Area constant pre-loading and unloading (often called a K0 test) are a preferred way to simulate the geological processes from, for example, the build-up and melting of the ice cap that covered the Scandinavian countries during the ice ages. This approach also aims to minimize soil disturbance from extraction and handling of the sample before shearing.
Top image shows GDSTAS Triaxial Automated System, now capable of indirect as well as direct K0 constant area testing (courtesy of Torben Thorson, Geo).
The Challenge of Controlling Constant Sample Area in Triaxial Tests
The so called K0 test may be manually performed, but is extremely tedious and generally inaccurate as it requires an operator to be constantly adjusting the cell pressure in order to maintain constant area as the sample is loaded. With the advent of computer controlled triaxial testing systems with software control of axial strain/stress and radial stress, the K0 (constant area) test may be performed automatically under software control.
GDS Instruments were one of the first companies to develop a computer controlled K0 test by developing what we call the ‘direct’ method of control. In this direct method, the user selects a constant rate of change of cell pressure, and the computer monitors the area change either by calculating the area from the volume change of the back pressure controller or by directly reading a local radial strain belt. When a change in area is detected, the software instructs the height of the sample to be adjusted as a proportion of the radial change observed. The radial strain is then measured again, and further changes in height are applied as necessary, and this iterative process continues. We call this the direct method because the relationship between the radial strain observed and the axial strain applied to maintain constant volume can be calculated directly and so the test is well controlled and requires no user input. GDS users have had good success with this method for over 25 years since it was first introduced.
Fig 2: In the direct method, cell pressure ‘leads’ and the area is corrected by adjusting axial strain.
A number of users have expressed that more traditionally a K0 test would be performed with axial strain or axial stress as the primary governing ‘lead’ control parameter, with the cell pressure being the secondary control in order to maintain the area. We call this the ‘indirect method’ because the nature of adjusting the cell pressure to control radial strain does not have an obvious relationship, instead it relies on many parameters such as soil stiffness, anisotropy, stiffness of the system (i.e. the cell wall), stiffness of the cell fluid and control system as well as time rate effects of all of these mentioned parameters. In summary, the challenge is how much to change the cell pressure to achieve a particular radial strain change, with the additional challenge that strain responses are far from instant.
Fig 3: In the indirect method, axial strain (or stress) ‘leads’ and the area is corrected by adjusting the radial stress.
Results: Diameter Constant
Figure 4 shows the result. The test progressed from a deviatoric stress from 0kPa to 300kPa and as can be seen, the radial strain for both loading and loading was maintained to within 2µm in both the loading and unloading stages.
Fig 4: Current diameter maintained to within 2µm (courtesy of Torben Thorson, Geo).
Results: Stress Path
The resulting stress path is shown in figure 5
Fig 5: Resultant Stress path (courtesy of Torben Thorson, Geo).
Conclusion
Maintaining the diameter (area constant) to within 2um was considered a huge success, perhaps better than was even expected. As such, K0 (area constant) using this indirect method (axial stress or strain as the lead control) was released in April 2025 as part of the Advanced Tier 3 K0 test module.
About Geo
Geo is a Danish engineering consultancy, offering the most extensive expertise in Denmark, within the fields of soil and water.
Geo deliver a complete consultancy including fieldwork and laboratory tests, design and planning, control and inspection as well as qualified documentation. Geo works both onshore and offshore, nationally and internationally. Geo is a privately owned industrial foundation.