Cyclic Triaxial Testing: A Primer

Abstract

Cyclic triaxial tests are frequently used in the laboratory to assess the liquefaction susceptibility of soils. This paper will serve a two-fold purpose: First, it will serve to explain how the mechanics of the tests represent the stresses that occur in the field. Topics covered include the differences in the stress paths for the soil in the field and in the lab, the differences in the actual stresses applied in the lab and the field, the differences between stress-controlled and strain-controlled tests, and the effects of other aspects of the testing methodology. The development of adjustment factors for converting the laboratory test results to the field is also briefly discussed. The second purpose of the paper is to serve as a guide to interpreting cyclic triaxial test results. The topics covered will include an examination of the two main liquefaction modes and the impact that the failure criteria selected have on the analysis, the differences between stress-controlled and strain-controlled test results, energy dissipation, and pore pressure generation. The author has run more than 1500 cyclic triaxial tests over the course of his career. He has found that, while the test is fairly straightforward to perform, it requires a much deeper understanding of the test mechanics and data interpretation in order to maximize the information gained from performing the test. This paper is intended as a guide, helping engineers to gain further insights into the test and its results. It has a target audience encompassing both those who are running their first tests and those who are looking to increase their understanding of the tests they have performed.

1. Introduction

For sixty years, cyclic triaxial testing has been a key method for evaluating the liquefaction potential of sandy soils. Despite notable differences between in situ earthquake loading conditions and laboratory test environments, cyclic triaxial tests continue to be widely used. While field conditions differ from those replicated in the lab, these tests have contributed valuable insights, both in characterizing the liquefaction behavior of specific soils and in exploring how various parameters influence liquefaction susceptibility [1,2,3].

The author has run more than 1500 cyclic triaxial tests over the course of his career. He has found that, while the test is fairly straightforward to perform, a very deep understanding of the test mechanics and data interpretation is required if one is to maximize the information gained from performing the test.

This paper aims to serve as a comprehensive resource for engineers seeking to deepen their understanding of cyclic triaxial testing and its interpretation. It is intended to serve both the practitioners conducting these tests for the first time and those with experience who wish to enhance their interpretation of test outcomes. While existing textbooks, training courses, and user manuals provide valuable guidance, this work consolidates information from the published literature and integrates insights drawn from the author’s experience in performing cyclic triaxial tests for more than 35 years.

This paper will examine both the mechanics of cyclic triaxial testing and provide insights into analysis of the test results. The paper begins with an overview of cyclic triaxial testing, followed by a discussion of the test mechanics, including stress paths applied during an earthquake and those applied in the lab. Other differences between field and lab loadings will be explained; finally, the development of the factors used to apply the laboratory test results to the field conditions will be covered.

In the second half of the paper, insights into analyzing the soil’s behavior during the test will be provided, with a particular focus on liquefaction modes, the differences between stress-controlled and strain-controlled test results, energy dissipation, and pore pressure generation. Finally, the application of cyclic triaxial testing to field investigations will be discussed.

2. Introduction to Cyclic Triaxial Testing

This section will provide brief introduction to cyclic triaxial testing theory and execution. After several important terms are defined, a brief overview of the test will be provided. The section will continue with an examination of the basic inputs used to conduct a cyclic triaxial test and conclude with a review of the typical outputs from a cyclic triaxial test.

2.1. A Brief Overview of Cyclic Triaxial Testing

The liquefaction resistance of a soil is often measured in the laboratory using reconstituted specimens tested in cyclic triaxial tests. In this method, a specimen is formed within a latex membrane, placed inside a triaxial cell, saturated, consolidated, and then subjected to a pulsating deviator load [4,5,6]. For a contractive specimen, as the applied deviator stress or the applied axial strain cycles between compression and tension, pore water pressures within the specimen increase, effective stress decreases, and axial straining occurs [7]. The specimen is considered to have liquefied when either the pore pressure equals the initial effective confining stress (i.e., the effective stress acting on the specimen first becomes equal to zero) or when a level of axial strain chosen by the operator is reached [8].

2.2. Terminology Relevant to Cyclic Triaxial Testing

To help evaluate and describe a soil’s liquefaction susceptibility in a cyclic triaxial test, several ratios are commonly employed: the cyclic stress ratio, the pore pressure ratio, the cycle ratio, and the dissipated energy ratio. These ratios are frequently used in conjunction with one another in graphical formats to characterize the progression of excess pore pressure in relation to cyclic loading and to quantify liquefaction.

The cyclic stress ratio (CSR) is defined as the ratio of the applied shearing stress to the initial effective confining stress. In a cyclic triaxial test, the shearing stress on the plane of interest is one-half of the applied deviator stress. Therefore, the cyclic stress ratio is simply the applied deviator stress divided by twice the initial effective confining stress as may be seen in Equation (1) [9].

$$\mathrm{C}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{c} \mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}={\displaystyle \frac{\mathsf{\tau }}{{\mathsf{\sigma }}_{\mathrm{o}}^{\prime }}}={\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{d}}}{{2\mathsf{\sigma }}_{\mathrm{o}}^{\prime }}}$$

(1)

The pore pressure ratio at any point during the loading sequence, denoted as r_u,i, is defined as the ratio of the excess pore pressure (u_xs,i) to the initial effective stress (${\mathsf{\sigma }}_0^{\prime }$) acting on the specimen. It is presented as shown in Equation (2) [10].

$${\mathrm{P}\mathrm{o}\mathrm{r}\mathrm{e} \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=\mathrm{r}}_{\mathrm{u},\mathrm{i}}={\displaystyle \frac{{\mathrm{u}}_{\mathrm{x}\mathrm{s},\mathrm{i}}}{{\mathsf{\sigma }}_0^{\prime }}}$$

(2)

While pore pressure ratio can be calculated at any point in the loading sequence, the residual excess pore pressure is measured specifically at the points in the loading cycle when the applied stress or the applied strain is zero. These points are linked to the plastic deformation of the soil skeleton. Because no external loading is being applied at the time when the measurement is taken, the residual pore pressures reflect only the changes in pore pressure resulting from the permanent deformations of the soil skeleton and not the transitory pore pressures due to the application of the loading. Figure 1 presents a plot of both the pore pressure ratio and the residual pore pressure ratio from a stress-controlled cyclic triaxial test on clean sand. The deviator stress that was applied during the test is also plotted. It can be seen that the symbols marking the residual pore pressure ratio align vertically with the points where the deviator stress crosses the zero axis. This alignment indicates that the residual pore pressures were measured when the deviator stress was equal to zero.

