Crack Area Ratio Research Articles

Multi-scale investigation on staged deterioration mechanism of sliding-zone soils induced by reservoir fluctuations

Water level fluctuations in the reservoir deteriorate soils and rocks on the bank landslides by drying-wetting (D-W) cycles, which results in a significant decrease in mechanical properties. A comprehensive understanding of deterioration mechanism of sliding-zone soils is of great significance for interpreting the deformation behavior of landslides. However, quantitative investigation on the deterioration characteristics of soils considering the structural evolution under D-W cycles is still limited. Here, we carry out a series of laboratory tests to characterize the multi-scale deterioration of sliding-zone soils and reveal the mechanism of shear strength decay under D-W cycles. Firstly, we describe the micropores into five grades by scanning electron microscope and observe a critical change in porosity after the first three cycles. We categorize the mesoscale cracks into five classes using digital photography and observe a stepwise increase in crack area ratio. Secondly, we propose a shear strength decay model based on fractal theory which is verified by the results of consolidated undrained triaxial tests. Cohesion and friction angle of sliding-zone soils are found to show different decay patterns resulting from the staged evolution of structure. Then, structural deterioration processes including cementation destruction, pores expansion, aggregations decomposition, and clusters assembly are considered to occur to decay the shear strength differently. Finally, a three-stage deterioration mechanism associated with four structural deterioration processes is revealed, which helps to better interpret the intrinsic mechanism of shear strength decay. These findings provide the theoretical basis for the further accurate evaluation of reservoir landslides stability under water level fluctuations.

Mechanical properties and risk characterization of surrounding rocks containing various blocks of arch-shaped holes under biaxial compression

In most rock engineering, the rock mass was cut into different blocks by natural structural planes, and the stability of underground openings was affected by the type, number, position and mechanical properties of rock blocks. In this study, the biaxial compression tests were conducted using rock-like material specimens with prefabricated arch-shaped holes and different types of blocks, and the failure and crack propagation properties of surrounding rocks were studied. Firstly, the location and danger degree of blocks in rock mass were classified, and the rock block danger analysis (BDA) method was proposed. Secondly, the support effect on the stability of surrounding rocks with different blocks was studied. Then, the deformation, strength, crack area ratio, and debris distribution characteristics of specimens were analyzed. Finally, the reasonable support schemes were proposed for surrounding rocks with different types and sizes of blocks. The test results showed that the σ-ε curve of holed rocks was similar to that of intact rocks, and the micro-cracks evolved into macro-cracks at crack destabilization expansion stage, followed by large deformation of whole specimens and spalling. Under support condition, as the block size increased, the crack area ratio decreased and the stability of holed specimens improved. Furthermore, the biaxial compressive strength of the surrounding rock and the stability of the holed specimens decreased as the block danger coefficients increased.

Insights into dynamic cracking and failure mechanisms of weakly cemented siltstone under impact loading

Soft strata composed of weakly cemented rock normally suffer from the dynamic load in underground energy mining engineering, yet there is a notable lack of research into the dynamic mechanical characteristics of such materials. In this study, the split Hopkinson pressure bar system was adopted to conduct compression tests under four different impact pressures to reveal the dynamic mechanical performances of the weakly cemented siltstone (WCS). Results showed that under different strain rates, dynamic stress-strain curves of the specimen displayed similar trends. The dynamic compressive strength, critical strain and dynamic toughness of WCS all increased as the strain rate increased, while the dynamic elastic modulus had almost no strain rate effect. Besides, combined with the high-speed camera, the dynamic failure process of WCS was analyzed, and the crack area ratio was defined to quantitatively analyze the damage evolution law of WCS under impact loading. Moreover, the dynamic failure mechanism of WCS was clarified from the microstructure level. Finally, the scaling law model for calculating the dynamic compressive strength was proposed for WCS, and the modeling results exhibited a close agreement with the test results. The research results can provide mechanical parameters and a theoretical basis for the safety assessment of weakly cemented rock strata during energy mining.

