Effects of fineness and dosage of fly ash on fracture properties and strength of concrete.Appl. Numerical analysis of the mechanical behavior of various jointed rocks under uniaxial tension loading.Appl.

## Effect of Slag Particle Size on Fracture Toughness of Concrete

*Introduction**Research Signiﬁcance**Experimental Details 1. Materials**Results and Discussion 1. Compressive Strength**Conclusions*

This implies a unique effect of using finer slag on improving the fracture resistance of concrete. The related tendency of the critical stress intensity factor (KSIC) of slag concretes is similar to the fracture energy.

## Cracking Behavior of RC Beams Strengthened with Different Amounts and Layouts of CFRP

### Literature Review

16] performed a series of experimental tests on reinforced concrete beams that were strengthened with externally bonded CFRP sheets in flexure. The present study evaluated the effect of CFRP reinforcement ratio on failure patterns of reinforced concrete beams.

### Experimental Plan and Setup

The CFRP reinforcement ratio was varied in the form of flexural and shear strips resulting in different reinforcement layouts and failure patterns of the concrete beams. Therefore, the total CFRP reinforcement ratio is the sum of the CFRP reinforcement ratio in bending and shear.

### Results and Discussions

For example, the peak moment carrying capacity of beam B5 occurred at a curvature value of 0.0028, while the peak strength of beam B6 was observed at a curvature value of 0.0038. The test results show that beams with a higher CFC shear reinforcement but with a lower amount of bendable CFC reinforcement cannot make a significant contribution to the overall strength of the beam.

### Analytical Prediction of Beam Capacities

The flexural and shear capacities of reinforced CFRP beams are calculated from Equations (2) and (7), as recommended by ACI 440.2R [33]. The flexural capacity of the beam is primarily a function of the amount of CFRP applied to the tensile face of the beam.

### Cracking Behavior of Beams 1. Control Specimen C-1

Therefore, the crack propagated obliquely to the compression plane of the beam and resulted in the loss of beam strength. At a deﬂection value of 5.2 mm, no significant cracks were observed, but small hairline cracks were observed near the left support of the beam, as shown in Figure 11a.

### Conclusions

The choice of CFRP flexural reinforcement can affect the failure mode and strength gain of the RC beams. An advanced review on debonding failures of FRP laminates externally bonded to concrete. Int.

## Determination of Fracture Properties of Concrete Using Size and Boundary Effect Models

### Size and Boundary Effect Models

Then, a modified Hu-Guan boundary effect model with a new definition of equivalent crack length is proposed. Definition of two nominal stresses in (a) Hu-Guan boundary effect model and (b) Hu-Zhang boundary effect model.

### Model Veriﬁcation and Comparison

Hu-Guan's boundary effect model and its modified version somehow still overestimate the tensile strength of the material with β1=1. Test results in [30] and the corresponding adjusted curves of (a) Hu-Guan's boundary effect model with β1=1, (b) adjusted Hu-Guan's boundary effect model with β1=1, (c) Koval-Gao's size and boundary effect model and (d) Bažant's Type 2 size effect law.

### Conclusions

The occurrence of elevated temperature inversion in the fracture properties of concrete and its use in the maturity model.Eng. Calculation of superposition of double K fracture parameters of concrete using wedge splitting geometry and boundary effect.J.

## Eﬀects of Fineness and Dosage of Fly Ash on the Fracture Properties and Strength of Concrete

### Experimental Details

Consequently, the strength of each fly ash mixture exceeded that of the control mixture at later ages. Nevertheless, the presence of finer fly ash had a beneficial effect on the GF of concrete. The use of finer fly ash has a beneficial effect on the fracture energy (GF) of concrete already at an early age (14 days).

## Meso-Scale Simulation of Concrete Based on Fracture and Interaction Behavior

### Finite Element Modeling Method

In the main study of this paper (Section 6.4), cohesive elements are inserted only between aggregates and mortar elements (inter-fault transition zones, ITZ) and within the mortar. In the tension and compression simulations, the final vertical displacements of the upper joints are 0.09 mm and 0.9 mm, respectively. In the first 20 s and in the last 80 s, the vertical movements of the upper nodes are accelerated and uniform, respectively.

