Dynamic Triaxial testing is performed on soils when it is necessary to evaluate their strength and deformation properties under cyclic loading conditions. These conditions might include dynamic loading coming from earthquakes, passing vehicles and trains, sea waves, wind, vibration machines, etc. There are many variations of Dynamic Triaxial tests, and the user should select the one that most accurately simulates the conditions in the field.
This guide, published by VJ Tech Ltd, is intended to give a brief introduction to the basic principles of cyclic Triaxial testing to the technicians who perform dynamic testing in geotechnical laboratories. Among others, it includes a description of the apparatus used in these tests and common and advanced testing procedures. It is strongly advised that the laboratory staff who undertake testing using the Dynamic Triaxial apparatus, have been trained on the equipment, have a basic knowledge of soil mechanics, and understand the required testing procedures before attempting actual tests. In the last section of this guide, books for further reading are suggested.
Apparatus and Accessories
A Dynamic Triaxial apparatus is usually an advanced version of a static Triaxial system. A sketch of a typical Dynamic Triaxial system is shown in Figure 1. It comprises the following components:
This needs to be sturdy enough to withstand the amount of load applied to the sample without deforming significantly. Also, it needs to withstand the vibration of the dynamic actuator and cope with the sudden changes in load during a cyclic test. Some variations of load frames can be used for both Static and Dynamic Triaxial tests.
The dynamic actuator enables the load frame to apply cyclic load to the soil sample. It comes in different load capacities (e.g., 5 to 500 kN) and frequencies (0.1 to 20 Hz). The selection of the most suitable system will depend on the type of applications that the user is interested in and the type of specimens to be used for testing. Table 1 presents some typical frequency values for the most common applications. Normally, frequencies up to 1 Hz are considered adequate for most applications.
There are two main types of servo controllers available, Electromechanical and Hydraulic. The Electromechanical controller uses electrical power to convert it into mechanical energy and apply the load to the sample. On the other hand, a Hydraulic servo controller compresses oil to move the piston and apply the load. The capacity of the cyclic Electromechanical motors can range between 5 and 50 kN while a Hydraulic controller can reach capacities up to 500 kN. Regarding the frequency of the cyclic loading, the Electromechanical motors can reach a maximum of 10 Hz (i.e., 10 cycles per second) while the Hydraulic ones can reach 20 Hz. Finally, Electromechanical motors can be either one or three phases, with the latter achieving a higher load.
Dynamic actuators must have the ability to apply cyclic loading to the specimens using a specified waveform. The most common type of waveform is the sinusoidal, but other types might also be considered (Figure 2).
Triaxial Cell, specially modified for performing Dynamic tests.
The Triaxial Cell that is used in Dynamic testing is a modified version of the static Triaxial Cell. It uses an enhanced piston with a low friction seal to prevent overheating and reduce degradation during the cyclic movement of the ram. The Cells have three ports which are used for the control of the Confining Pressure, the application of Back Pressure to the specimen, and one with a transducer for the measurement of Pore Water Pressure (PWP) (Figure 1). Specially designed exit ports, that allow using internal sensors (On-Sample transducers) mounted on the specimen or Bender Elements, might also be available. The Top Caps that are used in Dynamic testing are usually fixed to the loading ram to allow for tension (negative stress) and are connected to the Back Pressure controller through the Back Pressure valve, from which the sample can be Saturated and Consolidated.
Automatic Pressure Controllers for adjusting Cell and Back Pressure
During the cyclic loading of the sample, the loading ram is moving in and out of the cell periodically. This causes the Cell Pressure to increase and decrease accordingly, altering the horizontal and vertical total stresses. There are, typically, four ways to overcome this issue. In the first case, an air pocket is left at the top of the cell which will “carry” the pressure fluctuation due to its high compressibility (in comparison to water which is practically incompressible). The second method involves the use of a Pneumatic Pressure Controller and an Air-Water Interface (Figure 3). With this configuration, the adjustment of the pressure is very quick and allows the Cell Pressure to remain constant even at high loading frequencies. Recent developments for the control of Cell Pressure include very accurate Automatic Hydraulic Pressure Controllers, with the ability to adjust quickly to pressure fluctuations, and Dynamic Pressure Controllers which perform cyclic adjustment of the Cell Pressure. The method chosen depends on the required accuracy and the available budget.