Variation in sprinkler irrigation droplet impact angle on the physical crusting properties of soils

The angle at which a droplet impacts determines its shearing and compaction effects on soil, which in turn affects the formation and properties of the physical soil crust. To investigate the effect of the droplet impact angle on soil physical crusting, this study considered droplet quantity, quality, and velocity and proposes an energy-weighted method for calculation of the equivalent droplet impact angle. Droplet information was acquired using a spraying platform with a controllable droplet impact angle and two-dimensional video disdrometer (2DVD). Six groups (38.10°, 49.43°, 58.77°, 68.88°, 76.81° and 84.10°) of droplet impact angles were established to obtain the parameters of the soil physical crust characteristics at different droplet impact angles by indoor soil tank tests. The results show that: 1) the stable values of crack length density (CLD), crust thickness (Ct), soil bulk density (BD), cohesion force (Cf), and internal friction angle (IfA) are strongly positively correlated with droplet impact angle; 2) the stable value of the crack area ratio (CAR) is strongly negatively correlated with the droplet impact angle, with maximum and minimum values of 6.94% and 5.57%, respectively; 3) the content of macro aggregates (MAA) tends to increase and then decrease with the increase in droplet impact angle, and the content of MAA has a maximum value of 50.2% at the impact angle of 68.88°. The content of micro aggregates (MIA) tends to decrease and then increase with the increase in the drop impact angle, with a minimum value of MIA of 20.4% at the impact angle of 58.77°; 4) the maximum soil bulk density of 1.99 g·cm−3 at an impact angle of 84.10° is significantly greater than the initial soil bulk density (1.35 g·cm−3); 5) the energy-weighted equivalent droplet impact angle takes into account the effects of both large and small droplets and characterises the overall impact angle of the sprayed droplet from an energy perspective. The results of this study provide new ideas for determining suitable sprinkler irrigation parameters to reduce soil erosion and promote the sustainable development of irrigated agriculture.

Radiation-induced alteration of sandstone concrete aggregate

This study investigates the alteration of felsic sandstone-type rock, which is used as a coarse aggregate in concrete, subject to the effects of gamma-ray and neutron irradiation. The effects of three gamma-ray doses (27, 55, and 108 MGy) and four neutron fluence levels (1.22, 2.19, 6.99, and 14.30 × 1019 n/cm2, E ≥ 0.01 MeV) were investigated. Quartz and albite were found to be the major rock-forming minerals, with microcline intermediates, chlorite, and muscovite as the minors. Gamma rays caused no significant changes to the physical properties of the sandstone aggregates, even at high doses (108 MGy). In contrast, neutron irradiation caused alterations that became more pronounced at higher neutron fluences. The solid was confirmed to expand through metamictization of the rock-forming minerals. Quartz and muscovite were the most affected phases, whereas albite and microcline intermediates were only slightly affected, and chlorite was almost unaffected. The decrease in density was measured by He and water pycnometry, and this value was almost reproduced by calculations using the rock-forming mineral composition of the pristine sample measured using X-ray powder diffraction/Rietveld analysis and the cell volume change of the major forming minerals. In addition, light optical microscopy and scanning electron microscopy images confirmed the presence of intergranular and intragranular cracks. Intergranular cracks appeared to have initiated from the quartz grains, which expanded significantly. The intragranular cracks were frequently observed in the albite and microcline intermediates. These cracks can be described as radial cracks starting from the expanding quartz, caused by enforced displacement for deformation consistency with quartz expansion. The crack area ratio quantified by SEM image analysis corresponds to the discrepancy of the volume expansion difference calculated by He or water pycnometry and dimensional change measurements. An evaluation of solid expansion and crack openings in aggregates is important to estimate concrete degradation.

