1. Modeling the Growth and Interaction of Stylolite Networks, Using the Discrete Element Method for Pressure Solution
Nataliia Makedonska1, David Sparks2, Einat Aharonov1
1 Institute of Earth Sciences, Hebrew University, Givat Ram, Jerusalem 91904, Israel
2 Department of Geology and Geophysics, Texas A&M University, College Station, Texas, USA
Introduction ==
Modeling Stylolites
as a Form of Localized Pressure Solution
Mechanical and Chemical compaction in constant stress sn sn
Bonded contact (blue)
Contact broken by bending (green)
Contact broken by tension (brown)
Contact broken by shear (yellow)
Newly formed contact (black)
Pressure solution (also termed chemical compaction) is considered the most important ductile deformation mechanism operating in the Earth’s upper crust. This mechanism is a major player in a variety of geological processes, including evolution of sedimentary basins, hydrocarbon reservoirs, aquifers, earthquake recurrence cycles, and fault healing.
Stylolite seams are surfaces on which dissolution has been highly concentrated, relative to the surrounding area. Stylolites are often marked by the concentration of the insoluble constituents of the rock, such as clay, iron oxide, quartz sand and other particles. It has been proposed that grain dissolution is greatly enhanced along clay-filled contacts, because the clay acts as a catalyst to dissolution (Aharonov & Katsman, 2009). sp sp
Modeling of clay in a grain-grain contact
Some contacts are taken to have clay on them. As grain dissolution continues, insoluble clay will accumulate on the contacts.
After ~0.15 strain on a contact, the rate constant begins to increase to 100 times it’s initial value at a strain of 0.25. sn
Rate constant sp sp
Pressure solution in rocks often localizes into solution seams or stylolites. Field observations of stylolites often show elastic/brittle interactions in regions between pressure solution features, including shear fractures, veins, and pull-apart features. To understand these interactions, we use a grain-scale model based on the Discrete Element Method, that allows granular dissolution at stressed contacts between grains. The new model captures both the slow chemical compaction process and the more abrupt brittle fracturing and sliding between grains.
Grain convergence, t0
t =12000
t =24000
t =36000
t =48000 ==
Compaction vs. time
Cohesive and dissolving contact (blue)
Broken contacts (yellow)
Contacts dissolving with clay (green)
regions with increased clay content sn sn
Statistics of broken contacts
Radius of bond, ac
0.15, 0.3, 0.5
Uniform stress –solid
Differential stress - dashed
Two offset clay-rich regions are prescribed, which have enhanced dissolution rate. High dissolution rates keep stresses across most of the stylolite near zero, except for a tensile region near the tip, and a compressional concentration outside the tip. Stresses are compared with those predicted theoretically using Eshelby transformation theory (Katsman, Aharonov, Scher, 2006).
Numerical Model
and Initial Parameters
Contact radius, a, begins to increase when dissolution has removed all cement.
Total Vertical Strain
time
With increasing time, strain progresses by both dissolution and grain rearrangement due to breaking bonds and frictional sliding.
Compaction is always faster in systems with differential stress.
Dissolution rate depends strongly on contact radius; for cases with more cement (larger bond radius), dissolution progresses more slowly. sp sp
Pressure Solution Discrete Element Method (PSDEM) combines friction and brittle deformation with pressure dissolution on grain contacts, by allowing the grains to change size and shape as a function of the stress that is applied on their contact.
Rock is simulated as collection of cohesive grains, following the bonded-particle method of Potyondy and Cundall, Spherical particles are joined by a cylinder of cement with radius a=aC min(Ri, Rj), where aC<1. The force between bonded grains is given by a linear elastic relation; for unbonded grains, a non-linear Hertzian contact is used. sp
a=aC Rj sp Ri Rj
time
Compressional Stress concentrations outside stylolite tip
Much more damage occurs under differential stress. Most bond breaking occurs by torsion, except for low cement cases.
Cohesive bonds break by:
tension
bending
time
shear
Chemical compaction
Chemical vs. total compaction
time
Dissolution in a grain-grain contact
Dissolution is represented by penetration of contacting grains into each other with a rate that depends on local conditions. The elastic repulsive force between grains depends on the difference between the separation of the grain centers and an equlibrium length of the contact, leq. This equilibrium length shortens with time to simulate dissolution.
Time
Mechanical compaction
Dissolution Strain
Dissolution Strain
Dissolution Strain
Average normal stress on grain contacts.
Broken bonds in shear zone
Contact radius, a, begins to increase when dissolution has removed all cement.
Normal stress across cross-section
time
Total Vertical Strain
The rate of grain convergence:
We can approximate the strain due just to chemical compaction from the average shortening of the equilibrium length of contacts. The average dissolution is not strongly affected by stress state.
The difference between the dissolution strain and the total strain is an indication of mechanical strain achieved by breaking bonds, which occurs much more frequently in the differential stress cases.
Ceff –effective rate constant for diffusion-limited convergence
σn – effective normal stress on contact
ρs – mass density of solid phase
Distance
Distance
t =6000
t =18000
Initial grain
configuration
Parameters of GD modeling (dimensionless)
Applied normal force, sn x 10-4, 7.5 x 10-4
Applied horizontal force, sp x 10-4, 2.5 x 10-4
Applied force ratio, sn/sp , 3
Radius of cement cylinder, ac , 0.3, 0.5
Normal spring stiffness, kn
Shear stiffness, ks
Surface friction coefficient, ms 0.3
Damping coefficient, g
Dissolution coefficient , C eff m2 s
Summary
Grains are placed in between two rough walls made from glued half circles. The vertical normal stress, sn, is applied to every grain in top wall, and a horizontal normal stress, sp, is applied to every grain in left and right boundaries.
Here we present a new numerical model of pressure solution, based on the Discrete Element Method. This approach allows granular dissolution at stressed contacts between grains, combined with fracturing and faulting.
The new model captures both the slow chemical compaction process and the more abrupt brittle fracturing and sliding between grains. Field observations of interactions between pressure solution features and veins, shear fractures and pull-apart are reproduced very well with the new Pressure Solution Discrete Element Method. (HOW IS THIS SHOWN?, THERE IS NO DISCUSSION OF FIELD)
We apply our model into simulation of stylolites via localization of dissolution. Simulation results show distinct brittle features, such as cracks and shear zone between two stylolite tips. Tension and compression regions on grain’s stresses were observed near stylolite tips.