109
Honour Lectures /
Conférences honorifiques
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
That is to say we have a P
target
% degree of confidence that μ
p
lies in the range μ
g
(1+or-∆). We can rewrite Eq.3 as
target
p
g
g
P
P
(4)
If the coefficient of variation of the population is δ, then we
assume that the coefficient of variation of the group is also δ.
p
g
p
g
(5)
Combining Eq.2, 4, and 5 we get.
2
2
, 1
, 1
2
2
g
g
n
n
t
or n
t
n
(6)
Eq. 6 is solved by iteration since n influences the value of t.
Student t distribution solvers are available on the internet. The
number n represents the number of soil samples to be tested in
order to obtain the value of the modulus within plus or minus
∆% from the exact answer with a P
target
probability of success. If
we assume that a triaxial test sample to obtain a modulus value
has a volume of 10
-3
m
3
, then the number n of samples gives the
volume of soil that must be drilled during the investigation to
satisfy the criterion. The percent volume tested becomes
3
10
s
t
t
V n
V V
(7)
In our example the initial volume was 1000 m
3
, so we can
calculate what percentage of the soil volume should be tested.
Fig. 4 gives the results and indicates that in order to be 98%
sure that the answer will be within plus or minus 20% from the
true value, the amount of sampling is 0.001 percent of the total
volume.
Figure 4. Required volume of soil to be tested as a percent of
the total volume involved in the soil response to predict a soil
property with a 98% confidence level and within a percent error
for given coefficients of variation of the soil property.
Consider now an 8 story building which is 40 by 40 m at its
base. The volume of soil involved in the response of the
building to loading is at least 40 by 40 by 40 m or 64000 m
3
.
The required sampling is 0.001% or 0.64 m
3
which corresponds
to 640 triaxial tests. Further assuming that we will drill 40 m
deep borings allowing us to conduct 20 triaxial tests per boring,
this would require some 32 borings. In practice, we would
typically drill 4 or 5 borings for such a building. This shows that
we do not test the soil enough in our current soil investigations
to meet the set criterion. Note that the assumptions made in the
student t distribution calculation include the assumption that the
soil is uniformly variable. In other words, there are no
heterogeneity trends or anomalies in the soil mass. If there were
such anomalies, the amount of soil volume to test would
increase. If we use the same approach for different volumes we
can generate the number of borings necessary to meet the
criterion of 98% confidence of predicting within + or – 20% for
a soil with a coefficient of variation equal to 0.3. Fig. 5 shows
the number of borings required as a function of the soil volume
involved in the response to the loading. The estimated line for
current practice is plotted on the same graph (based on the
author’s experience) indicating that current practice does not
meet the criterion established. Note that the discrepancy
increases with the size of the project. Indeed the ratio between
the required number of borings N
r
and the current number of
borings N
c
increases with the size of the imprint.
Figure 5. Comparison of number of borings in current practice
and number of borings required for a precision of + or - 20%
with a 98% degree of confidence for a soil parameter coefficient
of variation of 0.3.
5 WHAT CAN BE IMPROVED ABOUT THE PMT
EQUIPMENT?
Only a few things, I think. We are at the point of maturity in this
area. If anything, we need to be able to run controlled stress
tests or control strain tests equally well. Controlling strain or
volume has the advantage of not having to guess at the limit
pressure to decide on the pressure steps. Controlling pressure
has the advantage of not having to wait for a long time if the
hole is too big. The devices which control stress require
compressed gas bottles which can be dangerous. Control
volume devices are safer in that respect and still allow control
stress tests. Most civil engineering structures apply stress
control steps.
With regard to the issue of the three cells versus mono-cell
probes, it has been shown (Briaud, 1992) that for probes with a
length to diameter ratio longer than 6, the difference between
the expansion of the mono-cell and the expansion of an
infinitely long cylinder for an elastic soil are within 5 % of each
other. Therefore as long as the probe has a length to diameter
ratio of 6 or more, there is no need for three cells in a
pressuremeter probe.
The diameter of the probe has an impact on the quality of the
test for the following reason. The thickness of the ring of
disturbed soil created by the carving or washing process during
drilling is approximately constant regardless of the diameter of
the drill bit. As such, the larger the pressuremeter diameter is,
the less influence this disturbed zone will have on the
pressuremeter curve. Therefore, it is best to increase the
diameter of the pressuremeter probe. A larger diameter will also
have a positive impact on the reliability of the borehole
diameter as it is much easier to drill a well calibrated 150mm
diameter hole than a 50mm diameter hole. Using lightweight yet
rugged 150 mm diameter, 1 m long PMT probes will improve
PMT test quality.
