Marone, C.

Rathbun, A.

Earth-prints Repository

Onset of Strain Localization in Sheared Glacial Till
Andrew P. Rathbun, Chris J. Marone
arathbun@geosc.psu.edu, cjm@geosc.psu.edu
Department of Geosciences, Penn State University, University Park PA 16802 
Penn State Rock and Sediment 
Mechanics Laboratory
ExperimentsSummary
Experimental Setup
Sample Characteristics
Fabric Development
 Granular Till Layer
 Normal 
  Stress
Shear Stress
 Load Point
Blocks:
10 x 10 cm2 contact area
Blocks grooved 0.8 mm
with a wavelength of 1 mm
Experimental Design:
Double-direct shear configuration
All experiments run at room temperature 
Saturated experiments conducted with the 
reservoir open to the atmosphere
Experiments conducted at 0.5, 1, and 5 MPa 
normal stress
Shear stress steps in creep experiments 
were 5 % of the shear strength
In rate controlled experiments driving 
velocity was 1-300µm/s
Caesar till collected in Central Ohio, USA, from the Scioto Lobe of the Laurentide Ice Sheet
Samples are air-dried and sieved to less than 1 mm
Bulk sample: 98.9% sand/1.0% silt, 0.1% clay
Experimental range: 98.7% sand/1.2% silt/0.1% clay
0
2
4
6
8
10
0 0.5 1 1.5 2 2.5 3
h
i
 = 1 cm, σ
n
 = 1 MPa
h
i
 = 0.5 cm σ
n
= 1 MPa
h
i
 = 1 cm σ
n
 = 5 MPa
h
i
 = 1 cm σ
n
 = 0.5 MPa
∆
Shear Strain
Ch
an
ge
 in
 L
ay
er
 T
hic
kn
es
s (
µm
)
Constant shear stress (creep) experiments. Boxed 
regions represent displacement controlled 
sections.  Displacement control establishes a 
consistent shear fabric. 
Shear creep experiments are ideally suited to assess the onset of shear localization due small amounts 
of strain during creep.  Shear stress is held constant for 45 minutes then increased by steps of 5% of the 
steady  state shear strength.  The amount of shear strain during each step is less than 0.1 during stable 
creep.  The amount of shear strain before creep is varied to investigate the onset of localization. Changes 
in dilation during creep are used as proxy for fabric development and shear localization. Frictional 
properties and shear strength are investigated under constant driving velocity . 
Most strain occurs during displacement 
control and high shear stress. During 
stable creep shear strain is less than 0.1.
The amount of shear strain before creep is varied 
from 0 to 2.6. Layer thickness (corrected for shear 
thinning) is near constant by a shear strain of 0.2.
Layer dilation progressively decreases until 
shear strain of 1, then remains constant. 
Layer thickness influences dilation at low 
shear strain. At low strain greater normal 
stress leads to greater dilation. 
Shear strain rate shown as a function of initial strain 
before creep. Data are shown for a range of  
normalized shear stress. Strain rate decreases with 
increased strain and the degree of shear localization 
of strain.
Layer dilation implies that fabric develops rapidly at low shear strains then remains constant. 
Changing layer thickness and normal stress only effect dilation and fabric development at low 
shear strains. Increased shear strain reduces the resulting shear strain rate from stress increases.  
0.45
0.5
0.55
0.26 0.28 0.3
Shear Stress (MPa)
Layer Thickness (µm)
Shear Strain
p1167
10 µm
∆h
Layer Thickness
Detrended Layer Thickness
Sh
ea
r S
tre
ss
 (M
Pa
)
La
ye
r T
hic
kn
es
s (
µm
)
1.  Velocity Dependence of Friction
	 Caesar Till is a velocity-strengthening material at all shear strain and normal stresses tested.
2.  Fabric Development
	 Changes in layer dilation shows that fabric develops gradually until a shear strain of 1, then remains 
	 constant until a shear strain of 2.6.
3.  Shear Localization
	 During distributed deformation, dilation scales with layer thickness. By a shear strain of 1, layer 	
	 thickness does not effect dilation implying a transition from distributed to localized deformation.  	
	 Localized shear decreases shear strain rate. 
Conclusions
Strain localization plays a key role in determining the frictional stability of brittle shear zones, 
which in turn influences the rheology and seismic/aseismic behavior of fault zones and 
deforming glacial till. Recent studies show that seismic, stick-slip motion occurs in dilatant till 
layers.  It appears that dynamic stresses and fluid migration during localized shear may induce 
stick-slip instability. However,  the laboratory data necessary to test such hypotheses are 
incomplete. We report on detailed laboratory experiments to measure the onset of shear 
localization of Caesar till sampled from the Scioto Lobe of the Laurentide Ice Sheet, collected in 
central Ohio, USA.
 