The Back Pressure controller is usually hydraulic and pumps water into the sample through the top end. It is used to saturate the sample by pushing water in and therefore forcing the pore air to dissolve into it. Back Pressure controllers often can measure the volume of the water that moves in and out of the sample and, therefore determine the volume changes of the sample after its saturation.
Load measuring sensor (Load Cell)
Load Cells are usually submersible (located inside the cell) to avoid the friction that appears between the loading ram and the cell. Moreover, the use of submersible load cells is considered essential in Dynamic Triaxial testing because they are not affected by the up thrust that is caused due to the increment of the confining pressure. Also, they are firmly fixed to the top caps to allow for tension. The capacity of the Load Cell depends on the sample size (the bigger the diameter of the sample the higher the load it can withstand) and the accuracy that the user needs. Typically, the Load Cells used have capacities between 1 kN and 50 kN.
Displacement measuring sensor
The Displacement Sensor must be mounted on the loading ram to follow the exact deformation of the sample during the cyclic loading. They are usually Linear Strain Conversion Transducers (LSCTs) and they can have a maximum stroke of 100 mm. An alternative method of measuring the deformation of the soil sample is the use of electromechanical actuator pulses which are converted into displacement while the motor is moving.
Pore Water Pressure measuring sensor
Pore Water Pressure is measured using a pressure sensor connected to a port at the bottom of the soil sample. The pressure sensor used for this purpose must have the ability to measure pressures at a higher rate (i.e., faster) than in a static Triaxial system.
Data Acquisition System (DAS)
The Data Acquisition System needs to be able to capture data at a high speed, up to 500 samples per second. In this way, the resultant waveforms are plotted very accurately, and soil behaviour can be captured in detail.
1.2 Testing Standards
The most used testing standards for Dynamic Triaxial tests are ASTM D5311-13 and ASTM D3999-11. The first one refers to the procedure for cyclic Triaxial testing in soils, under load control, to determine the cyclic shear strength or liquefaction potential of a soil sample. The second method refers to the determination of the Secant Modulus and Damping properties from a Cyclic Triaxial test. However, there is a wide range of test variations that the user can adopt which can be found in the literature.
1.3 Testing Procedures
a. Sample Preparation
The preparation of a soil specimen, subjected to cyclic loading, is identical to the preparation that is followed in static Triaxial tests (see also: Triaxial Testing – An Introduction support document by VJ Tech). Special consideration should be given to the state properties of the sample, such as the initial density, water content, compaction method, etc. as all these factors affect the results. The sample is sealed within a rubber membrane to avoid direct contact between the soil and the confining fluid. Two saturated porous discs are inserted at the top and bottom of the sample, in contact with the Top Cap and Base Pedestal, respectively.
To saturate a soil specimen in Dynamic Triaxial tests, we follow the same procedure as in static Triaxial tests, i.e., by gradually elevating the Back pressure so that pore air is dissolved into pore water. Saturation checks are performed by elevating the confining pressure to the specimen and keeping the drainage valve closed. The B-value is then calculated as the change in the Pore Water Pressure to the change in the Confining Pressure:
where ΔU is the change in the Pore Water Pressure of the specimen which is caused when the Confining Pressure changes by ΔCP.
Usually, when the B-value is greater than 0.95 the soil is considered fully saturated, though for some soils lower values are considered acceptable.
Consolidation of the soil specimen is necessary to establish the desired stress state and apply the correct effective stresses prior to the cyclic loading. Consolidation can be either Isotropic (i.e., σ1 = σ3, in other words, no axial stress is applied to the sample through the ram and deviator stress remains at 0 kPa) or AnIsotropic (σ1 ≠ σ3, in other words, the sample is loaded to increase the vertical stress; therefore, some deviator stress is applied to the sample). During consolidation, the drainage valve remains open to allow drainage and dissipation of the excess Pore Water Pressure.
During Isotropic consolidation, the change in sample volume will be equal to the volume of water that was removed from the sample, since this was already saturated in the previous stage. Therefore, the volume of water that drains out of the sample is recorded and plotted against the square root of time (Figure 4a). Moreover, the dissipation of the excess Pore Water Pressure can be plotted against time (Figure 4b). Consolidation is considered completed when either the excess Pore Water Pressure has been dissipated by 95% or when the volume change has ceased.