The cycle ratio represents the normalized number of loading cycles at any point during the test. It is calculated as the ratio of the cycle number of the cycle of interest (N_i) to the total number of cycles required to trigger liquefaction (N_L). It is presented as shown in Equation (3) [10]:

$$\mathrm{C}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{i}}}{{\mathrm{N}}_{\mathrm{L}}}}$$

(3)

The dissipated energy ratio is the ratio of the cumulative normalized dissipated energy per unit volume (W_si) at the point of interest relative to the normalized dissipated energy per unit volume required to initiate liquefaction (W_sL). It is presented as shown in Equation (4) [12]:

$$\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}={\displaystyle \frac{{\mathrm{W}}_{\mathrm{s}\mathrm{i}}}{{\mathrm{W}}_{\mathrm{S}\mathrm{L}}}}$$

(4)

2.3. Cyclic Triaxial Test Inputs

The loading in a cyclic triaxial test can be either stress-controlled, in which case an axial deviator stress is applied cyclically to the specimen, or it can be strain-controlled, in which case an axial strain is applied to the specimen. Other inputs to the test are the total confining and effective consolidation stresses [13,14]

For a stress-controlled test (also referred to as a load-controlled test), the intensity of cyclic loading is represented by the cyclic stress ratio. In cyclic triaxial tests, the maximum shear stress occurs on a plane inclined at 45° to the horizontal, and is equal to one half of the applied deviator stress [15]. Thus, the CSR is calculated as the deviator stress divided by twice the initial effective confining stress, as previously presented in Equation (1).

Figure 2 presents the results from a stress-controlled cyclic triaxial test conducted on a reconstituted Ottawa C-109 sand specimen, prepared to a relative density of 40% [16]. The specimen was subjected to a CSR of 0.30 and initial liquefaction occurred during the fifth cycle of loading. Figure 2a shows the variation in effective stress and Figure 2b shows axial strain, which are both plotted against the number of load cycles. Figure 2c presents the stress–strain behavior, while Figure 2d presents the total stress path (TSP) and the effective stress path (ESP).

For a strain-controlled test (also referred to as a displacement-controlled test), the intensity of cyclic loading is represented by the maximum applied axial strain. The cyclic resistance curve for a strain-controlled test is typically plotted as the peak applied shear strain against the number of cycles required to cause liquefaction [17,18].

Figure 3 presents the results from a strain-controlled cyclic triaxial test conducted on a reconstituted Ottawa C-109 sand specimen, prepared to a relative density of 40% [16]. The specimen was subjected to a single-amplitude axial strain of 0.3% (i.e., ±0.3%) and initial liquefaction occurred during the fifth cycle of loading. Figure 3a shows the variation in effective stress and Figure 3b shows the induced deviator stress, which are both plotted against the number of load cycles. Figure 3c presents the stress–strain behavior, while Figure 3d presents the total stress path (TSP) and the effective stress path (ESP).

The two remaining test parameters controlled by the operator are the total confining stress (i.e., the cell pressure) and effective consolidation stresses. The total confining stress can be shown to have no impact on the liquefaction of the specimen [19]. In fact, its final value is usually chosen to ensure that the sample achieve a sufficient B-value [20] during back pressure saturation.

The effective consolidation stress plays an important role in determining liquefaction behavior [21]. At a given density and a given maximum applied deviator stress or axial strain, a specimen subjected to a larger initial effective confining stress will require a greater number of cycles of loading and a greater amount of energy dissipation to achieve liquefaction [21].

2.4. Cyclic Triaxial Test Outputs

The data collected from a cyclic triaxial test is typically interpreted in one of two ways. It can be used to develop a cyclic resistance curve. It can also be used to establish the amount of energy dissipation required to initiate liquefaction.

2.4.1. Cyclic Resistance Curves

A laboratory liquefaction analysis typically involves performing three to five tests at different loading levels on identical specimens. This loading is the cyclic stress ratio if the tests are stress-controlled or the maximum axial strain if the tests are strain-controlled. The loading values are then plotted as the ordinate against the number of cycles required to induce liquefaction as the abscissa and a best-fit curve drawn. This forms a cyclic resistance curve, which illustrates the relationship between loading intensity (represented by the cyclic stress ratio or the applied axial strain) and duration (represented by the number of cycles of loading) required for liquefaction triggering.

Figure 4 shows the cyclic resistance curve for reconstituted Ottawa C-109 sand specimens at 40% relative density based on a series of stress-controlled tests. The data point labeled “A” corresponds to the test shown in Figure 2. Similarly, Figure 5 shows the cyclic resistance curve for reconstituted Ottawa C-109 sand specimens at 40% relative density based on a series of strain-controlled tests. The data point labeled “A” corresponds to the test shown in Figure 3.

2.4.2. Normalized Dissipated Energy per Unit Volume

In addition to cyclic resistance curves, the normalized dissipated energy per unit volume has emerged as an effective parameter for evaluating the liquefaction susceptibility of soils. This parameter reflects the energy required to induce liquefaction in a unit volume of soil normalized with respect to the initial effective mean confining stress. It is a function of the stress and strain behavior of the soil over the course of cyclic loading and has demonstrated strong correlations with pore pressure generation and liquefaction onset [3,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39].

In an energy-based liquefaction analysis, the factor of safety against liquefaction is defined as the ratio of the energy required to cause liquefaction in a soil to the energy imparted to the soil by the earthquake. This formulation offers a unified framework to account for variable stress paths, strain amplitudes, and loading histories.

The normalized dissipated energy per unit volume, W_s, for cyclic triaxial tests can be calculated using Equation (5) [3]:

$${\mathrm{W}}_{\mathrm{s}}={\displaystyle \frac{1}{2{\mathsf{\sigma }}_{\mathrm{o}}^{\prime }}}\sum _{\mathrm{i}=1}^{\mathrm{n}-1}\left({\mathsf{\sigma }}_{\mathrm{d},\mathrm{i}+1}+{\mathsf{\sigma }}_{\mathrm{d},\mathrm{i}}\right)\left({\mathsf{\epsilon }}_{\mathrm{a},\mathrm{i}+1}+{\mathsf{\epsilon }}_{\mathrm{a},\mathrm{i}}\right)$$

(5)

where W_s is the normalized dissipated energy per unit volume; ${\mathsf{\sigma }}_{\mathrm{o}}^{\prime }$ is the initial effective stress acting on the specimen; n is the number of load increments applied to the specimen in order to cause liquefaction; σ_d,i and σ_d,i+1 are the applied deviator stresses at load increments i and i + 1; ε_a,i and ε_a,i+1 are the axial strains at load increments i and i + 1.