Flexural behavior of the UHPCC containing glass powder as partial substitute of cement/silica fume

This study aims to achieve the sustainability and environmental protection of ultra-high performance cementitious composite (UHPCC) by substituting cement/silica fume with glass powder (GP), and to investigate the influence of various GP substitution levels on flexural behavior. The damage patterns of GP-UHPCC are also investigated by using digital image control technique and RFPA3D program. The crack opening displacement, crack length, internal damage degree of all test series with various GP substitution levels were quantitatively characterized. The results indicate that GP as partial substitution in UHPCC is able to contribute to improving flexural strength. The energy absorption capacity of the specimen with 20% GP substitution level in all loading phases is the largest among all specimens. In addition, the crack area ratio and AE-accumulative energy of high GP substitution levels (15%–30%) is obviously higher than that of low levels (0%–10%). Generally speaking, GP substitution level of 15%–30% is found the most effective range for improving flexural behavior in this study.

Sour Environmental Severity for Hydrogen-Induced Cracking Susceptibility

The severity of sour environments has been determined in accordance with the European Federation of Corrosion 16 and NACE MR0175/ISO 15156-2:2015 standards for carbon and low-alloy steels, based on the experimental results of sulfide stress cracking (SSC). However, the severity map obtained from SSC test results cannot be applicable to the hydrogen-induced cracking (HIC) susceptibility. In this study, the hydrogen permeability and crack area ratio of HIC under various pH and H2S partial pressures (pH2S) were measured to establish the link between the sour environmental severity and HIC susceptibility using grades X65 to X80 steels for linepipes. In addition, the hydrogen concentration at the location of the HIC was calculated by the finite element analysis. The results showed that the sour environmental severity map obtained from hydrogen permeation tests changes with time because the hydrogen permeability reached maximum values in the early stage and steady-state values in the later stage. Then, the HIC susceptibility did not correspond to the maximum permeability, but to the steady-state hydrogen permeability. In addition, the hydrogen content at the location of the HIC did not correspond to the maximum hydrogen permeability but corresponded to the steady-state hydrogen permeability, because HIC occurred in the center segregation part and the hydrogen atoms required a certain time to diffuse from the metal surface to the mid-thickness. These results suggest that the HIC susceptibility is dominated by the severity map obtained from the steady-state hydrogen permeability.

Study on Crack Development and Micro-Pore Mechanism of Expansive Soil Improved by Coal Gangue under Drying-Wetting Cycles.

Expansive soil is prone to cracks under a drying–wetting cycle environment, which brings many disasters to road engineering. The main purpose of this study is use coal gangue powder to improve expansive soil, in order to reduce its cracks and further explore its micro-pore mechanism. The drying–wetting cycles test is carried out on the soil sample, and the crack parameters of the soil sample are obtained by Matlab and Image J software. The roughness and micro-pore characteristics of the soil samples are revealed by means of the Laser confocal 3D microscope and Mercury intrusion meter. The results show that coal gangue powder reduces the crack area ratio of expansive soil by 48.9%, and the crack initiation time is delayed by at least 60 min. Coal gangue powder can increase the internal roughness of expansive soil. The greater the roughness of the soil, the less cracks in the soil. After six drying–wetting cycles, the porosity and average pore diameter of the improved and expanded soil are reduced by 37% and 30%, respectively, as compared to the plain expansive soil. By analyzing the cumulative pore volume and cumulative pore density parameters of soil samples, it is found that the macro-cracks are caused by the continuous connection and fusion of micro-voids in soil. Coal gangue powder can significantly reduce the proportion of micro-voids, cumulative pore volume, and cumulative pore density in expansive soil, so as to reduce the macro-cracks.

