PART 6 THE HOLDING TEST
6.1 Background
The measurement of consolidation with the SBPM arises from the work by Randolph
and Wroth (1978). The paper gives an analytical solution for the consolidation
of soil around a driven pile assuming radial pore water flow, and an elastically
deforming soil skeleton under plane strain conditions. The solution combines
Hooke’s law with Darcy’s law and the authors suggest it could be
applied to a pressuremeter measuring pore water pressures after expansion
to a fixed volume. This suggestion was adopted and written up by Clarke et
al (1979) and forms the basis of the procedure and analysis described here.
The analysis assumes the material deforms as linear elastic/perfectly plastic. There is a well known closed form solution for an undrained expansion in such material (Gibson & Anderson 1961) already referred to earlier. The solution is
pc = po+cu[1+ ln(gce)-ln(gye)] ... [Equ.47]
using nomenclature previously applied.
An inspection of equation [47] shows that subtracting the yield stress,
po + cu results in an expression for the magnitude
of excess pore water pressure generated by the expansion:
u/cu = ln[gce/gye] ... [Equ.48]
For a particular value of shear strength, therefore, the magnitude of the excess pore water pressure is merely a function of the ratio gye (the shear strain to initiate plasticity) to gce (the current cavity shear strain). gye is obtained from cu/G. In linear elastic terminology G/cu is rigidity index.
The holding test is a procedure whereby a quick undrained expansion is carried to some large cavity strain (about 8% is typical) at which point the expansion is halted and the radius of the expanded borehole is fixed. The excess pore pressure decays, and the time taken for 50% of the excess to dissipate is introduced into the following expression:
ch=T50ro2/t50 ... [Equ.49]
Where
The time factor T50 is taken from a published curve of the variation of time for 50% consolidation against the pore pressure ratio Umx/Cu. The source is Randolph, Carter and Wroth (1979) and an edited version of this plot is given in figure 21.
Fig.21 Randolph et al (1979) Variation of Time for 50% Consolidation
To produce a value for horizontal consolidation the steps are as follows:
6.2 The Holding Test Analysis in Practice
Figure 22 is an example of the observed stress decay from EP1 Test 5. Total
stress and the output of the pore water pressure transducers are plotted
and it is apparent that the effective stress is increasing slowly as a
consequence of consolidation. The performance of the two pore water pressure
transducers is similar but each starts from a different pressure.
It seems that much of the excess pore water pressure is lost in a short time after commencing hold and there is a suspicion that this is an artefact of the test rather than a true reflection of the characteristics of the soil.
Fig.22 Decay of stress during the holding test
For this reason we do not take the time for 50% decay from direct observation, but plot the natural logarithm of the decay versus time and take the half life from the most linear part of the data, i.e. from 150-400 minutes in this example. The same data as figure 22 are plotted in figure 23 with the results.
Fig. 23 Decay of Stress during Holding Test
For the pore water pressure curves it is the excess that is plotted, i.e. the ambient pore water pressure is deducted from the measured pore water pressure readings zeroed with respect to ground level.
The response of the total stress transducer is interesting. It is a fundamental assumption of the Randolph and Wroth analysis that the soil skeleton deforms elastically throughout so that the effective stress acting at the borehole wall (the surface of the pile in their analysis) should increase. For a driven pile where the soil has been taken to limit pressure, ultimately the limit pressure should act as the effective stress on the pile. The authors were well aware that this was not true in practice but argued the consequences for the analysis were minor, because consolidation behaviour is dominated by soil response at intermediate radii. The field data invariably show large changes in the total stress, albeit usually smaller than the changes in excess pore water pressure. In figure 23 the total stress response has been treated as if it was entirely due to consolidation. The excess pore water pressure component is obtained by deducting the yield stress from the total stress. The result is a value for the half life rather smaller than that from the measured pore water pressure decline.
Although the distribution of excess pore water pressure throughout the loaded soil mass is logarithmic there is no reason why the decay should be exponential. In particular as the voids ratio will be changing and hence the permeability it is likely that the rate of consolidation is also not constant. However in many such tests we have looked at it appears that the decay is exponential for a significant period of time. We surmise that much of the adjustment to permeability and voids ratio takes place in the initial period immediately following the start of the hold.
The non-linear elastic/perfectly plastic model predicts a slightly different
Umx than the linear elastic/perfectly plastic model because it
results in pore water pressure being generated throughout the elastic phase.
In the tests analysed on this contract the non-linear analysis of Bolton
& Whittle has been used to predict
gye and hence the time factor T50.
In practice this amounts to using a lower value of stiffness in the analysis
than the simple elastic case and is not a major source of uncertainty. The
preferred way of incorporating non-linear elastic behaviour would be to redo
Randolph & Wroth substituting the Bolton & Whittle (1996) analysis
for the Gibson & Anderson (1961) solution.
6.3 Deriving Permeability From Consolidation
Randolph, Carter and Wroth (1978) give the following expression relating
permeability to consolidation:
ch = kh/g wmv = [kh/gw][2G(1-n ¢)/(1-2n ¢ )] ... [Equ.50]
Where
The expression is correct assuming the soil skeleton only deforms elastically. Results for permeability obtained from SBPM tests quoted in the report assume n ¢ is 0.33 and G is the yielding value of stiffness, Gye.