3. The Mechanics of Cyclic Triaxial Testing

Cyclic triaxial tests are designed to model the loads imposed on a soil mass during an earthquake. However, important differences exist between the loading conditions experienced by soils in the field and those applied to laboratory specimens during cyclic triaxial testing. Additionally, several factors can influence a specimen’s resistance to liquefaction, potentially causing it to differ from the behavior observed in situ.

This section begins with a brief review of the fundamental theory behind cyclic triaxial testing, followed by a discussion of the key differences between laboratory and field loading conditions. It then summarizes the factors affecting cyclic triaxial test results and concludes with a review of the definitions of liquefaction.

3.1. Test Methodology

A cyclic triaxial testing procedure methodology is provided by ASTM D5311 [40]. A second suggested methodology is that recommended by Silver [41] for the U.S. Nuclear Regulatory Commission. The procedure for a cyclic triaxial test can be broken into three major activities: specimen preparation; saturation and consolidation; cyclic loading. Each of these activities will be discussed in the next few subsections.

3.1.1. Specimen Preparation

Cyclic triaxial tests are most commonly performed on reconstituted specimens rather than on undisturbed specimens. While some researchers have had success freezing and sampling in situ sand deposits, the cohesionless nature of most liquefiable soils makes them difficult and expensive to sample without disturbance.

The accuracy and reliability of cyclic triaxial test results are heavily influenced by the method used to prepare soil samples. Sample preparation affects the soil fabric, density, homogeneity, and saturation level. These factors control the cyclic strength and liquefaction potential of granular soils. Therefore, understanding the effects of different preparation techniques is vital for replicating in situ conditions and obtaining consistent, interpretable results in laboratory cyclic triaxial tests.

Among the most commonly used preparation techniques for reconstituted specimens are moist tamping, wet pluviation, dry pluviation, and slurry deposition. Each method induces a distinct soil structure. For instance, moist tamping often results in a more loosely packed and heterogeneous sample due to layer-by-layer compaction, which may introduce density variability across the specimen height [42]. In contrast, wet and dry pluviation techniques promote a more uniform distribution of particles and yield more homogenous specimens [43,44].

The method of sample preparation also significantly affects liquefaction resistance. Yoshimi et al. [45] demonstrated that samples prepared by moist tamping displayed lower cyclic resistance compared to those prepared by wet or dry pluviation. This difference is attributed to the more open fabric and weaker inter-particle contacts produced by tamping. Conversely, pluviated samples generally exhibit higher resistance due to denser packing and more stable particle arrangements.

Slurry deposition, another preparation method often used for very fine sands and silts, can simulate depositional processes in natural alluvial and lacustrine settings. However, this method may lead to stratification or segregation if not carefully controlled and can lead to unpredictability in cyclic behavior [30].

Saturation is a critical step post-preparation. High levels of saturation (Skempton’s B-value > 0.95) are required for reliable cyclic testing, as the undrained condition is assumed during cyclic loading. The use of back pressure to achieve saturation is common practice and should be applied consistently across specimens, regardless of preparation technique [7]. However, some preparation methods, particularly moist tamping, make achieving full saturation more challenging due to trapped air within the sample [6].

Overall, the choice of preparation method should be aligned with the research objective. For studies aiming to replicate natural depositional conditions and assess field performance, wet or dry pluviation is generally preferred. Conversely, for comparative studies or parameter sensitivity analyses, the simplicity and repeatability of moist tamping may suffice, provided its limitations are recognized.

In conclusion, the method of sample preparation has a profound effect on the outcome of cyclic triaxial tests. Researchers must consider the induced soil fabric, achievable saturation, and consistency when selecting a preparation technique to ensure valid and representative results.

3.1.2. Back Pressure Saturation and Consolidation

Depending upon the specimen preparation method used, prior to back pressure saturation, the air in the pore spaces of the specimen is often flushed out using carbon dioxide. This is performed because, during back pressure saturation, CO₂ can be forced into solution at lower pressures than air. Following the administration of CO₂, the specimen is often further flushed with three or more pore volumes of de-aired water to saturate the voids as fully as possible. The specimen is now ready to begin back pressure saturation.

Back pressure saturation is the process of incrementally raising both the cell pressure and the back pressure acting on the specimen while maintaining a near-constant effective stress on the specimen to ensure its complete saturation. During this process, the specimen is maintained under a constant effective stress of something less than the final consolidation stress; this is performed to prevent the accidental over-consolidation of the specimen. Both the cell pressure and back pressure are gradually increased in small increments. The degree of saturation is monitored via the B-value, with saturation considered complete once some minimum B-value is achieved.

Following saturation, the specimen is consolidated (most often isotropically) to a predetermined effective stress level. Consolidation time varies depending on the soil type: it can be as low as several minutes for clean sands and up to 24 h for pure silts and clays. These times are selected corresponding to the time required to complete primary consolidation and approximately one cycle of secondary compression.

The changes in specimen volume and height that occur during saturation and consolidation are used to calculate the post-consolidation void ratios and relative densities.

3.1.3. Cyclic Loading

Cyclic loading is most frequently controlled by a computer and data acquisition system (back pressure saturation and consolidation may also be controlled by this system). After consolidation, the cyclic loading parameters are input into the control system. These parameters include the deviator stress (to achieve the target cyclic stress ratio) or axial strain, the loading frequency (usually between 0.1 and one Hz), the loading shape (most commonly sinusoidal), and the liquefaction criteria chosen (either initial liquefaction or some limiting axial strain).

Prior to the commencement of loading, a valve is closed to prevent drainage and the test is initiated. Cyclic loading continues until the specimen meets the chosen liquefaction criteria.

3.2. Differences in Stresses and Stress Paths Between Field and Cyclic Triaxial Test Loadings

Cyclic triaxial tests are widely used to evaluate the cyclic strength or liquefaction resistance of soils. However, the stress conditions applied during these tests differ significantly from those experienced by a soil element in the field during an earthquake. Seed and Lee [21] and Seed and Peacock [19] provide detailed comparisons between the stress states in the field under seismic loading and those applied to isotropically consolidated specimens tested in the lab. This section explores those differences.