The type and level of Consolidation to be applied to the sample depends on the application in which the test results will be used. Although Isotropic Consolidation is usually considered adequate, it cannot replicate the exact stress conditions in the field. In general terms, soils are subjected to a higher vertical than horizontal stress because of the weight of the overlaying soil strata. This is expressed with parameter K, which is defined as the ratio between the total horizontal stress (σh) and the total vertical stress (σv):
The higher the depth of a soil layer the lower the K value, as the weight of the overlaying soil is increasing. In most cases, 0 < K < 1, however, there are cases where K can become greater than 1 (e.g., after an excavation). An example of an Anisotropic Consolidation test is shown in Figure 5, where the ratio between the axial and horizontal effective stresses is equal to 0.75. The application of deviator stress to the sample, during the Anisotropic consolidation, causes an excess Pore Water Pressure which needs to dissipate completely. For this reason, the rate of sample loading needs to be low enough to allow for this. Finer soils require a much lower loading rate than coarse ones. Sample volume change in Figure 5 indicates the volume of the water draining out of the sample; therefore, Anisotropic Consolidation is considered complete when water drainage is finished.
d. Cyclic loading
Cyclic loading can be applied to the specimen using the mechanical or hydraulic actuator of the dynamic system. The amount of cyclic loading to be applied depends on several factors, such as the effective stresses established after the Isotropic Consolidation (or the difference between the cell and Back Pressure), the soil type, the soil state (density, moisture, etc.) and the loading characteristics (frequency, waveform type). As a general rule, the cyclic loading is usually double the Isotropic effective stress, multiplied by a factor (i.e., Stress Factor). Stress Factor usually ranges between 0 and 1 and its effect on the number of cycles that a soil can withstand is shown in Figure 6. As an example, for soil that has been isotopically consolidated to an effective stress of 100 kPa, cyclic loading should be ±100 x SF Newton.
Note that in cohesion less soils (e.g., sands), the negative axial stress that is applied during the cyclic loading should not exceed the effective stress that has been applied during Consolidation, otherwise, the top platen might detach from the top surface of the specimen. For example, a specimen that has been isotopically consolidated at 100 kPa can accept negative stress up to -100 kPa (ASTM, D3999-11).
During cyclic loading, Pore Water Pressure increases AS in the example shown in Figure 7. The best way to evaluate this increment is to use the Pore Water Pressure ratio (ru) which is defined as:
where Au is the change in Pore Water Pressure and the effective axial stress at the beginning of cyclic loading. When ru=1, the excess Pore Water Pressure becomes equal to the initial effective stress which indicates that the shear strength of the sample has become zero and therefore failure initiates.
e. Failure criteria
The most common failure mode that occurs in soil specimens that are subjected to cyclic loading is liquefaction. Liquefaction is defined as the total loss of shear strength which happens when pore pressure increases so much that it becomes equal to the total stress. Based on Terzaghi’s definition for effective stress:
where is the total stress acting on a soil element, is the effective stress, and is Pore Water Pressure. At the liquefaction state, total stress (σ) is equal to the Pore Water Pressure (U), therefore the effective stress (σ’) becomes:
In other words, when liquefaction occurs, soil grains are no longer in contact with each other (i.e. effective stress = 0) and the soil behaves like a liquid. Liquefaction mostly occurs in loose sands under undrained conditions with a small proportion of silt/clay.
The definition of failure initiation in a sample is subjective. Many researchers have proposed several failure criteria for cyclically loaded specimens. Some of them are:
· When Pore Water Pressure ratio (ru) becomes equal to 1 (see section 4d)
· When Double Amplitude or Single Amplitude shear strain (Figure 8) becomes 6% (Wu et al, 2004)
b. Stress Path
One of the factors which has an impact on the dynamic testing results is the stress history of the soil sample, i.e. how this soil layer has been progressed since it was deposited. Factors that can affect the stress history of a soil are saturation – desaturation (change in effective stresses), deposition of new soil layers on top of it (increment of vertical stress), degradation of overlaying soil layers (reduction in vertical stress), earthquakes (horizontal loading) etc. Therefore, in several instances, it is important to either replicate these conditions to a soil sample or re-create new scenarios that might affect their stress regime. For example, an excavation will reduce the vertical load to the soil which will have an effect on the dynamic loading.