A computational model for thick concrete slab demolition using soundless chemical demolition agent

Soundless chemical demolition agents (SCDAs) provide a feasible route to meet the demolition in the modern construction industry. Exploration of how to efficiently demolish reinforced concretemembers with SCDAs is in deep demand. To investigate the method and computational model of demolishing thick concrete slab, static crushing experiments of 12 thick concrete slab specimens with different parameters were carried out. To remove the constraint of reinforcements, the reinforcements in the upper part of the thick concrete slab specimens were cut off along the hole connection and its extension line before grouting. The results showed that cracks were formed at the cutting seams on the upper surface due to the defect caused by cutting reinforcements, and these cracks extended to the bottom of the specimens. The development of cut seam width was over 80% on the first day, and 20% in the following day. Besides, the ratio of the area of the cut seams on the upper surface of the specimen to the area of the upper surface of the specimen (i.e. crack area ratio) was proposed to evaluate the influence of the compressive strength of concrete, hole spacing, and hole diameter in the concrete demolition. Finally, a new computational model for calculating hole spacing by taking time, compressive strength of concrete, hole diameter, ambient temperature, and crack area ratio into consideration was proposed. The proposed computational model was verified with experimental data and was expected to guide the application of SCDAs in civil engineering.

Investigation on Dynamical Mechanics, Energy Dissipation, and Microstructural Characteristics of Cemented Tailings Backfill under SHPB Tests

As mining depth increases, the backfill mining method is more and more widely used in underground mines. The dynamic load generated by the blasting can affect the stability of the cemented tailings backfill (CTB). The CTB samples were prepared to conduct a test of the split Hopkinson pressure bar (SHPB) to investigate the dynamic disturbance of CTB. The present paper discusses dynamical mechanics, energy dissipation, and microstructure analysis of CTB. Micro-computer tomography (micro-CT) scanning of CTB samples after the SHPB test was performed to analyze the evolution of internal cracks. The experimental results showed that when the average strain rate (ASR) increased from 30 to 98 s−1, the dynamic uniaxial compression strength (DUCS) of the CTB showed a trend of first increasing and decreasing with the increase in ASR. The dynamic stress–strain pre-peak curve of CTB directly enters the linear elastic stage. As ASR increases, the absorbed energy of the CTB shows a trend of first increasing and then decreasing. Moreover, according to the micro-CT scanning results, the crack area of CTB accounts for about 16% of the sample near the incident bar and about 1% near the transmitted bar. The crack area ratio is exponentially related to the specimen height. These findings can provide reasonable dynamical CTB strength data selection for underground pillar mining.

Formation and Impact of Microcracks in Plasma Erosion of M26 Boron Nitride

This Paper investigates the role of microcracks in Hall thruster wall erosion. The formation and growth of microcracks on the surface of M26 grade boron nitride composite due to repeated thermal shock was quantified, and the subsequent impact of microcracks on plasma erosion was assessed. Thermal shock cycles (20 → 800 → 20°C) were provided by a radiation oven to induce thermal stresses similar to those incurred by a Hall thruster wall. The average ratio of crack area to total area was observed to grow as a power law with subunity exponential from 4–5% before thermal cycling to 15–18% after 20 thermal shock cycles. Cycled and control samples were simultaneously exposed to argon plasma with average ion energy of 130 eV. All samples were observed to preferentially retain boron nitride relative to silica, and microcracks were not observed to significantly impact surface composition or feature development.

Electromagnetic interference shielding of multi-cracked high-performance fiber-reinforced cement composites – Effects of matrix strength and carbon fiber

High-performance fiber-reinforced cement composites (HPFRCC) can be adopted as a building material for electromagnetic interference (EMI) shielding due to its high-volume content of conductive steel fibers incorporated. Structures made of HPFRCC are, however, highly possible to have very tiny microcracks, formed by environmental factors, so that the relationship between the crack areas and the EMI shielding effectiveness needs to be evaluated. For this, two different matrix strengths of 100 and 180 MPa and two different volume contents of carbon fibers, i.e., 0.1, and 0.3%, were considered, and various cracking areas in the HPFRCC were intentionally created in this study. The lower-strength composites provided better shielding effectiveness as compared to the higher-strength composites for both the non- and multi-cracked states due to a presence of iron(III) oxide and smaller silica fume contents. The addition of 0.3% carbon fibers was effective on improving both the electrical conductivity and shielding effectiveness of HPFRCC. The efficiency of carbon fibers on the shielding effectiveness increased at higher frequencies and micro-cracked states. The shielding effectiveness of HPFRCC was deteriorated with increased total crack area ratio that is from the multiple microcracks and macro localized cracks. The biggest reduction rate of the shielding effectiveness in the multi-cracked HPFRCC was found to be 23% at the modulus of rupture point as compared with the non-cracked counterpart. Such a deterioration of EMI shielding effectiveness of HPFRCC by crack formation needs to be thus considered in its practical application.