First, the stresses acting on a soil element in the field during an earthquake will be explained, followed by a description of the stress conditions in a cyclic triaxial test.

3.2.1. Stresses Acting on a Soil Element in the Field During an Earthquake

For simplicity, this discussion will be limited to the case of a soil element located beneath a level, unladen ground surface. This situation has no initial shear stress acting on the plane of interest and this is the case that an isotropically consolidated cyclic triaxial test was designed to simulate.

Before an earthquake, a soil element beneath level ground is subjected to initial vertical and horizontal stresses, as shown in Figure 6a. The horizontal stress typically corresponds to the at-rest (K₀) earth pressure. In this state, the vertical and horizontal stresses act as principal stresses, with no shear stresses on the element’s faces assuming that the soil is located under an undeveloped section of level ground.

During seismic loading, the soil element in the field is subjected to cyclic and reversing horizontal shear stresses caused by the upward propagation of shear waves. These shear stresses deform the element without altering the vertical or horizontal confining stresses. This dynamic loading condition is illustrated in Figure 6b,c.

Figure 6 also presents Mohr’s circles, representing these conditions. The smaller inner circle, labeled “Case (a)”, corresponds to the initial state with no applied shear stress. When seismic shear stresses (τ) are applied on horizontal planes accompanied by complementary shear stresses on vertical planes, the Mohr’s circle expands, as shown by the larger circle labeled “Cases (b) and (c)”. Case (b) represents the case for a positive horizontal shear stress and Case (c) represents the case for a negative horizontal shear stress.

Figure 7 presents the total and effective stress paths from a cyclic direct simple shear test performed on a reconstituted specimen of Ottawa C-109 sand at 40% relative density. It was loaded at a CSR of 0.07 and failed in 10 cycles of loading. These stress paths are the same as would be experienced by a soil element in the field loaded to the same cyclic stresses.

Since the shear stresses on opposing faces are equal in magnitude, the Mohr’s circle expands and contracts concentrically, maintaining a constant mean confining stress, assuming the influence of the intermediate principal stress is neglected.

3.2.2. Stresses During a Standard Cyclic Triaxial Test

In a standard cyclic triaxial test, the stress application does not mimic the stresses applied in the field. Instead of applying pure shear stresses, a cyclic deviator stress is applied axially to the soil specimen, while the horizontal stress (i.e., the cell pressure) is held constant.

Figure 8 illustrates the Mohr’s circles for a stress-controlled cyclic triaxial test. In an isotropically consolidated specimen, the stress state on a plane inclined at 45° to the horizontal simulates the shear stress conditions on a horizontal plane in the field. On this plane, the maximum shear stress is equal to one-half of the deviator stress, and the normal stress is equal to the mean confining stress.

Figure 9 presents the total and effective stress paths from a cyclic triaxial test performed on a specimen of reconstituted Ottawa C-109 sand at 40% relative density. It was loaded at a CSR of 0.28 and failed in 9.4 cycles of loading. Comparing the stress paths in Figure 7 and Figure 9 shows the significant differences between the loading an element undergoes in the field and in a cyclic triaxial test. These differences are one of the main reasons that correction factors are applied to the results of cyclic triaxial tests before using them to predict liquefaction in the field.

Another key difference between field and laboratory conditions lies in the stress paths applied to the soil. As illustrated in Figure 6 and Figure 7, field loading involves the application of a pure shear component to an anisotropically consolidated soil element.

Due to the initial stress state of the specimen, the resulting total and effective stress paths do not cross the zero-shear stress axis (q = 0), indicating that the soil element in the field never reaches a state of zero shear stress. In contrast, during a cyclic triaxial test on an isotropically consolidated specimen, the total and effective stress paths each cross the zero-shear stress axis twice in each loading cycle, as shown in Figure 8 and Figure 9.

3.2.3. Static Versus Cyclic Total Stress

In contrast to field conditions, where the mean total confining stress remains constant during seismic loading, a standard cyclic triaxial test subjects the specimen to fluctuating mean total confining stress throughout each loading cycle. Specifically, the mean total stress varies between the initial confining pressure minus half the deviator stress and the initial confining pressure plus half the deviator stress. This variation introduces a fundamental discrepancy between laboratory testing and in situ stress conditions (see Figure 8).

To more accurately simulate field stress conditions in the laboratory, the standard cyclic triaxial testing procedure can be modified by varying the cell pressure in tandem with the applied deviator stress. In this modified configuration, the mean total confining stress is held constant by decreasing the cell pressure by half the deviator stress as the latter increases, and increasing it by the same amount as the deviator stress decreases. This adjustment maintains constant normal stress on planes inclined at 45° to the horizontal, while allowing the shear stress to vary from zero to one-half of the deviator stress. Consequently, this setup better replicates the stress state experienced on a horizontal plane in level ground during seismic events. The stress conditions and corresponding Mohr’s circles for this modified testing procedure are illustrated in Figure 10, while Figure 11 shows the variations in deviator stress and cell pressure over 10 loading cycles at a cyclic stress ratio of 0.23.

In conventional cyclic triaxial testing, the use of constant cell pressure assumes that, in fully saturated specimens, any variation in total confining stress is offset by an equivalent change in pore water pressure. As a result, effective stress, which governs both deformation and pore pressure development, remains constant. This assumption implies that the mechanical response of the specimen is not significantly affected by whether the total confining stress is held constant or varied during loading.

Supporting this assumption, Polito [46] conducted cyclic triaxial tests on four mixtures of sand and non-plastic silt using both constant and variable total stress protocols. When the number of cycles to initial liquefaction was plotted against CSR for each soil, both testing methods produced a single, unified cyclic resistance curve. This result indicates that the method of cell pressure control does not influence the cyclic resistance of the specimen.

Figure 12 presents effective stress paths for two cyclic triaxial tests on Ottawa C-109 sand at 35% relative density [46]. Both specimens were loaded at CSR = 0.23, with one tested under constant and the other under variable total confining stress conditions. The specimens reached initial liquefaction after 12.6 and 10.1 cycles, respectively. Despite the slight difference in the number of cycles to failure, the effective stress paths show that the mechanical response of the specimens was essentially unaffected by the method of confining stress control.