### Calibration of Numerical Simulation

By increasing the plastic deformation capacity in a local area, the stress distribution becomes more uniform, allowing the particles to remain at a higher average stress level. A mesh size of 1.0 mm is chosen for further experiments due to good simulation accuracy and acceptable time consumption. In the following, the standard models used for analysis and parametric studies are models with ten different aggregate distributions and calibrated parameters.

### Tension Simulation Result

Figure 9 shows the strain-stress curves of specimens with one or two dominant cracks. In order to observe the whole deformation process, the deformation of the sample is increased geometrically, as shown in Figure 10. The deformation of the MII elements is very similar to the deformation of the nearby ITZ elements.

### Compression Simulation Result

The sums of the lengths of the ITZ and MII elements with different degrees of damage are summed, as shown in Figure 15. Since the nonlinear behavior of the specimen is simulated by the damage of the ITZ and MII elements, the total length of the elements represents the damage state of the specimen. The rate of damage development of the sample gradually accelerates and reaches a constant rate with increased deformation.

### Parametric Study

In this section, the effect of mode II fracture energy on the performance of concrete under tension and compression is studied. In the case that the mode II fracture energy is equal to the mode I fracture energy (ξ=1), the total fracture energy is 48.2% lower than that of the standard model (ξ=25). Figure 23 shows the failure modes of the models with the same aggregate distribution and different aggregates' mechanical properties.

Three-Dimensional Physical and Numerical

## Modelling of Fracturing and Deformation Behaviour of Mining-Induced Rock Slopes

### Geological Settings

In the area of the eastern final slope, the iron ore body is located in the middle of the area, strikes almost east¿east, and dips in the northeast direction at about 70◦. The eastern final slope is located on the east side of the XIV prospecting line three sets of mutually intersecting dominant joints are found in the rock mass. The typical rock types and the associated mechanical parameters of the rock mass found in the Yanqianshan Ice Age are listed in Table 1.

### Physical Model Tests 1. Model Contaniner

According to the similarity ratios and the geometric similarity ratio shown in Table 2, the prototype joint spacing was divided by the geometric ratio to obtain the corresponding joint spacing required in the test. In the case of Yanqianshan Iron Mine, the average joint distance in the prototype is about 30-40 cm. The strength of the adhesive was determined by the mass fraction of the various components.

### Discrete Element Modelling

The whole process of deformation and failure of the layers could be identified and investigated by the new method. The horizontal direction (X) of the eastern and western boundaries, as well as the horizontal direction (Y) of the southern and northern boundaries of the model slopes were all fixed boundaries. The results of the numerical analyzes on the influence of joint distance on strata movements are given in Figure 8.

Physical Test Results

### Discussion

The bed movement and deformations observed in physical model tests and numerical simulations show that the presence of dominant joints has a significant influence on bed movement and slope failure. Nevertheless, the observed deformation mechanism of the physical model was qualitatively consistent with what was observed in the field. The strain rate tensor and velocity field analysis have been done extensively in the analysis of the deformation mechanism of the earthquake fault [32,33].

### Mesoscopic Parameter Calibration and Basic Theory 1. Specimen Preparation and Mesoscopic Parameter Calibration

The schematic diagram of the principal stress tensor when microcracks appear is shown in Figure 3. In PFC, when the absolute value of the difference between the actual velocity of the particles in the measurement circle and the calculated velocity is minimized, the strain rate tensor in the measurement circle can be obtained by establishing a system of equations [36]. If the strain rate value in the measurement circle is zero, it means that no microcracks appear in this area.

### Analysis of Numerical Simulation Results

Here is the particle velocity field on both sides of the newly formed cracks near the T4 type IV crack tip. Because there is a trend of relative shear between the particles, the particle velocity field on both sides of the newly formed cracks is near the T2 type I crack tip. The type of particle velocity field on both sides of the newly formed cracks determines the type of crack in the measurement area.

Numerical Analysis of the Mechanical Behaviors of Various Jointed Rocks under Uniaxial

## Tension Loading

### Numerical Modelling

In the following analysis, rock test models are built with different joint conditions (single, multiple parallel and intersecting joints) and the effect of the joints on the tensile properties is investigated by using a uniaxial. In the case of rock specimens with two joints, the effects of the perpendicular distance between the two joints (d), the angle between the joint and the horizontal direction (α) of parallel joints, and the joint density (n) on the complete stress-strain response were investigated by numerical simulation . In the case of rock specimens with multiple joints, the effects of the perpendicular distance between the two cracks (d), the angle at which the two joints intersect (β), and the joint density (n) of intersecting joints on the complete stress–strain response were investigated by numerical simulation.

