Civil Engineering Reference
In-Depth Information
displacements at the ends of the sample, (2) displacements where the loading ram joins
the top platen, (3) movements in the load cell and (4) movements in the cell.
The errors that can arise due to the compliances illustrated in Fig. 13.7(a) can be
very significant and can easily swamp the required measurements of small strains.
In conventional triaxial tests the measured axial strains are unreliable at strains smaller
than about 0.1% irrespective of the resolution and accuracy of the transducer or dial
gauge. If a hydraulic triaxial cell is used and if very careful measurements are made of
the displacements in the apparatus, it is possible to obtain reliable measurements of
axial and volumetric strains smaller than 0.01%. One way to improve the accuracy
of measurements of strain in triaxial tests is to use gauges inside the cell mounted
directly on the sample, as shown in Fig. 13.7(b). Using these kinds of instruments
strains smaller than 0.001% can be measured reliably.
It is very difficult to measure the stiffness of soil at very small strains (i.e. less than
about 0.001%) in triaxial tests by direct observations of strains. The simplest method
is to calculate the shear modulus from the velocity of dynamic waves. The very small
strain shear modulus
G
0
is given by
V
s
g
G
0
=
γ
(13.7)
where
V
s
is the velocity of shear waves through the sample,
γ
is the unit weight of
9.81m/s
2
. Shear waves can be generated and their velocity measured
directly using shear elements set into the top and bottom platens or from resonant
frequencies in torsional shearing. The equipment and techniques for making these
measurements are rather specialized and if you need to determine
G
0
you will need
help; it is enough now to know that the techniques are available.
Note that in these dynamic tests the rates of loading are very large and saturated soil
will be undrained. This does not matter for measurement of shear modulus since, for
shearing alone,
G
=
the soil and
g
=
G
u
. The undrained bulk modulus of saturated soil is theoretically
infinite (since
0 for undrained loading) and so we cannot easily determine the
small strain bulk modulus
K
0
of saturated soil from the velocity of compression waves.
Figure 13.8 summarizes the principal features of the application and measurement of
soil stiffness over a wide range of strain. In the field, strains in the ground near retaining
walls and below foundations are relatively small and are usually less than 1%, except
in small regions near the edges of foundations. Stiffness cannot be measured reliably in
ordinary triaxial tests at strains less than 0.1% unless special procedures are followed,
so the ordinary triaxial test is not much good for measuring soil stiffness in the range of
practical interest. Stiffness at small strains can be measured reliably using local gauges
attached to the sample and the shear modulus at very small strain
G
0
can be obtained
from measurements of shear wave velocity.
δε
=
v
13.6 Stiffness of soil at small and very small strains
At large strains (i.e. greater than about 1%) the state of lightly or heavily overconsol-
idated soil will have reached the state boundary surface and the stiffness parameters
in Eq. (13.1) depend on the current state (
v
,
p
and
η
) as given by Eqs. (12.18) to
(12.20). For states inside the state boundary surface, at small and very small strains,