Polito [46] further examined the normalized dissipated energy per unit volume required to induce liquefaction using normal probability plots. Each soil type showed a single normal distribution regardless of whether constant or variable confining stress was applied. Hypothesis testing at the 5% significance level confirmed that there were no statistically significant differences in the mean normalized dissipated energy per unit volume between the different test methodologies.

Overall, the experimental results confirm that, in fully saturated specimens, variations in total confining stress are counterbalanced by corresponding changes in pore water pressure. As a result, the effective stress remains consistent, and the mechanical behavior of the specimen is unaffected. Thus, cyclic triaxial tests using constant cell pressure provide a valid and reliable means of evaluating liquefaction potential, despite their simplification of in situ stress conditions.

3.2.4. Rotation of Principal Stresses

The rotation of principal stresses also differs between field loading and triaxial testing. In both cases, prior to loading under level ground conditions, the horizontal and vertical planes serve as planes of principal stress. In the field, when pure shear is applied, the principal stress planes rotate smoothly to a new orientation, depending on the applied stresses.

In a triaxial test, however, principal stress rotation is limited to either 0 or 90 degrees due to the axial nature of the loading. Here, principal stresses remain aligned vertically and horizontally. Rotation occurs only when the major and minor principal stresses reverse, specifically during the transition from loading to unloading, and vice versa, in isotropically consolidated specimens. As the axial load falls below the confining pressure, the major principal stress shifts from vertical to horizontal. Conversely, during reloading, the major principal stress shifts back to vertical.

Principal stress rotation significantly influences soil behavior during cyclic loading. In reality, seismic loading induces multi-directional stress paths, whereas standard cyclic triaxial tests apply unidirectional loading, neglecting stress rotation. Studies have shown that rotating principal stresses reduce cyclic resistance and accelerate pore pressure buildup compared to fixed-axis loading [47,48]. This is attributed to increased particle rearrangement and shear strain accumulation. Therefore, tests that incorporate stress rotation, such as hollow cylinder torsional shear tests, better replicate field conditions and yield more conservative estimates of liquefaction potential.

3.2.5. Intermediate Principal Stress

The stress conditions also differ with regard to the intermediate principal stress. In an isotropically consolidated triaxial specimen, the intermediate principal stress, which is always equal to the horizontal stress, matches the minor principal stress during the compression phase (when vertical stress is major) and matches the major principal stress during extension (when horizontal stress is major).

These differences affect the mean confining stress, generally defined as the average of the three principal stresses. Ishihara [49] demonstrated that a soil’s cyclic resistance more closely correlates with its mean effective confining stress than with either its vertical or horizontal effective stresses individually.

The intermediate principal stress (σ₂) significantly influences soil behavior during cyclic loading, especially under complex stress states like those during earthquakes. Standard triaxial tests ignore σ₂, assuming it equals σ₃, which limits realism. However, studies using true triaxial apparatuses have shown that increasing σ₂ enhances shear strength and cyclic resistance due to stress path stability and particle interlocking [50,51]. Neglecting the effects of σ₂ may thus underestimate liquefaction potential or deformation.

3.2.6. Uniformity of Loadings

In cyclic triaxial testing, it is common practice to represent complex field earthquake motions using uniform cyclic loading to simplify laboratory simulations. This involves converting irregular seismic stress or strain histories into an equivalent number of uniform cycles with a representative amplitude. The goal is to replicate the same energy input or pore pressure generation effects observed during an actual earthquake [52].

Typically, the equivalent number of uniform cycles, often denoted as N_eq, is estimated based on the effective stress history and is often assumed to be 10–15 cycles for major earthquakes, although this can vary depending on magnitude and site conditions [53]. Uniform sinusoidal loading, usually with a frequency of 0.1–1 Hz, is then applied in the lab to replicate these field effects under controlled conditions.

While this simplification enables standardized testing, it does not account for features like frequency content, stress reversals, or principal stress rotation. Advanced techniques and equipment like stress-path triaxial and torsional shear tests are sometimes employed for more realistic simulations [54].

3.2.7. Components of Loadings

During an actual earthquake, a soil element experiences stresses from multiple directions simultaneously. A cyclic triaxial test, however, applies only a single component of loading, analogous to one horizontal component of earthquake motion acting on a plane inclined at 45 degrees within the specimen. Seed and Pyke [55] found that this difference causes laboratory specimens to fail under a cyclic stress approximately 10 percent higher than what would be required under multi-directional field loading.

4. Interpretation of Cyclic Triaxial Test Results

Once a cyclic triaxial test has been completed, the results must be reviewed. Beyond the simple number of cycles to trigger liquefaction and the more complicated amount of normalized dissipated energy per unit volume, significant insight can be gained from examining the test results. The most important aspect that can be obtained by analysis of the test data is the determination of the liquefaction mode, i.e., flow liquefaction or cyclic mobility. Additionally, the type of loading chosen, be it stress-controlled or strain-controlled, will have a marked effect on energy dissipation and pore pressure generation. These effects can be best examined using the data from cyclic triaxial tests.

4.1. Liquefaction Failure Modes: Flow Liquefaction and Cyclic Mobility

Soil liquefaction generally manifests in two distinct failure modes: flow liquefaction and cyclic mobility [56,57,58]. In sands, these modes are primarily governed by the soil’s relative density and its behavior under undrained shear conditions.

4.1.1. Flow Liquefaction

In loose, contractive soils under cyclic loading, flow liquefaction occurs. This failure mode is associated with soils having void ratios greater than the critical void ratio corresponding to the in situ effective confining stress. Under cyclic loading, such soils exhibit a progressive buildup of excess pore water pressure, leading to a continual reduction in effective stress and, consequently, in shear strength. As loading progresses, the resulting deformation promotes additional pore pressure generation, further reducing shear strength. This self-reinforcing cycle ultimately drives the stress state of the soil toward the steady-state line, as illustrated by Point A in Figure 13 (after [12]). Once the stress path reaches the steady-state line, the soil enters a steady-state condition and flow liquefaction ensues. Flow liquefaction is typically accompanied by large and sudden permanent deformations.

Figure 14 displays a representative plot of axial strain versus number cycles of loading for a specimen undergoing flow liquefaction. Markers indicate the specific points at which commonly used liquefaction criteria were met. The strain history shows negligible axial deformation through the early stages of loading, followed by a sharp, rapid increase in strain immediately preceding the onset of initial liquefaction. This deformation pattern is the characteristic behavior of flow liquefaction.