Antimicrobial Bioresorbable Mg-Zn-Ca Alloy for Bone Repair in a Comparison Study with Mg-Zn-Sr Alloy and Pure Mg.

Magnesium-zinc-calcium (Mg-Zn-Ca) alloys have attracted increasing attention for biomedical implant applications, especially for bone repair, because of their biocompatibility, biodegradability, and similar mechanical properties to human bone. The objectives of this study were to characterize Mg-2 wt % Zn-0.5 wt % Ca (named ZC21) alloy pins microstructurally and mechanically, and determine their degradation and interactions with host cells and pathogenic bacteria in vitro and in vivo in comparison with the previously studied Mg-4 wt % Zn-1 wt % strontium (named ZSr41) alloy and Mg control. Specifically, the in vitro degradation and cytocompatibility of ZC21 pins with bone marrow derived mesenchymal stem cells (BMSCs) were investigated using both direct culture and direct exposure culture methods. The adhesion density of BMSCs on ZC21 pins (i.e., direct contact) was significantly higher than on pure Mg pins in both in vitro culture methods; the cell adhesion density around ZC21 pins (i.e., indirect contact) was similar to the cell-only positive control in both in vitro culture methods. Interestingly, ZC21 showed a higher daily degradation rate, crack width and crack area ratio in the direct exposure culture than in the direct culture, suggesting different culture methods did affect its in vitro degradation behaviors. When cultured with Gram-positive bacteria methicillin-resistant Staphylococcus aureus (MRSA), ZC21 reduced bacterial adhesion on the surface more significantly than that of ZSr41 and Mg. The in vivo degradation and biocompatibility of the ZC21 pins for bone regeneration were studied in a mouse femoral defect model. The in vivo degradation rate of ZC21 pins was much slower than that of ZSr41 alloy and Mg control pins. After 12 weeks of implantation in vivo, the ZC21 group showed the shortest gap at the femoral defect, indicating that ZC21 pins promoted osteogenesis and bone healing more than ZSr41 and Mg control pins. Overall, the ZC21 alloy is promising for bone repair, while providing antibacterial activities, and should be further studied toward clinical translation.

Oxidation and cracking/spallation resistance of ZrB2–SiC–TaSi2–Si coating on siliconized graphite at 1500 °C in air

A ZrB2–SiC–TaSi2–Si coating on siliconized graphite substrate was prepared by a combination process of slurry brushing and vapor silicon infiltration. The high-temperature oxidation behavior and cracking/spallation resistance of the as-prepared coating were investigated in detail. It was revealed that the oxidation kinetics at 1500 °C in static air followed a parabolic law with a relatively low oxidation rate constant down to 0.27 mg/(cm2·h0.5). The crack area ratio of the as-prepared coating was determined as 3.8 × 10−3 after severe thermal cycling from 1500 °C to room temperature for 20 times. Apart from the formation of ZrO2 as skeleton phase with SiO2 as infilling species, the good oxidation and cracking/spallation resistance of the coating also could be attributed to its unique duplex-layered structure, i.e., a dense ZrB2–SiC–TaSi2 major layer filled with Si and an outermost Si cladding top layer. Meanwhile, the strong adhesion strength of the SiC transition layer with the graphite substrate and the outer ZrB2–SiC–TaSi2–Si layer was a vital factor as well.

