Introduction to Cyclic (Dynamic) Triaxial Testing

1 Introduction

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 is most accurately simulating the conditions in the field.

This guide, published by VJ Tech Ltd, is intended to give a brief introduction on the basic principles of cyclic Triaxial testing to the technicians that perform dynamic testing in geotechnical laboratories. Among others, it includes a description of the apparatus used in these tests, 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 in 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.

1.1  Apparatus & 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:

·          Load Frame

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.

·         Dynamic Actuator

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 controller 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 phase, with the latter achieving 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 the degradation during the cyclic movement of the ram. The Cells have usually 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 in order 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 the 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 the 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 have the ability to 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) in order 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 due to the fact that 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 in order 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 in order 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 the 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 commonly used testing standards for Dynamic Triaxial tests are ASTM D5311-13 and ASTM D3999-11. The first one refers on 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 are 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, to be subjected into 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.

b.     Saturation

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.

c.     Consolidation

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 is 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 (σ_h) and the total vertical stress (σ_v):

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 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

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 (r_u) which is defined as:

where  is the change in Pore Water Pressure and  the effective axial stress at the beginning of cyclic loading. When r_u=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 to 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 (r_u) becomes equal to 1 (see section 4d)

·         When Double Amplitude or Single Amplitude shear strain (Figure 8) becomes 6% (Wu et al, 2004)

1.4  Advanced testing procedures

a.     Ko consolidation

A special case of Anisotropic consolidation, without lateral deformation of the sample, is the Ko consolidation. This type of test simulates the Consolidation process that a soil specimen undertakes when it is subjected to an Oedometer test. In Oedometer tests (i.e. 1-D Consolidation), specimens are consolidated under vertical stresses while their diameter remains constant due to a confining ring they are placed in. This process is possible to be reproduced in a Triaxial apparatus (Bishop & Henkel, 1957) before the specimen is subjected to cyclic loading. There are two methods to consolidate the specimen under Ko conditions. In the first method, the effective axial stress increases slowly using the Cell Pressure controller while the diameter of the sample is monitored. Whenever the diameter tends to decrease (by no more than 0.005% of the axial strain) vertical stress increases to keep it constant. In the second method, vertical stress is ramped slowly to a target while the effective horizontal stress is adjusted in order to keep the diameter of the specimen constant. The first method tends to be used more widely in soil testing industry while the second method causes discrepancy in the achieved Ko value. Figure 9 shows an example of Ko Consolidation on a 50 mm diameter Triaxial specimen, prior to being subjected to cyclic loading. The effective mean stress and deviator stress have been ramped up, while the diameter of the sample has remained practically constant (variation of less than 0.25 microns).

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 prior to the cyclic loading. There are generally two ways of plotting stress paths, the Cambridge system and the MIT system, with the earlier been 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:

and

In terms of effective stresses, the stress parameters become:

and

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 of either multiple specimens at different cyclic load 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. 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 (G_o) of a 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 penetrates slightly into the top and bottom of the sample. One of the piezo-ceramic plates is producing a shear wave which travels within the sample and is captured from the other element (Figure 11). The distance and time of travel indicates the velocity of the wave through the sample (shear wave velocity) and as such the G_o is defined as:

where is the bulk density of the soil and  the shear wave velocity. Bender Element tests can be run through the cyclic Triaxial test and G_o 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.

1.5  VJ Tech Dynamic Triaxial systems

The type of the Dynamic Triaxial equipment should be chosen in a way that it satisfies the testing requirements of the specific laboratory. Parameters to be considered are:

-       What is the maximum load needed?

-       What is the maximum frequency?

-       What type of cyclic test to be conducted?

-       What types of soil are going to be tested?

-       Is it necessary to determine accurately soil deformation using On-Sample measurements?

-       Is it necessary to determine accurately the Pore Water Pressure within the sample during testing?