4.1.2. Cyclic Mobility

In contrast, cyclic mobility occurs in denser, dilative soils with void ratios below the critical void ratio for a given effective confining stress. This condition is represented by Point B in Figure 13. During cyclic loading, these soils initially undergo contraction, generating excess pore pressure and reducing effective stress. However, as straining continues, the dilative tendency of the soil then counteracts this process, reducing pore pressure, increasing effective stress, and partially restoring shear strength. As a result, the soil maintains its structural integrity and resists large-scale deformation, even if it briefly intersects the steady-state line.

Figure 15 presents a typical axial strain versus cycles of loading curve for a specimen exhibiting cyclic mobility. Again, the points at which the liquefaction criteria were met are annotated. Unlike flow liquefaction, this behavior is characterized by relatively uniform axial strain development during each cycle and a near-complete recovery of strain at the end of each loading cycle.

4.1.3. Selection of Strain-Based Liquefaction Criteria

Liquefaction can be defined in several ways within the context of laboratory testing. Laboratory-based evaluations typically involve subjecting soil specimens to cyclic loading at varying cyclic stress ratios or applied strain and monitoring the number of cycles required to induce liquefaction. The resulting data are compared against the expected loading and the anticipated number of loading cycles during seismic events to assess the potential for liquefaction under field conditions.

Although the general framework for cyclic triaxial testing is well established, the definition of liquefaction within this testing context remains a topic of ongoing debate. The most widely adopted criterion is “initial liquefaction”, defined as the point at which the effective confining stress in the specimen first reduces to zero. Nevertheless, a range of alternative stress-based and strain-based criteria have been proposed in the literature. The selected criterion has a significant influence on the interpretation of test results and the implications for subsequent geotechnical analyses. Common definitions include initial liquefaction (i.e., zero effective stress) [4,59,60,61,62], as well as thresholds based on single-amplitude and double-amplitude axial strain [63,64,65,66].

A recent study by Polito [67] investigated the effectiveness of various strain-based liquefaction criteria in predicting the number of loading cycles required to reach initial liquefaction. The study encompassed more than 200 cyclic triaxial tests on sands, non-plastic silts, and sand–silt mixtures. For each test, parameters were derived using multiple failure criteria and applied to the energy-based model by Green, Mitchell, and Polito [32] which was then used to predict pore pressure generation. The failure criteria chosen were initial liquefaction, and 0.5%, 1.0%, 2.5%, and 5.0% single-amplitude strain. These liquefaction criteria were chosen as they are typical of liquefaction criteria chosen in many published studies.

The model predictions indicated that the use of 0.5% and 1% single-amplitude axial strain as liquefaction criteria tends to underestimate the number of cycles required to reach initial liquefaction, particularly in specimens exhibiting cyclic mobility behavior. This underestimation may be seen in Figure 16. While these thresholds may be considered conservative, their application can result in significant overestimation of liquefaction susceptibility, potentially leading to unnecessary and costly ground improvement measures.

Conversely, liquefaction criteria of 2.5% or 5% single-amplitude axial strain, as well as initial liquefaction defined by zero effective stress, provided consistent and reproducible results across a wide range of tests. These criteria demonstrate better agreement with observed pore pressure response and are thus recommended for future applications. This may be seen in Figure 17.

4.2. Effect of Chosen Liquefaction Criteria

The liquefaction criteria chosen when performing a cyclic triaxial test, be it initial liquefaction or some level of axial strain, will affect the number of cycles of loading and the quantity of normalized dissipated energy per unit volume required to initiate liquefaction. Less obviously, if the test is used to generate parameters for pore pressure models, the liquefaction criteria chosen may affect the accuracy of those models.

4.2.1. Cyclic Resistance of Soils Undergoing Flow Liquefaction

For soils exhibiting flow liquefaction behavior, the selection of a specific liquefaction criterion was found to have minimal impact on the number of loading cycles required to initiate failure. This is primarily due to the rapid development of axial strain following the onset of initial liquefaction, which results in the satisfaction of all commonly used strain-based criteria within a single loading cycle. This characteristic response is clearly illustrated in Figure 14.

Further evidence of this behavior is presented in Figure 18, which shows cyclic resistance curves developed using various liquefaction criteria. These curves are based on three stress-controlled cyclic triaxial tests conducted on Yatesville sand at a relative density of 26%. The strong agreement among the curves derived from the five different liquefaction criteria indicate that, in cases of flow liquefaction, the choice of failure criterion has negligible influence on the interpreted cyclic resistance.

4.2.2. Cyclic Resistance of Soils Undergoing Cyclic Mobility

In contrast, for soils exhibiting cyclic mobility behavior, the choice of liquefaction criterion has a pronounced influence on the interpreted cyclic resistance. These specimens tend to accumulate axial strain progressively over multiple loading cycles, leading to distinct cyclic resistance curves corresponding to each liquefaction criteria. This gradual strain development is clearly illustrated in Figure 15.

Figure 19 further demonstrates this behavior by presenting cyclic resistance curves derived using different liquefaction criteria. The curves are based on three stress-controlled cyclic triaxial tests conducted on Yatesville sand at a relative density of 69%. As shown, the divergence among the curves increases with the magnitude of the axial strain criterion. This trend underscores the importance of criterion selection when evaluating the cyclic resistance of soils subject to cyclic mobility, as it can significantly affect the interpretation of liquefaction potential.

4.2.3. Dissipated Energy in Flow Liquefaction and Cyclic Mobility

The normalized dissipated energy per unit volume (NDEPUV) required to initiate liquefaction varies significantly between specimens undergoing flow liquefaction and those exhibiting cyclic mobility, even under similar cyclic stress ratios and number of loading cycles. When evaluating cyclic triaxial test results in terms of the amount of energy that must be input into the specimen to trigger liquefaction, it is important that the engineer understand that specimens that undergo cyclic mobility will require significantly larger amounts of energy input into them than specimens that undergo flow liquefaction. This difference in energy requirement has a marked impact when performing an energy-based liquefaction analysis.

Figure 20 presents the normalized dissipated energy per unit volume (calculated using Equation (5)) as a function of loading cycles for the tests previously presented in Figure 14 and Figure 15. Using a liquefaction criterion of 5% single-amplitude axial strain, the specimen experiencing cyclic mobility required approximately six times more energy than the specimen undergoing flow liquefaction, despite similar numbers of cycles to failure.

