.3.l.g and h: globally, it can be said that the transient peak and minimum stresses in the model assumption have a greater value relative to the static value than to the linear assumption.
d. Figures 6.3.3.l.i, j, and k show the comparison of peak stress (i), static stress (j), and minimum stress (k), for the linear and model assumptions. The two peak stress (i) histories are the same as the stress increases, but show small differences as they decrease, since the model peak stress is lower, as expected from the behavior of the model. The minimum stress (k) histories are quite different and show large differences in amplitudes. This is due to the fact that the minimum stress corresponds to the point on the logarithmic decay curve, which gives the biggest difference in stress for a given transducer output. The static stress value (j) according to the model is substantially lower than the value given by the linear assumption. In a certain way it can be said that the model takes into account the existence of an "integration" part in the filtering effect the soil has on the stress dynamics. Another conclusion is that this difference repeated over an entire driving history will result in a substantially different set of final values of the residual stress field after driving.
Figure 6.3.3.1.l shows the entire dynamic history, blow by blow both, both in the linear and model assumptions of the transducer located at Z/ A= 26.67, R/ A= 2.67, (PT3, T90), which illustrate completely what is described above in terms of peak, minimum, and static stresses.
6.3.3.2 Calculated stress distribution
Figure 6.3.3.2 presents the values of the radial distribution of the static radial stress field once the model has been applied (T70, PTl to PT5). The same test and transducers presented in Figure 6.3.1.l.b were chosen so that comparison would be facilitated. Globally, as mentioned in the previous section, the behavior is the same as in figure 6.3.1.l.b., with amplitudes and residual stress, however, sensibly less important.
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From the model, we now know that the soil experiences very large transient stresses that will be largely dissipated since the static stresses are comparatively small. We expect therefore a lesser effect from pile driving on the soil than the linear assumption was previously telling us.
Figures 6.3.3.3.a and b present the values of the vertical distribution of the static radial stress field once the model has been applied (T90, PTl to PT6). The same test and transducers presented in Figures 6.3.1.2.a and b were chosen so that comparison would be facilitated. As stated above, the same global behavior for the driving history is observed, but sustantially lower stress levels are obtained. In Figure 6.3.3.3.b, the normalization of the static radial stress by the overburden stress is not meaningful anymore.
Figure 6.3.3.4 shows the comparison of the linear and model assumptions for a pair of transducers seeing radial and vertical stresses (TAO, PT2 and PT6). For both the vertical stress and the radial stress history, similarity in behavior is observed between the linear assumption and the soil-cell model results, with a reduction in the level of stress for both cases calculated by the use of the model.
Contours of the radial stress field are shown in Figures 6.3.3.5 a and b, for a pile depth of D / A