Porosity and hydraulic conductivity[ edit ] Porosity can be proportional to hydraulic conductivity ; for two similar sandy aquifers, the one with a higher porosity will typically have a higher hydraulic conductivity more open area for the flow of waterbut there are many complications to this relationship. The principal complication is that there is not a direct proportionality between porosity and hydraulic conductivity but rather an inferred proportionality. There is a clear proportionality between pore throat radii and hydraulic conductivity.
The value of is determined by the current contact-stiffness model. Note that the normal stiffness,is a secant modulus in that it relates total displacement and force. The shear stiffnesson the other hand, is a tangent modulus in that it relates incremental displacement and force.
An uppercase will be used to denote a secant modulus, and a lowercase will be used to denote a tangent modulus. The computation of the normal contact force from the geometry alone makes the code less prone to numerical drift and able to handle arbitrary placement of balls and changes in ball radii after a simulation has begun.
The shear contact force is computed in an incremental fashion.
When the contact is formed, the total shear contact force is initialized to zero. Each subsequent relative shear-displacement increment results in an increment of elastic shear force that is added to the current value.
The motion of the contact must be considered during this procedure. The contact velocity can be resolved into normal and shear components with respect to the contact plane. Denoting these components by and for the normal and shear components, respectively, the shear component of the contact velocity can be written as The shear component of the contact displacement-increment vector, occurring over a time step ofis calculated by and is used to calculate the shear elastic force-increment vector The frictional resistance of the contact is given by where is the friction coefficient between the disks.
To simulate a relatively brittle rock-like material, it is necessary to cement these disks with a bonded model. This study uses the parallel bond model, which resists not only the contact forces but also the moments between the disks at a cemented contact Figure 1.
The function mechanism of the parallel bond model is described by where are the force components about the center of the cemented-contact zone, and are the moments about the center of the cemented-contact zone, and are the normal and shear bond stiffness per unit area, respectively, and are the rotation angle components, and, and are the area, polar moment of inertia, and moment of inertia of the bond contact cross section, respectively.
The strength of the cemented contact is then given by where is the radius of the bonded zone between the disks, is the length of the bonded zone between the disks Figure 1and and are the tensile and shear strength of the bond contact, respectively.
Tensile cracks occur when the applied tensile stress exceeds the specified tensile strength of the parallel bond. Shear cracks occur when the applied shear stress exceeds the specified shear strength of the parallel bond,either by rotation or by the shearing of the disks.
The tensile strength at the contact immediately drops to zero once the crack occurs, and the shear strength reduces to the residual friction strength see 5 [ 1922 ], as illustrated in Figure 2. Illustration of the yield process for a parallel bond. Microparameters of the Rock Sample The intact synthetic model material selected in this study is represented by compacted disks cemented with the parallel bond model.
Therefore, the micromechanical parameters consist of two categories: The PFC code allows one to simulate the macromechanical behavior of the selected synthetic model material by selecting appropriate values for the micromechanical parameters, such as the disk size distribution and packing, disk and parallel bond stiffness, disk friction coefficient, and bond strengths [ 1922 ].
To select the appropriate micromechanical parameter values for the synthetic intact material, one needs to basically go through a trial and error procedure by iteratively varying the micromechanical parameter values to match the required macromechanical behaviors of the selected synthetic material.
This procedure is known as the calibration of the intact synthetic material based on the micromechanical parameters. In this study, a special calibration sequence was followed to rationalize the micromechanical parameter calibration and to minimize the number of iterations.
First, the disk and parallel bond moduli and the ratios of normal to shear stiffness were set equal between the disks and parallel bonds to reduce the number of independent parameters [ 22 ]. After calibrating the aforementioned deformation micromechanical parameters, the peak strength between the numerical and laboratory specimens was matched by gradually reducing the normal and shear bond strengths of the parallel bonds.
During this procedure, it is important to fix the ratio of normal to shear bond strengthbecause these parameters affect the failure mode of the specimen. Therefore, a series of numerical simulations were conducted to match the failure mode of the cylindrical specimen between the numerical and laboratory specimens by varyingwhile keeping the other parameters unchanged.
The obtained failure modes with varying for the cylindrical specimens used in the numerical simulations are displayed in Figure 3. Failure patterns in the cylindrical sample subjected to uniaxial compression.
As seen in Figure 3as the specimen is compressed under uniaxial stress, numerous cracks tensile and shear cracks are produced through the breakage of parallel bonds. The failure mode of the numerically simulated synthetic cylindrical specimen with agrees well with the results from the laboratory specimen.
Thus, setting the ratio of normal to shear bond strength equal to one seems to increase the confidence of the numerical model in simulating the appropriate failure behavior of the synthetic material. The numerically obtained stress-strain curves were compared with the stress-strain curve obtained from the laboratory sample as shown in Figure 4.
Therefore, the disk contact modulus values need to be modified simultaneously with the value.Withdrawn Standards. ANSIZ American National Standard for Personal Protection - Protective Footwear. A4- Withdrawn Specification for Medium-Carbon-Steel Splice Bars. PRINCIPLES OF SOIL DYNAMICS is an unparalleled reference book designed for an introductory course on Soil Dynamics.
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