Stress history can be applied to the sample by running a Stress Path testing stage before the cyclic loading. There are generally two ways of plotting stress paths, the Cambridge system and the MIT system, with the earlier being the most often used. Based on the Cambridge system, stress paths can be plotted in terms of two variables, the deviator stress (q) and the total stress (p), which are defined as:
In terms of effective stresses, the stress parameters become:
where U is the Pore Water Pressure. However, since in Triaxial tests σ2 and σ3 are both equal to the confining pressure, parameter p can be expressed as:
During the stress path stage, deviator stress and total stress are adjusted in such a way to create the desired stress state in the specimen. Figure 10 shows a soil specimen which is subjected to various combinations of q and p.
c. Determination of Secant Modulus and Damping properties from cyclic Triaxial tests
The cyclic testing of a Triaxial specimen can lead to the determination of the modulus and damping properties. The process, in this case, involves testing either multiple specimens at different cyclic loads or deformation or the same specimen with a progressively increased cyclic load or deformation. The deformation of the sample should be elastic and no permanent changes in the specimen’s dimensions should be allowed. For most soils, this means that the axial strain should be less than 0.1%, even though this might be slightly different depending on the soil type and packing. The testing procedure is described in detail in ASTM D3999-11 standard.
d. Bender Elements and On-Sample transducers
Bender Element is a non-destructive testing technique that is used in parallel with other testing (e.g., Dynamic Triaxial) to provide an estimation of the small strain shear modulus (Go) of soil. To perform a bender element test, a special set of Base Pedestal and Top Cap is required to be used on the Triaxial cell. This set includes a pair of thin piezo-ceramic plates (i.e., bender elements) that penetrate slightly into the top and bottom of the sample. One of the piezo-ceramic plates produces a shear wave that travels within the sample and is captured from the other element (Figure 11). The distance and time of travel indicate the velocity of the wave through the sample (shear wave velocity) and as such the Go is defined as:
where Pb is the bulk density of the soil and V the shear wave velocity. Bender Element tests can be run through the cyclic Triaxial test and Go can be measured at different stages of the test, for example before and after Anisotropic Consolidation.
If the cyclic Triaxial test requires a very accurate measurement of the sample volume changes, then On-Sample transducers can be mounted on it. They usually include 1 or 3 sensors for measuring diameter changes (in the upper, lower and middle part of the specimen) and 1 to 3 sensors to measure height changes. In some occasions, miniature Pore Water Pressure transducers can be mounted into the sample to directly measure the variation of the Pore Water Pressure within the specimen.
e. Dynamic testing in Unsaturated soils
Recently, some efforts have been made to cyclically load unsaturated soil specimens, i.e. with both air and water contained within their pores. This is a particularly complex testing procedure due to the difficulty in measuring the volume change of unsaturated soils. One common technique is the use of normal Dynamic Triaxial apparatus in which the soil specimens are prepared under a specific moisture content, less than the saturated one. In this case, the whole testing procedure is performed in undrained conditions to preserve the sample moisture and therefore suction. Another way of performing such tests is the use of a combined unsaturated and dynamic cell, which can be used in order to allow for suction control (using the axis translation technique) within the specimen and provide accurate measurement of volume change through a volume change device.
For more information or to speak with one of our experts about our Dynamic Triaxial Testing equipment, please contact us.
- ASTM D5311 / D5311M-13, Standard Test Method for Load Controlled Cyclic Triaxial Strength of Soil, ASTM International, West Conshohocken, PA, 2013, www.astm.org
- ASTM D3999 / D3999M-11e1, Standard Test Methods for the Determination of the Modulus and Damping Properties of Soils Using the Cyclic Triaxial Apparatus, ASTM International, West Conshohocken, PA, 2011, www.astm.org
- Bishop, A. W., Henkel, D. J. 1962. The measurement of soil properties in the Triaxial test. E. Arnold, London.
- Polito, C. 2010. Regression models for validating cyclic Triaxial test results, Geotechnical Testing Journal, 34(2).
- Wu, J. Kammerer, A.M. Riemer, M.F. Seed, R.B. Pestana, J.M. 2004. Laboratory study of liquefaction triggering criteria, 13th World Conference on Earthquake Engineering, Vancouver, Canada.
1.6 Books for further reading