PART 1. AN INTRODUCTION
This appendix gives the calculation methods used to derive the results of
pressuremeter tests. Most of the theory is concerned with expansion
pressuremeter tests but all three types of test used on this contract are
considered.
1.1 The determination of material properties from pressuremeter tests in
soil.
There are two well established approaches to the interpretation of expansion
pressuremeter test data. The first, developed by Menard, uses empirical
correlations to allow measured co-ordinates of pressure and displacement
to be inserted directly into design equations. This approach depends on a
standardised test procedure and a large data bank of pressuremeter tests
correlated with observations of the response of finished structures.
The second approach, which will be described briefly here and is the usual
way of interpreting the pressuremeter test in the UK, relies on solving the
boundary problem posed by the pressuremeter test.
The aim of the pressuremeter test is to expand a long cylindrical cavity
within an undisturbed mass of soil. Fundamental strength properties of the
material can be deduced from measurements made of cavity pressure and
displacement.
In practice no instrument can be placed into the ground without affecting
in some way the surrounding soil. In the case of a self-bored pressuremeter
test the disturbance is often within the elastic range of the soil and can
be allowed for in the analysis procedure.
1.2 The pressuremeter test in soil - initially elastic response/failure
in shear
Consider that the soil is homogeneous, and shows simple elastic behaviour
before failing in shear. The stress path followed by an element of soil adjacent
to the cavity is given in figure 1 and the corresponding pressure /strain
curve is shown alongside.
The radial stress, ideally at the insitu horizontal stress for a perfect installation, increases at the same rate as the circumferential stress decreases, regardless of whether the material is deforming under plane strain or plane stress conditions. The line 0 - 0 represents stress equality, so that in the ideal case considered here the point po is the insitu lateral stress.
Once the radial stress increases above the insitu stress then the shear stress in the soil at the cavity wall will increase. If the insitu lateral stress is low, then it is possible that the circumferential stress would go into tension. However in this example the insitu stress is high enough to ensure that the shear stress limit is reached before tensile stresses can be generated.
The pressure necessary to initiate shear failure is denoted pf in figure 1. After this pressure the strain rate shows a substantial increase, and the form of this part of the pressure/strain curve is a function of the shear strength of the material.
Fig.1 Elastic response followed by failure in shear
Radial stress and circumferential stress now increase together. If the shear stress limit is constant, and is not influenced by pressure, and if the material deforms at constant volume, then the failure shear strength can be determined by the analytical solution developed by Gibson & Anderson (1961).
Before the shear stress limit is reached the pressuremeter response is elastic, both in loading and unloading. Assuming the soil deforms at a constant modulus and the installation is perfect then the slope of the initial loading path gives the shear modulus of the material, using the classic procedure of Bishop, Hill & Mott (1945). The diagram also indicates that reversing the direction of loading causes an initial elastic response giving an alternative means of deriving the shear modulus. This implies that small cycles of unloading and reloading taken anywhere in a test after reaching the shear stress limit can be used as a source of stiffness information (Hughes 1982).
As figure 1 suggests, the complete unloading of the pressuremeter can also be used to give strength and stiffness parameters comparable with those obtained from the loading path.
From the right hand side of the stress diagram it is apparent that the pressuremeter provides only a limited set of the necessary information for resolving the stresses and strains around the probe. Specifically it gives the changes in radius of the borehole wall (a special case of hoop strain) and the corresponding changes in radial stress at the borehole wall. There is no data for hoop stress or radial strain or movements in the vertical direction. Test procedures are chosen to allow the missing data to be inferred – for example an undrained expansion means shearing occurs at constant volume and hence changes of radial strain must be equal and opposite to changes in hoop strain. The unseen vertical axis data are rendered redundant by making pressuremeters long with respect to their diameter, allowing plane strain expansion to be assumed.
1.3 Defining strain
For a pressuremeter measuring the radius of an expanding cavity the conversion
from displacement to strain is [R-Ro]/Ro, where R is
the current radius of the cavity and Ro is the original radius of the cavity
in the insitu state. This is simple strain and when displacements
are measured at the borehole wall is termed cavity strain,
ec.
Ro can be approximated by the at rest radius of the instrument. The preferred approach is to identify when the applied pressure has reached the insitu lateral stress, and interpolate from this the corresponding radius, which then becomes Ro.
Note that although the pressuremeter measures the radius of the cavity wall, ec is actually a specific instance of circumferential or hoop strain. It is usually expressed as a percentage.
Figure 2 shows how pressures and strains in the expanding borehole are
defined.
Fig.2 Pressures and strains around the expanding cavity
The other strain commonly used is the constant area ratio, which is shear strain. As figure 2 indicates it can be expressed in terms of simple strain.
1.4 Average displacements versus the output of the separate axes
There are a number of displacement sensors in the expansion probe but recommended
practice is to quote parameters from the average displacement curve. This
is for two reasons:
These remarks assume that the instrument is in full working order throughout the test - failure of a displacement follower means that alternative strategies must be adopted.
The significance of the first point above has been demonstrated by an examination of cycles of unloading taken from separate arms (Whittle 1993) and by work with a six arm version of the SBP (Whittle et al 1995). In the case of the 3 arm SBP an exception is often made for the initial part of the loading prior to yield. In such circumstances the response of the separate arms may yield clues to the initial stress state in the surrounding soil, allowing an assessment of the degree of insertion disturbance.
For the LCPM where the state of stress around the probe is supposed to be within the elastic range of the material at all times then the output of the separate transducers is of interest. However no cell can register deflections without the local changes in stress having an influence all around the probe and so the average of all cells has a special significance.
1.5 The analysis program
We use (and supply to others) software for analysing a pressuremeter test.
The program is called INSITU, it has been in use for a number of years
and is well proven.
To use the program the user must first read in a text file of test data in engineering units. The program needs to know the type of instrument being used, and the user may choose to enter additional background information about the test.
The next task is to identify for the program the nature of the individual
data points. Broadly, the options are these:
There is a quick on-screen routine for marking the points. Once marked, they appear in different colours and have different shapes (so that the distinction can be made clear on a black and white printout). Most of the analyses use a limited set of the available data - for example the Gibson & Anderson analysis for undrained shear strength uses only points on the expansion curve.
The program implements all the standard analyses mainly in a graphical form. As figure 1 implies, there are significant changes of gradient in the pressure/strain curve which denote critical soil parameters. The user of the program is provided with on-screen tools to mark these breakpoints or to obtain the slope of the loading curve. The tools can be visualised as rulers, and the chosen position of any ruler is stored by the program in the file of test data. The evidence for any derived parameter is a screen dump of the appropriate analysis that shows the position of any rulers set by the user and quotes the parameter obtained.
Even when the user declines to make a choice it is good practice to provide the screen dump as evidence of why a choice is difficult.
The results for a test appear as a summary sheet of derived parameters followed by a number of plots showing the application of the various procedures.
Sometimes analyses are required which are not included in the INSITU program. In such instances commonly available spreadsheet software is used to implement the new analysis. Inevitably in such circumstances there is some risk of human error affecting the conversion of data in engineering units to the form required for analysis. INSITU has comprehensive export facilities and wherever possible is used as the data source for the spreadsheet.
The program is primarily for use with expansion pressuremeter tests of relatively short duration. The LCPM and PERM tend to make large files and so extensive use is made of spreadsheet facilities to present and interrogate the data.