Coupled effect of PP fiber, PVA fiber and bacteria on self-healing efficiency of early-age cracks in concrete

Both bacteria and fiber can promote self-healing of cracks in concrete by accelerating calcium carbonate precipitation. Calcium carbonate in bacterial concrete grows from section surfaces of cracks, which might be altered after incorporating fibers. Therefore, this paper investigated coupled effect of PP fiber, PVA fiber and bacteria on self-healing efficiency of concrete. Optical density of bacteria cultivated in medium containing fiber was measured by using multifunction microplate reader, results showed that PP fiber and PVA fiber resulted in decrease of bacteria concentration. In addition, calcium carbonate induced by bacteria was synthesized in solution with fiber and characterized by using X-ray Diffraction, FTIR and particle size analyzer. Results revealed that the polymorphs of calcium carbonates were all calcite, while calcite generated in solution with PVA fiber showed lager particle size. In bacterial fiber reinforced concrete, crack width of 300–500 μm was obtained and autogenous healing performance was evaluated. The results showed that although repair ratio of crack area for specimens with bacteria and fiber was slightly lower than that with bacteria only, water tightness and flexural strength regain ratio were improved evidently. By measuring the amount of calcium ions in repair medium and observing calcium carbonate distribution in the cracks, it could be concluded that PP fiber and PVA fiber were conductive to calcium leaching and calcium ions utilization. Deposition was attached on surfaces of fibers and can even be observed on PVA fibers inside of cracks, which was due to effect of polarity groups and cell structure of polyvinyl alcohol fiber on calcium carbonate nucleation. Therefore, the study suggests that coupled effect of PP fiber, PVA fiber and bacteria has potential to enable excellent self-healing performance in concrete.

Investigation of Gas Transport Properties of PEMFC Catalyst Layers by Using a Microfluidic Device

Effective gas diffusivity and tortuosity factor of catalyst layers used in proton exchange membrane fuel cells were evaluated by using an in-house microfluidic device. Gas transport properties of the catalyst layers are one of the key factors to have high-performance catalyst layers and fuel cells. Two catalyst layers with different thickness were fabricated and evaluated. The only difference between the two catalyst layers in their fabrication processes was a blading gap in the applying process by a doctor blade method. The resultant thicknesses of the catalyst layers were 5 and 11 μm. Porosity and pore size distribution were almost the same, while crack area ratio of the thick catalyst layer was larger than that of the thin catalyst layer. The effective diffusivity of the thick catalyst layer was slightly larger than that of the thin catalyst layer. The crack area can affect the gas diffusivity.

Desiccation Characteristics and Desiccation-Induced Compressive Strength of Natural Fibre-Reinforced Soil

In this study, desiccation characteristics of natural fibre-reinforced soil were investigated. The soil was mixed with sisal fibres (25 mm) at the fibre content of 0.5% and 1%. The effects of soil thickness on the desiccation characteristics were investigated using specimens with thickness of 6, 12 and 24 mm. Digital image analysis was used to study variation of crack morphology, width, surface crack area ratio, crack growth rate and shrinkage strain of the desiccated soil. The gravimetric measurements of moisture content were used to investigate rate of moisture loss and evolution of cracks with change in moisture. The effects of saturation and desaturation on the compressive strength of the soil were investigated by subjecting the compacted soil to wet and dry cycles. The results showed that crack morphology of the reinforced soil was characterised by small cell areas of irregular shapes, short and thin cracks and non-orthogonal crack intersections. Specimens with fibre content of 0.5% showed lower rate of moisture loss than unreinforced soil. This was attributed to the reduction of free moisture caused by fibre moisture absorption. Specimens with fibre content of 1% indicated higher rate of moisture loss than unreinforced soil due to an increase in the volume of water pathways. Crack width and surface crack area ratio showed reduction of 74% and 35%, respectively, with 1% fibre content. The crack growth rate and shrinkage strain significantly reduced with fibre inclusion. Increase in the soil thickness caused an increase in crack width and evaporation for both reinforced and unreinforced soil. Increasing number of wet and dry cycles up to 15 caused compressive strength degradation of 41% and 66% for compacted reinforced and unreinforced soil, respectively. Natural fibre inclusion can effectively be applied to control desiccation cracking of the soil which is beneficial in maintaining integrity of soil for various civil engineering applications.