VJ Tech provides a range of cyclic Triaxial apparatuses to meet all kinds of requirements, from simple to advanced testing systems. The following systems can be adjusted based on the user requirements, for more information please contact sales@vjtech.co.uk.

i. Dynamic Triaxial Testing System with BASIC 5Hz/5kN Load Frame (Figure 12)

This System is capable of providing fully automatic Dynamic Triaxial testing, and consists of the following:

-       A 50 kN BASIC frame fitted with a 5 Hz/5 kN electro-mechanical actuator,

-       Single Axis Dynamic Servo Controller (DSC3000M) for actuator control

-       DSC3000M is also used to log Load, Displacement and Pore Water Pressure raw data

-       Air Pressure Controller to control Cell Pressure (using an Air/Water Interface Cylinder)

-       Hydraulic Automatic Pressure Controller for Back Pressure control

-       50 mm (2") Dynamic Triaxial Cell, it can be upgraded up to 150 mm

-       Easy test setup, control and results viewing & output through VJTech csDYNA software

ii. Dynamic Triaxial Testing System with a Triscan Pro 50 kN load frame (Figure 13)

This System is capable of providing fully automatic Dynamic Triaxial testing, and consists of the following:

-       A TriSCAN Pro 50 kN frame fitted with a 5 Hz/5 kN electro-mechanical actuator

-       Single Axis Dynamic Servo Controller (DSC3000M) for actuator control

-       DSC3000M is also used to log Load, Displacement and Pore Water Pressure raw data

-       TriSCAN Pro Load frame is also capable of Static Testing

-       Pro Pneumatic APC to control Cell Pressure (using an Air/Water Interface Cylinder)

-       Pro Hydraulic Automatic Pressure Controller for Back Pressure control

-       50 mm (2") Dynamic Triaxial Cell, it can be upgraded up to 100 mm

-       Easy test setup, control and results viewing & output through VJTech csDYNA software

iii. Dynamic Triaxial 10 Hz - 20 kN with Dynamic Cell Pressure Controller (Figure 14)

This particular System includes a Dynamic Pressure Controller for Cell Pressure control and is capable of providing fully automatic high frequency and load dynamic Triaxial testing. It consists of:

-       A 100 kN BASIC frame fitted with a 10 Hz /20 kN electro-mechanical actuator,

-       A Dynamic Pressure Controller for controlling Cell Pressure

-       A Dual Axis Dynamic Servo Controller (DSC3000MM) for actuator control & Transducer data logging on both axes

-       The DSC3000MM consists of 2 synchronised DSCs, one for vertical load (3-phase) and another for DPC (single phase)

-       A Hydraulic Automatic Pressure Controller is used for Back Pressure

-       150 mm Dynamic Triaxial Cell with 12 outlet ports

-       Cell can accommodate Bender Elements or On-Sample Transducers

iv. Dual Axis Dynamic Triaxial (Hydraulic) System with Dynamic Pressure Controller (Figure 15)

The VJ Tech Dual Axis Dynamic Triaxial (Hydraulic) System with DPC is capable of providing fully automatic high frequency and high load dynamic Triaxial testing. It consists of:

-       A TriSCAN Pro 250 kN frame fitted with a 20 Hz /50 kN Hydraulic actuator

-       A 3-Phase Hydraulic Power Pack for control of Actuator

-       A Dynamic Pressure Controller for controlling Cell Pressure

-       A Dual Axis Dynamic Servo Controller (DSC3003HM) for actuator control & Transducer data logging on both axes

-       A Hydraulic Automatic Pressure Controller is used for Back Pressure

-       150 mm Dynamic Triaxial Cell with 12 outlet ports

-       The cell can accommodate Bender Elements or On-Sample Transducers

v. Single Axis Dynamic Triaxial (Hydraulic) System with 20 kN, 1 Hz Actuator (Figure 16)

The VJ Tech Single Axis Dynamic Triaxial (Hydraulic) System with DPC is capable of providing fully automatic high load dynamic Triaxial testing and very high load Static Testing. It consists of:

-      A Dynamic Triaxial Hydraulic Unit (DTH) consisting of a 500 kN Hydraulic Triaxial Load Frame of four column-based construction and Horizontal Beam with integral 1Hz hydraulic actuator and accumulators

-       A 300 mm Dynamic Triaxial Cell configuration

-       A 3-Phase Hydraulic Power Pack for hydraulic power to actuator

-       A Single-Axis Dynamic Servo Controller (DSC1000H) for control of actuator, transducer data logging and a fast Ethernet or USB interface for PC connection

-       2 x Large Capacity Hydraulic Automatic Pressure Controller (APCH) 1250 cc, 2 MPa for Back Pressure

-       Easy test setup, control and results viewing & output through VJ Tech csDYNA software

1 References

-       - 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, 13^th World Conference on Earthquake Engineering, Vancouver, Canada.

1.6  Books for further reading

-       - Mitchell, J.K. Soga, K. 2005. Fundamentals of Soil Behaviour, John Wiley & Sons, New Jersey

-       - Briaud, J.L. 2013. Geotechnical Engineering: Unsaturated and Saturated Soils, John Wiley & Sons, New Jersey