### Eﬀects of Joints on the Tensile Properties 1. Eﬀect of the Dip Angle of A Single Joint

As can be seen, it is negatively correlated ton, and the relationship varies with different values of α. The cutting angle of the joint clearly has a remarkable effect on the tensile properties of the rock samples. As can be seen, Etis is negatively correlated ton, and the relationship varies with different values of β.

### Discussion

With the increase in the development of rock mass fissures, the Young's moduli decrease markedly. In a certain interval, the influence on the tensile strength is negligible with the increase in the development of rock mass fissures. A numerical study of the influence of heterogeneity on the strength characterization of rock under uniaxial tension.Mech.

Numerical Modeling Approach on Mining-Induced Strata Structural Behavior by Considering the

## Fracture-Weakening Eﬀect on Rock Mass

*Mechanical Behavior of the Caved and Fractured Zones**Numerical Modeling Procedure 1. Overview of the Study Site**Fracturing Weakening Eﬀect on the Mining-Induced Stress Redistribution and Strata Movement**Discussion and Validation**Conclusions*

6], have focused on the magnitude and development in height of the FZ caused by mining. The simulation results of the three aspects and their behavior are analyzed in the following text. The extreme difficulty in measuring voltage in the region of the unfilled goaf [1] is due to the inaccessibility of the goaf.

## Studies of Fracture Damage Caused by the Proppant Embedment Phenomenon in Shale Rock

### Materials and Methods

The percentage of fracture surface damage (PDWe) for the profile, along the measurement section was determined according to the equation expressed by. It is determined according to the Equation expressed in The percentage reduction of fracture width (PRWf) filled with proppant, taking into account the phenomenon of embedment, was determined according to the Equation expressed in

### Execution of a Laboratory Simulation of the Embedment Phenomenon and Analysis of the Obtained Test Results

Next, a laboratory simulation of the phenomenon of proppant embedment in the fracture surfaces of the test unit was performed shown in Figure 6. The size of the fracture width determines the flow of hydrocarbons through the fracture packed with proppant grains to the wellbore. Investigations of the embedding phenomenon after the hydraulic fracturing treatment of unconventional reservoirs. Nafta-Gaz.

### Materials and Methods 1. Grouting Materials

The stable water head system was used to provide a constant water flow by adjusting the height of the head to control the water velocity. A rectangular coordinate system was established and the location of the joint hole was defined as the origin. Considering the diversity of the factors affecting the grouting effect and based on our previous research, the fracture roughness (JRC) (A), initial water flow rate (B), gel time (C) and fracture opening (D) were selected as the investigated factors in the experiment.

### Tests Results and Analyses 1. Grout Propagation Process

The change in water flow was monitored all the time using a camera. The change curve of "double platform decreasing type" of the water flow rate is shown in Figure 10b. The sealant spread primarily into the grooves and had little effect on the water surface velocity.

### Discussion and Limitations

Investigations on the Diffusion Mechanism of Grout in Dynamic Injection Method and Clogging in Water Intrusion of Underground Engineering.Chin. Experimental investigation of the sealing efficiency of chemical injection in rock fracture with flowing water. Tunn. Experimental investigation of chemical injection of inclined fractures for sand and water flow control. Tunn.

## Numerical Investigation of Mineral Grain Shape Eﬀects on Strength and Fracture Behaviors of

### Modeling Methodology

Non-continuous mechanical behavior of rock materials can be observed due to the interactions and movements of the rigid particles. The interaction of the particles is treated as a dynamic process with states of equilibrium that develop when the internal forces balance. The force and moment carried by the parallel bond is represented by FiandMi, indicated in Figure 2.

### Model Descriptions

As shown in equation (1), flatness is the ratio of the maximum Feret's diameter of the grain to the minimum Feret's diameter. According to Equations (1) and (2), the flatness and roughness of the three mentioned mineral grain groups were calculated, and the results are shown in Figure 5. As can be seen from Figure 5a, the flatness of the strip-shaped grain group was significantly higher than that of the triangular and square grain groups.

Analysis of Grain Shape Eﬀects