Rheologic testing of wet kaolin reveals frictional and bi-viscous behavior typical of crustal materials



[1] New rheological data for wet kaolin support its use in analog table-top experiments that simulate deformation of the Earth's crust. Creep tests at small strain reveal that wet kaolin (62–66% water by mass) exhibits both elastic and viscous deformation characteristic of a Burger's material. When sheared to failure, the shear strength is relatively insensitive to the strain rate. The shear strength appears sensitive to the amount of initial compaction within the rheometer, which may indicate a normal-stress dependency typical of frictional materials. Stepped velocity tests at large strain demonstrate velocity weakening rate and state frictional behavior after yielding. Because the wet kaolin exhibits deformation characteristic of both frictional materials and bi-viscous materials, this material is well suited to simulate a variety of crustal deformational processes in scaled analog experiments.

1. Introduction

[2] Analog models allow direct observations of geologic deformation at scales that can be accommodated within a laboratory and at rates that permit rapid analysis. Unlike natural systems where boundary conditions are poorly known and observations of deformation are limited or indirect, analog models enable explicit control of boundary conditions and direct observation of a variety of physical features.

[3] Wet clay has been used in analog models since the 1960s [e.g., Cloos, 1968; Withjack and Jamison, 1986; An and Sammis, 1996; Spyropoulos et al., 1999; Clifton et al., 2000; Ackermann et al., 2001; Bellahsen et al., 2003; Eisenstadt and Sims, 2005; Henza et al., 2010]. Wet clay has primarily two advantages over the more frequently used sand within analog models: 1) upon deformation, clay produces clear and distinct fault surfaces that reveal detailed fault slip information, such as can be used for fault-scaling relations [e.g.,Clifton et al., 2000; Ackermann et al., 2001], and 2) faults within wet clay are more easily reactivated than faults within sand [e.g., Eisenstadt and Sims, 2005; Henza et al., 2010], which may better replicate deformation of natural systems.

[4] Wet kaolinite clay, in particular, has proved effective in analog modeling of crustal rocks because it has 1) relatively low plasticity index, compared to illite or montmorillonite clay, 2) relatively low viscoelasticity and 3) friction coefficients similar to crustal materials [e.g., Mitchell, 1993; Henza et al., 2009]. These three properties allow kaolinite to produce both distributed deformation and localized faulting with cohesive strength that scales appropriately to crustal rock [e.g., Eisenstadt and Sims, 2005].

[5] Although some of the mechanical properties of wet kaolin have been measured, such as shear strength [Eisenstadt and Sims, 2005] and friction coefficient [Henza et al., 2009], we lack a complete characterization of the rheology of the wet kaolin. Sandbox analog modeling has been invigorated in the past decade by the careful characterization of sand rheology [e.g., Lohrmann et al., 2003; Schellart, 2000], facilitating numerical simulations and enhancing our understanding of the faulting processes within the analog models [e.g., Buiter et al., 2006]. Just as Weijermars' [1986]careful analysis of the rheology of bouncing putty has guided subsequent analog modeling efforts of rock flow, a detailed characterization of the rheologic properties of wet kaolin can advance its application in analog modeling of faulting. In this paper, we present new rheologic data for wet kaolin that characterize the pre-failure and failure (faulting) behavior of the material. The results provide much needed constraints on wet kaolin rheology and highlight the utility of wet kaolin as a crustal analog material for investigations of faulting.

2. Wet Kaolin Clay

[6] This study uses kaolin clay produced primarily for the pottery industry and prepared as #6 tile clay. The high silt content of this kaolin is evident from a tooth test and a low measured plasticity index of 9–10. In order for analog experiments to adequately simulate crustal deformation at scales that are five orders of magnitude smaller than the crust, the strength of the analog materials needs to be about five orders of magnitude smaller than the strength of the crustal material [Hubbert, 1937]. One benefit of clay over other materials, such as sand, is that the cohesion can be systematically reduced by increasing the water content. The amount of water required to achieve cohesion five-orders lower than rock materials depends on the type of clay mineral. The high plasticity of some clay minerals, e.g., montmorillonite, necessitates water content so high that the clay will flow upon deformation rather than producing localized faults. In contrast, the low plasticity and high silt content of the #6 tile clay produces localized faults at water content appropriate for scaling to crustal strength.