Layer Formation from Polymer Carbon-Black Dispersions

It has been well-established that effects such as cracking are observable when wet layers are dried. In particular, the layer thickness, as well as the surface tension of the liquid, is responsible for this behavior. The layer formation of polymer electrolyte fuel cells and electrolyzer electrodes, however, has not yet been analyzed in relation to these issues, even though the effect of cracks on cell performance and durability has been frequently discussed. In this paper, water propanol polymer-containing carbon-black dispersions are analyzed in situ with regard to their composition during drying. We demonstrate that crack behavior can be steered by slight variations in the initial dispersion when the solvent mixture is near the dynamic azeotropic point. This minor adjustment may strongly affect the drying behavior, leading to either propanol or water-enriched liquid phases at the end of the drying process. If the evaporation of the solvent results in propanol enrichment, the critical layer thickness at which cracks occur will be increased by about 30% due to a decrease in the capillary pressure. Microscopic images indicate that the crack area ratio and width depend on the wet layer thickness and initial liquid phase composition. These results are of much value for future electrode fabrication, as cracks affect electrode properties.

Surface morphology of soil cracks in Yuanmou Dry-hot Valley Region, Southwest China

Surface morphology of soil cracks is one of the important factors influencing the water evaporation rate in cracked soil in Yuanmou Dry-hot Valley Region, Southwest China. Quantitative study of the complicated surface morphology of soil cracks is a prerequisite for further studies of soil-cracking mechanisms. The present paper establishes a quantitative indicator system by application of concepts and methods originating from Fractal Geometry and Network Analysis. These indicators can effectively express the complicated features of soil-crack network structure. Furthermore, a series of values related to soil-crack morphology was obtained by image processing on field photos of soil-crack quads, and gradation criteria for the degree of development of soil cracks were determined. Finally, the changes in values of the morphological indicators under different degrees of development were analyzed in detail. Our results indicate that (1) the degree of development of soil cracks can be divided into five grades, i.e., feeble development, slight development, medium development, intensive development and extremely intensive development; (2) the values of the indicators change predictably with increasing degree of development of soil cracks. The area density (Dc) increases, and both the area-weighted mean ratio of crack area to perimeter (AWMARP), which reflects the intensity of cracking, and the index r, which is related to the connectivity of a soil crack, grow uniformly (albeit with different forms). AWMRAP increases at a geometric rate while r shows logarithmmic growth, indicating a gradual increase in the connectivity of a soil crack. Nevertheless, the area-weighted mean of soil-crack fractal dimension (AWMFRAC) shows a decreasing trend, indicating a gradual decline in the complexity of cracks as area density increases.

Finite Element Analysis for Monitoring Interface Crack between Solder Ball and Copper by Direct Current Potential Difference Method

In order to validate the applicability of the direct current potential difference method (DC-PDM) to the identification of interface cracks, electric field analysis was carried out for a copper plate with a solder ball joined on its surface by the finite element method. The analysis was carried out for different crack depths under the following four conditions: (a) when the shape of interface crack between solder ball and copper changes, (b) when the radius of solder ball changes, (c) when the distance between the bottom of inserted copper wire and the interface changes, and (d) when the angle of inserted copper wire changes. It was found from the analysis results that a large crack area ratio gave a large increase in the potential difference and that the effect of crack shape and the angle of copper wire on the potential difference was small. Finally, the relationship between the crack area ratio and the increase in potential difference was given by a single formulated curve for all the conditions discussed in the present analysis.