This protocol allows to acquire particle scale data of granular soils using x-ray micro-tomography and develop a understanding of the micro-scale processes and mechanisms underlying the microscopic behavior of granular materials. The main advantage of this technique is that it provides a full access to the particle scale information of granular soils including particle morphology, microstructure, breakage, displacement, and rotation within the deformation of granular materials. This method can also be applied to the investigation of other types of stone-based natural or synthetic materials such as rocks, soil-rock mixture, concrete, ceramics, asphalt and even polymer composites.
Begin with design of the experiment well in advance as described in the text protocol. Determine test material, particle size, sample size, and sample initial porosity. To prepare a soil sample on the board, first add a small amount of silicone grease around the lateral surface of the top end of the base plate.
Then place a porous stone on its upper surface. Put a membrane around the lateral surface of the top end. Add a small amount of silicone grease on the contact surfaces between the two parts of the sample maker and place the sample maker on the base plate to allow the membrane to pass through it.
Lock the sample maker. Create suction inside the sample maker through its nozzle using a vacuum pump. Fix the membrane to the lateral surface of its upper end.
Ensure that the membrane is attached to the inner surface of the sample maker. Drop the test granular material from a certain height into the sample maker using a funnel until it is completely filled. The upper surface of the soil sample should be the same level as the upper edge of the sample maker.
Place another porous stone on top of the soil sample. Apply some silicone grease around the lateral surface of a stainless steel cushion plate and place it on top of the porous stone. Remove the top side of the membrane from the sample maker and fix it to the cushion plate.
Remove the suction inside the sample maker nozzle and create suction inside the valve on the base plate. Finally, remove the sample maker. A miniature dry sample is produced.
Now, fix the confining cell on the base plate and fix the chamber top plate on the top of the confining cell. Affix the rest of the loading apparatus on the chamber top plate. Add a constant confining pressure of 25 kilopascals to the sample and remove the suction inside the sample.
Gradually increase the confining pressure to a predetermined value using the confining pressure offering device. To scan a section of the sample, set the computed tomography or CT-scanner to image capture mode. Then, start the rotation stage to rotate the entire apparatus across 180 degrees at a predetermined constant rotation rate to capture CT projections of the sample at different angles.
For a high-spatial resolution CT scanner, a full scan of the sample usually requires the sample to be scanned at several different heights. Apply an axial load on the sample with a constant loading rate. Here, a loading rate of 0.2 percent per minute is used.
Users can set a different loading rate according to the experiment requirement. Pause the axial loading at a pre-determined axial strain. Wait until the measured axial force reaches a steady value, and carry out the next scan.
Repeat these steps until the end of loading. We construct CT slices of the sample based on the CT projections after phase retrieval using the PITRE software. Load the projections into PITRE from the menu load image.
Click the icon projection sinogram. Enter relevant parameters in the appeared window and click single to reconstruct a CT slice. Implement image filtering on the CT slices.
An anisotropic diffusion filter is used to perform image filtering. Now, perform image binarization on the filtered CT slices. To do so, implement the image binarization by applying an intensity value threshold to the CT slices.
This value is determined according to the intensity histogram of the CT slices using Otsu's method. Separate individual particles from the binarized CT slices using a marker-based watershed algorithm and store the results in a 3-D labeled image. Validate the results by comparing the calculated particle size distribution from the CT image to those from a mechanical sieving test.
A matlab script is used to extract particle properties, including particle volume, particle surface area, particle orientation, and particle centroid coordinates. Intrinsic matlab functions are used to acquire these properties for each particle. Extract contact foxholes from the binarized CT slices by implementation of a logical and operation between the binary image of the CT slices and the binary image of watershed lines acquired from the implementation of the marker-based watershed algorithm.
To quantify the strain field of the sample, use a grid-based method to calculate the strain field during any two consecutive scans, based on the particle translation and particle rotation. Analyze inter-particle contact evolution of the sample. Based on the extracted contact foxholes, the labeled images of particles, and the particle tracking results, analyze the branch vector orientation of the lost contacts and the gained contacts within the sample during each share increment.
The stress-strain curve and a 2-D slice of a Leighton Buzzard sand sample under triaxial compression are shown. Displayed here are particle kinematics results at the 2-D slice during the test. Most of the particles are successfully tracked and their translations and rotations are quantified.
A localized band is developed in both the particle displacement map and particle rotation map at the end of the test. Shown here is the normalized orientation frequency of branch vectors of gained contacts and lost contacts in the sample during the test. The lost contacts exhibit a clear directional preference towards the minor principle stress direction during the test.
Calibration of the rotation axis as detailed in the text protocol is important because the successful reconstruction of CT slice not only relies on the appropriate positioning of the rotation stage. To avoid any ionized radiation to human bodies from the x-ray source, one needs to make sure all doors and windows of the scanning room are properly closed before each scan. Following a similar procedure, institute testing with x-ray diffraction or scattering can be performed.
This provides a tool for measurement of inter-particle contact forces and their propagation within the forming granular materials. The acquired experimental data can be used for the development of advanced constitutive models of sand, considering their grain-scale mechanical behaviors, and for numerical modeling of sands under loading.