3. Rheologic Properties

[7] We assess the properties of the wet kaolin in a TA Instruments AR2000ex torsional rheometer. The 1 × 19 mm, pancake-shaped sample is loaded in a parallel plate configuration, with stationary bottom plate and rotating upper plate (Figure 1). In order to drive shear localization within the clay rather than at the clay-steel boundary, a close-packed layer of 350μm diameter glass beads is glued to the surface of the upper plate. The sample geometry is such that strain increases linearly over the radius of the rotor. Consequently, the measured rheology is dominated by the outer rim of the sample, as both the circumference (area of contact) and the moment arm scale with radius. In the experiments we report engineering shear strain measured at this radius.

Figure 1.

Illustration of the TA Instruments AR2000ex rheometer with parallel plate geometry. Shear stress and strain are controlled through the upper rotor, which controls or measures angular displacement and torque. The surfaces are roughened with layers of 350 micron glass beads to localize deformation.

[8] We ran three sets of rheologic tests on the wet kaolin. To test the pre-failure behavior of the clay we ran a series of stepped creep-recovery tests under constant stress. By loading the kaolin in constant stress and then unloading to zero stress we can assess both the elastic and viscous creep components of deformation. In the second set of tests, we load the wet kaolin to failure under three different strain rates to measure the cohesive strength and test the dependency of peak strength on strain rate. In the third set of experiments, we used stepped hold tests with alternating fast and slow strain rates to explore the post-yield behavior of the clay.

[9] Analog experiments with wet kaolin are typically run with boundary velocities of 0.5 mm/min [e.g., Eisenstadt and Sims, 2005; Henza et al., 2010]. Depending on whether the wet kaolin is set up over a rubber sheet (i.e., distributed strain) or two juxtaposed plates (i.e., localized strain), the shear strain rate experienced by the kaolin due to boundary movement of 0.5 mm/min can range from ∼5 × 10−5/sec to ∼2 × 10−3/sec. The strain rates used in our tests for the failure strength of clay overlap this range (4 × 10−4, 1.2 × 10−3 and 2 × 10−3/sec). To assess the role of water content on rheology, we tested kaolin with both 62 and 66% water by mass.

3.1. Pre-failure Behavior of Wet Kaolin

[10] A series of low-stress creep-recovery tests was run to assess the pre-failure rheology of the wet kaolin. The resultant strains record both the elastic (instantaneous) and viscoelastic (time-dependent) components of deformation (Figure 2). The deformation in each step fits very well the model of a Burger's material, which incorporates both a Maxwell and Kelvin material in series (Figure 2 and equation (1)). The Burger's material is a commonly used phenomenological model for viscoelastic crustal deformation where multiple relaxation times are present [e.g., Hetland and Hager, 2005; Bürgmann and Dresen, 2008]. Under constant stress, σ0, the engineering shear strain, γ, in a Burger's material is a function of the shear moduli, GM,K, and viscosities, ηM,K, of the Maxwell and Kelvin parts of the series (subscripts M and K, respectively)

display math

Here t is time. Upon loading, a Maxwell material has an initial elastic deformation followed by time dependent viscous deformation. The Maxwell elastic component GM accounts for the instantaneous strain upon both loading and unloading. The Maxwell viscous component ηMproduces non-recoverable strain during the stress holds. The Kelvin component produces time dependent creep, which is recoverable due to the elastic portion of the Kelvin model that acts to pull the material back to the pre-stressed state when the external stress is relaxed.

Figure 2.

(a) Pre-failure creep-recovery curves for wet kaolin (b) for the stress history. The black curve shows least squares fits to (c) a viscoelastic Burger model. The elastic element accounts for the instantaneous, recoverable strain, the Kelvin element accounts for the recoverable, time-dependent strain, and the viscous element accounts for the unrecoverable, permanent strain.