This distinction is further illustrated in Figure 21, which shows the average normalized dissipated energy per unit volume (again calculated using Equation (5)) required to achieve initial liquefaction (open symbols) and various levels of axial strain (filled symbols). For the specimen that underwent flow liquefaction, the energy requirement increases modestly, approximately 1.5 times from 0.5% to 5% strain, due to the rapid strain accumulation post-initial liquefaction. Conversely, for specimen that underwent cyclic mobility, the energy requirement increases by a factor of approximately 3.5, reflecting the incremental strain accumulation and corresponding energy dissipation over the loading history.

4.3. Stress-Controlled vs. Strain-Controlled Cyclic Triaxial Tests

The loading in a cyclic triaxial test inherently takes one of two forms. Either the specimen is subjected to some cyclic deviator stress, resulting in a stress-controlled test, or it is subjected to some cyclic applied axial strain, resulting in a strain-controlled test. This section will examine similarities and differences in soil behavior, energy dissipation, and pore pressure generation in the two tests.

4.3.1. Stress-Controlled Cyclic Triaxial Tests

In stress-controlled cyclic triaxial tests, the maximum amplitude of the stress applied remains constant throughout the duration of the test as may be seen in Figure 22. Consequently, the strain response of the soil governs the evolution of energy dissipation and excess pore pressure generation. As cyclic loading progresses, positive pore pressures develop, reducing the effective stress acting on the soil skeleton. This reduction in effective stress diminishes the specimen’s resistance to deformation, thereby increasing the magnitude of shear strains even though the imposed shear stress amplitude remains unchanged.

During the initial stages of loading, energy dissipation is minimal due to the relatively small induced strains. However, as pore pressures increase and effective stress decreases, larger shear strains are mobilized, resulting in significantly higher energy dissipation in the later stages of the test.

The applied axial stresses and the resulting strain responses from a stress-controlled cyclic triaxial test conducted on a specimen of C-109 sand prepared at a relative density of 40% are presented in Figure 22 [16]. The specimen was subjected to cyclic loading at a cyclic stress ratio (CSR) of 0.22, with liquefaction occurring after 28.1 cycles of loading. During the test, the single-amplitude axial strains increased from approximately 0.06% in the initial cycles to 1.50% near the onset of liquefaction. The total normalized dissipated energy per unit volume at the point of failure was calculated to be 0.01758.

4.3.2. Strain-Controlled Cyclic Triaxial Tests

In contrast to stress-controlled cyclic triaxial tests, strain-controlled cyclic triaxial tests maintain a constant amplitude of applied strain throughout the loading sequence as can be seen in Figure 23. In this configuration, the soil’s shear resistance governs energy dissipation and excess pore pressure generation. Initially, when the effective stress is high, the soil offers greater resistance to deformation, and thus higher levels of energy are dissipated during each cycle. As cyclic loading continues and pore pressure accumulates, the effective stress and the corresponding resistance to deformation decrease, reducing the energy dissipation in subsequent cycles.

Thus, in strain-controlled tests, the majority of energy is dissipated during the early stages of loading when the soil’s resistance to deformation is large, while energy dissipation decreases in the later stages due to reduced soil stiffness and strength.

The applied axial strains and the corresponding stress responses from a strain-controlled cyclic triaxial test conducted on a specimen of C-109 sand prepared to a relative density of 40% are shown in Figure 23 [16]. The specimen was subjected to cyclic loading using a sinusoidal shear strain waveform with a maximum single-amplitude value of 0.10%. Liquefaction was observed after 24.0 cycles of loading. Throughout the test, the measured maximum shear stress progressively decreased from approximately 110 kPa at the onset of loading to less than 20 kPa near the point of liquefaction. At the time of failure, the total normalized dissipated energy per unit volume accumulated in the specimen was 0.01767.

4.3.3. Comparison of Energy Dissipation and Pore Pressure Generation in Stress- and Strain-Controlled Cyclic Triaxial Tests

A comparison of the normalized dissipated energy per unit volume ratio versus the cycle ratio for the two cyclic triaxial tests presented in Figure 22 and Figure 23 is presented in Figure 24. In the strain-controlled test, the dissipated energy ratio increases at a relatively constant rate throughout the loading process. Conversely, in the stress-controlled test, the dissipated energy ratio initially increases slowly at lower cycle ratios but increases significantly at higher cycle ratios. This behavior corresponds to the progressive increase in shear strain observed near the end of the test as the effective stress decreases. The engineer needs to be aware of these two energy dissipation patterns as they are directly related to the pore pressure generation patterns produced in the two types of tests.

These observations align well with theoretical predictions. Notably, despite differences in loading method and energy dissipation patterns, the total normalized dissipated energy per unit volume required to trigger liquefaction varied by less than 1% between the stress-controlled and strain-controlled tests in both the cyclic triaxial and cyclic direct simple shear experiments.

Figure 25 presents the residual pore pressure ratio, r_u, as a function of cycle ratio for the stress-controlled and strain-controlled cyclic triaxial tests. The results highlight clear differences in pore pressure generation between the two test types. In the strain-controlled test, excess pore pressures accumulated more rapidly during the early stages of loading, while in the stress-controlled test, significant pore pressure buildup occurred only in the latter stages. These trends closely mirror the patterns of energy dissipation seen in Figure 24.

To further investigate the relationship between pore pressure generation and energy dissipation, Figure 26 plots the residual pore pressure ratio against the dissipated energy ratio for the cyclic triaxial tests. Unlike the divergence observed when using the cycle ratio, the pore pressure response curves for the stress-controlled and strain-controlled tests are nearly identical when plotted as a function of dissipated energy ratio.

These findings highlight a fundamental insight: pore pressure generation in soils subjected to cyclic loading is more closely associated with energy dissipation than with the number of loading cycles. The dissipated energy ratio, defined as the fraction of energy dissipated relative to the total energy required to induce liquefaction, is independent of when that energy is dissipated during the loading sequence. Whether energy dissipation occurs predominantly in the early or in the later stages of loading, the resulting pore pressure response remains consistent when evaluated using this energy-based metric.

In contrast, the cycle ratio does not capture the magnitude or distribution of energy dissipation throughout the loading history. As a result, pore pressure development plotted against cycle ratio can vary substantially depending on the temporal pattern of energy input, potentially leading to inaccurate or misleading interpretations of soil behavior.