Experiments were conducted in a servo-controlled, double-direct shear apparatus with 
saturated samples at normal stresses of 0.5, 1, and 5 MPa. The layer thickness was either 0.5 or 1 
cm prior to shear. Till was sheared in constant velocity or constant shear stress (creep) boundary 
conditions. Creep experiments were employed to study frictional creep and the localization of 
strain. Creep was induced after an initial shear strain ranging from 0 to 2.6 to investigate the role 
of shear fabric on deformation. In creep experiments, shear stress increments began at ~ 2/3rds 
of the shear strength and continued until tertiary creep occurred. Stress steps were 5% of the 
shear strength and we determined the resulting strain rate and layer dilation.  
Creep experiments show a transition from distributed deformation to localized deformation at 
low strains. Velocity steps show that Caesar till is a velocity strengthening material, with the 
critical slip distance decreasing with strain up to 0.7 then remaining constant. Creep 
experiments show that dilatancy after a stress step decreases exponentially from ~10 µm at 
shear strain of zero to ~2 µm at a shear strain of 1. Beyond strains of 1 no variation in dilatancy is 
observed.   Decreasing initial layer thickness decreases dilation by the same factor at low strains, 
but has no effect at strains of 1 or greater. These results imply that shear becomes more localized 
over a finite displacement in a velocity strengthening material. Beyond the onset of localization 
variation in strain and driving velocity do not change the characteristics of strain localization. 
Localized deformation in till implies shallow deformation, which does not stabilize fast glacial 
slip and may lead to stick-slip motion.   
 
0
0.1
0.2
0.3
0.4
0.5
0.6
0
0.5
1
1.5
2
0 5 10 15 20
Shear Strain
Time x 103
Stress Control
p722
Sh
ea
r S
tre
ss
 (M
Pa
)
Sh
ea
r S
tra
in
 (s)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2 2.5
Shear Stress (MPa)
Shear Strain
τ
res
p722
Sh
ea
r S
tre
ss
 (M
Pa
)
0
0.1
0.2
0.3
0.4
0.5
0.6
8
9
10
0 0.2 0.4 0.6 0.8 1 1.2
Shear Stress (MPa)
Layer Thickness (mm)
Shear Strain
p1131 p1025
p1025
p1125
p1131
Sh
ea
r S
tre
ss
 (M
Pa
)
La
ye
r T
hic
kn
es
s (
m
m
)
0.535
0.54
0.545
0.55
2.42 2.44 2.46 2.48 2.5 2.52
Shear Stress/Normal Stress
Shear Strain
1 µm/s
    (v
o
)
3 µm/s
   (v)
a ln(v/v
0
)
b ln(v/v
0
)
p621
D
c
Sh
ea
r S
tre
ss
/N
or
m
al 
St
re
ss
-0.002
0
0.002
0.004
0.006
0.008
0.01
0.01 0.1 1 10
a-b
Normal Stress (MPa)
a-
b
Shear stress is increased in a series of steps. The 
trend of layer thickness changes as a result of the 
stress step. When shear thinning is accounted for, 
the layer dilates as a result of stress steps. 
The velocity dependence of 
friction is calculated from: 
All experiments show velocity-
strengthening frictional 
behavior (positive a-b).
10-8
10-7
10-6
10-5
0.0001
70 80 90 100
γ~0
γ = 0.15
γ = 0.25
γ = 0.55
γ > 1
Strain Rate (1/s)
Percent Shear Strength
Sh
ea
r S
tra
in 
Ra
te
 (1
/s)
€ 
a − b = ∆µss
∆ ln(V )
2 mm 1 mm
Distributed Deformation
Localized Deformation
SEM imagery of experiment p1344 shows heterogeneous distribution of high 
and low porosity zones


Onset of strain localization in sheared glacial till

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Onset of strain localization in sheared glacial till

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