[11] The wet kaolin exhibits all of the Burger's deformation components (Figure 2), but with stress dependent shear stiffness and viscosity. Each load step is matched to a Burger's material using different parameters (equation (1) and Table 1). The Maxwell elastic and viscous moduli are fit directly from the instantaneous and final strain, respectively; the Kelvin moduli are fit by a non-linear least squares optimization. The shear stiffness (Maxwell elastic component) is relatively constant with shear stress. However, the Maxwell viscosity systematically increases with shear stress reflecting a non-Newtonian rheology. Both the Kelvin elastic and viscous moduli generally increase with stress, especially between the first and second stress steps, suggesting strain hardening.

Table 1. Burger's Material Properties From Creep-Recovery Test (Equation (1))
Stress (Pa)Maxwell Elastic (Pa)Maxwell Viscous (Pa-s)Kelvin Elastic (Pa)Kelvin Viscous (Pa-s)
101.9 × 1042.3 × 1061.5 × 1040.6 × 106
202.4 × 1046.7 × 1062.5 × 1041.5 × 106
302.3 × 1047.9 × 1063.1 × 1041.2 × 106
402.0 × 1048.5 × 1063.0 × 1041.3 × 106

3.2. Failure Behavior of Wet Kaolin

[12] The wet kaolin was loaded to failure under constant shear strain rates. The slope of the stress-strain curve shows a typical roll-off as the failure strength is approached, indicating softening of the wet kaolin with higher load (Figure 3). The strain-rate dependent viscous properties of the wet kaolin contribute to the shear resistance during initial strain and failure but do not appear to change the peak strength. That is, the peak strength is reached at smaller strain for faster shear strain rate (Figure 3a, inset), but the ultimate strength of 60–100 Pa is largely independent of strain rate. In agreement with Eisenstadt and Sims [2005], we find that kaolin with greater water content has lower shear strength. The average shear strength of the 62% water content (w.c.) kaolin is 81 Pa, whereas the strength of the 66% w.c. kaolin is 66 Pa. Our results are also consistent with observations that the fault patterns within wet kaolin analog experiments are more sensitive to water content than strain rate [Bain and Beebe, 1954].

Figure 3.

(a) Shear stress vs. strain for experiments at different shear strain rates (3, 5 and 3 runs at 2 × 10−3, 1.2 × 10−3, 4 × 10−4 s−1 respectively). Inset focuses on the first 5% strain. The wet kaolin shows initially stiffer behavior at faster strain rates, but approaches the same yield strength at large strain. (b) Peak shear stress as a function of initial compaction during sample preparation. Compaction is measured from first contact with the 350 micron diameter glass beads. Colors show strain rates.

[13] The variations in peak strength between identical strain-rate experiments are at least partially related to varying residual normal stresses due to compaction during sample preparation (Figure 3b). In order to achieve complete coupling between the rotor and the wet kaolin, the glass beads coating the rotor are pushed a small distance into the clay. The peak shear strength is correlated with the reduction in sample height, i.e., compaction, imposed to achieve full coupling (Figure 3b). Even after the sample is allowed to relax for 2 minutes, samples with greater compaction likely retain larger residual compressive stresses. The increase in yield strength with inferred increase in normal compression suggests, at least qualitatively, a Mohr-Coulomb (or frictional) rheology at failure.

3.3. Post-failure Behavior of Wet Kaolin

[14] The post-failure properties of the wet kaolin are characterized by strain rate stepping experiments after yielding of the clay. The 66% w.c. kaolin has behavior similar to the 62% w.c. kaolin but at ∼15 Pa lower average shear stress levels (Figure 4). For both water contents, the kaolin evolves from a viscoelastic rheology prior to failure to a rate and state frictional rheology after failure. A step increase (decrease) in shear rate results in a step increase (decrease) in shear stress that subsequently relaxes (rebounds) to nearly the original stress value (Figure 4). The residual shear stress is slightly smaller during the faster strain rate steps, showing velocity-weakening behavior. These transient increases and decreases in shear stress mimic the evolution of friction in rocks and dry granular materials [e.g.,Marone, 1998].

Figure 4.

The variation of shear stress of the wet kaolin with stepped oscillations in shear strain rate, shown across the top of the figure. Residual strength under fast loading is lower than residual strength under slow loading, grey intervals. The kaolin with lower water content has lower shear strength but the same transient behavior as the kaolin with higher water content.