Therefore, to achieve a more reliable and loading-pattern-independent assessment of pore pressure generation, it is recommended that analyses be conducted with respect to dissipated energy ratio rather than cycle ratio. This energy-based framework offers a more robust basis for interpreting and comparing cyclic loading test results across varying loading protocols.

5. Applying Laboratory Results to the Field

Liquefaction is a phenomenon that is of critical concern in geotechnical engineering, particularly in regions susceptible to seismic activity. The cyclic triaxial test is a laboratory procedure commonly used to assess the potential for soil liquefaction by simulating cyclic loading conditions that mimic earthquake stresses. These results form the foundation for performing liquefaction analysis in the field. Converting laboratory test results into meaningful parameters for field application is essential for designing safe and effective mitigation strategies in geotechnical engineering [68].

Liquefaction susceptibility in the field is largely governed by the soil’s shear strength, its ability to dissipate excess pore pressure, and the dynamic loading applied to it, caused by seismic events. To evaluate liquefaction potential in the field, engineers typically use the simplified procedure detailed in [52,69]. When evaluating liquefaction potential, the analysis is often based on the factor of safety (FS). The factor of safety against liquefaction can be calculated using Equation (6) [52]:

$$\mathrm{F}={\displaystyle \frac{\mathrm{C}\mathrm{R}\mathrm{R}}{\mathrm{C}\mathrm{S}\mathrm{R}}}$$

(6)

where cyclic stress ratio, CSR, is the ratio of the shear stress generated by the earthquake to the vertical effective stress acting of the soil. Cyclic resistance ratio, CRR, is the soil’s resistance to liquefaction at a given depth, based on either laboratory testing or field data.

The CSR is calculated using the peak ground acceleration (PGA), the depth of the soil layer, and the soil’s unit weight. It is typically calculated assuming that the average shear stress applied is equal to 65% of the peak shear stress applied. Additionally, a stress reduction factor, r_d, is used to account for the soil element not being a truly rigid body. The cyclic stress ratio in the field can be estimated using Equation (7) [52]. The cyclic stress ratio calculated may then be adjusted for earthquake magnitude/cycles of loading, confining stress and initial shear stress as needed [69].

$$\mathrm{C}\mathrm{S}\mathrm{R}=0.65{\displaystyle \frac{{\mathrm{a}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\mathrm{g}}}{\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{v}}}{{\mathsf{\sigma }}_{\mathrm{v}}^{\prime }}}{\mathrm{r}}_{\mathrm{d}}$$

(7)

where a_max is the peak ground acceleration, g is the acceleration due to gravity, s_v and ${\mathsf{\sigma }}_{\mathrm{v}}^{\prime }$ are, respectively, the total and effective vertical stresses acting at the point of interest and r_d is the stress reduction factor.

If in the simplified procedure, the value of CRR is derived from laboratory cyclic triaxial test results, it must be adjusted for field conditions and soil characteristics. The conversion of laboratory cyclic triaxial test results to field applications requires understanding the relationship between laboratory-based test conditions and the actual field conditions. A number of empirical correlations and scaling methods have been developed to facilitate this conversion [1,2,70,71,72].

The CRR obtained from cyclic triaxial tests reflects the soil’s resistance to liquefaction under controlled laboratory conditions. However, to apply this to field conditions, adjustments must be made to account for factors such as confining pressure, stress history, and soil density.

Cyclic triaxial tests are typically performed under a specific confining pressure (σ₃), but in the field, the effective confining pressure will vary with depth. To convert laboratory results to the field, a scaling factor is used to adjust CRR for different confining pressures [73].

The cyclic triaxial test does not account for stress history or the age of the soil, which can affect the soil’s liquefaction resistance. Field studies have shown that, over time, soil can densify or experience cementation, which will increase resistance to liquefaction [74]. These effects are typically accounted for using empirical factors based on the soil’s relative density, consolidation history, and effective overburden pressure [75,76].

In some cases, the direct application of CRR from laboratory cyclic triaxial tests may not predict field performance accurately. For example, field observations during an earthquake may reveal a higher or lower liquefaction susceptibility than predicted by laboratory tests due to factors, such as the following:

• Field compaction: Field compaction techniques or construction methods can significantly increase the density of the soil, improving its resistance to liquefaction.
• Depth and layering effects: Liquefaction susceptibility can vary with depth due to changes in stratigraphy, groundwater conditions, and other site-specific factors.
• Groundwater fluctuations: The water table depth and the temporal fluctuations of groundwater levels can influence the soil’s susceptibility to liquefaction.

To address these discrepancies, engineers often use site-specific correction factors based on empirical relationships from observed liquefaction cases, such as the results from previous earthquake events or case studies, to refine predictions made from laboratory tests [77].

The conversion of laboratory results into a usable form for field liquefaction analysis is a critical step in geotechnical design. Once the laboratory CRR values are adjusted for field conditions, these values can be used in conjunction with field data (such as soil stratigraphy, SPT N-values, and CPT measurements) to assess liquefaction potential.

Field liquefaction potential is typically assessed using the following methodology [69]:

• Calculate the CSR based on the peak ground acceleration and the depth of the soil layer. Adjusting for magnitude, confine stress and initial shear stress as needed.
• Determine the CRR from laboratory cyclic triaxial results; adjust for field conditions.
• Compare CSR with CRR: If CSR exceeds CRR, liquefaction is likely. This relationship is commonly expressed as a factor of safety (FS).
• If FS < 1, the soil is considered susceptible to liquefaction.

The conversion of cyclic triaxial test results to field liquefaction analysis involves complex adjustments to account for field conditions such as confining pressure, groundwater levels, and stress history. While laboratory tests provide a controlled and reproducible environment for evaluating soil behavior under cyclic loading, real-world factors must be considered when applying these results to assess liquefaction potential in the field. By combining laboratory data with field measurements and empirical corrections, engineers can develop more accurate predictions of liquefaction potential, enabling the design of safer structures that are more resilient during earthquakes.

6. Summary

This paper is intended to provide insight and guidance to those performing cyclic triaxial tests, whether it be their first test or their fiftieth. The paper covered the basic methodology of performing the test as well as an explanation of the differences between earthquake loading in the field and loadings in the lab. It offers guidance for interpreting test results, including determining the liquefaction mode, the differences between stress-controlled and strain-controlled test results, energy dissipation, and pore pressure generation.