4. Discussion

[15] We have experimentally characterized the behavior of wet kaolin, identifying bi-viscous creep before failure, strain rate-independent strength at failure, and rate and state friction-like behavior after failure. These new data on wet kaolin rheology provide much needed constraints on the behavior of this analog material and provides support for the use of wet kaolin as a table-top analog for crustal deformation.

[16] Burger's materials display time-scale dependent deformation that can account for a variety of observations within the Earth's crust [e.g.,Bürgmann and Dresen, 2008]. The crust deforms elastically at coseismic strain rates, as evidenced by the close match between coseismic deformation fields and elastic models [e.g., Chinnery, 1961]. In the time period between earthquakes, we see time-dependent deformation that can be fit well to a Burger's material [e.g.,Hetland and Hager, 2005]. Although it is impossible to draw a direct comparison between the components of wet kaolin rheology and crustal processes, the clay behavior captures important phenomenological aspects of crustal deformation.

[17] After yielding, the wet kaolin exhibits rate and state frictional rheology. Granular materials often exhibit rate-and-state frictional behavior, where the frictional strength depends not only on the normal stress and cohesion but also on the sliding velocity (rate) and time since last sliding (state) [e.g.,Marone, 1998]. Within granular materials the immediate response to a velocity step (Figure 4) is thought to arise from the visco-plastic deformation of microscopic frictional contacts. The rate and state behavior in wet kaolin likely reflects the role of charge-related bonding between particles, rather than the plastic yielding of asperities.

[18] The wet kaolin exhibits velocity-weakening deformation after yielding, where the steady-state shear stress at faster velocities is lower than at slower velocities. Velocity weakening is an important property for a crustal analog material. In the absence of significant strain-weakening, velocity-weakening is a critical agent for driving spontaneous localization of deformation along faults [e.g.,Scruggs and Tullis, 1998].

[19] Our measured yield strength of 60–100 Pa agrees with previous measurements for similar wet kaolin [Eisenstadt and Sims, 2005]. The appropriate length scale for table-top experiments to simulate frictional failure processes within the crust is determined by the ratios of analog and crustal material density and strength [e.g.,Hubbert, 1937; Henza et al., 2010]. Assuming a crustal strength ∼10–20 MPa and density of ∼2.5 g/cm3, the table-top experiments with wet kaolin of density 1.6–1.7 g/cm3 scale as one cm of clay to 10–20 km of crust. With this length ratio and a ratio of model to crustal velocity of 6 × 103, the time ratio is 2 × 10−9, so that 1 model minute is equivalent to ∼10 k years.

[20] In experiments using 2–3 cm thickness of wet kaolin, the model simulates not only the predominantly elastic upper lithosphere but also a portion of viscous lower lithosphere. The Maxwell relaxation time 2ηM/GM of the wet kaolin at 40 Pa (half of failure strength) is 15 min (Table 1). The viscous relaxation of accumulated stresses within the wet kaolin during a 1–2 hour experiment may mimic stress relaxation with the lower lithosphere over a million years.

5. Conclusions

[21] New rheological data for wet kaolin provide support for its use in scaled table-top analog experiments that simulate deformation of the Earth's crust. The wet kaolin exhibits both elastic and viscous deformation that is well fit to a Burger's material, which can characterize deformation at a variety of time scales in the Earth's crust. On short time scales the wet kaolin is elastic and exhibits rate-independent failure strength. Consistent with previous studies, this failure strength depends on water content. This study presents new data revealing the frictional nature of deformation within the wet kaolin. Within the rheometer, the shear strength is sensitive to the amount of initial compaction. Additionally, the wet kaolin exhibits rate and state behavior after failure, typical of frictional materials. Because the wet kaolin exhibits deformation characteristic of both bi-viscous and frictional materials, this material is well suited to simulate a variety of deformational processes in the crust. Perhaps the best approach may be to compare analog models of wet kaolin to models of sand, which is more elastic pre-failure and plastic at failure. Neither of these materials is a perfect analog for the Earth but each captures important aspects of crustal rheology.


[22] Emily Brodsky of UC Santa Cruz generously provided time and support for the wet kaolin testing and analysis. Cooke was supported by NSF grant EAR0738887. An anonymous reviewer provided helpful suggestions for the paper.

[23] The Editor thanks an anonymous reviewer for his or her assistance in evaluating this paper.