علی لکی روحانی

Steel fiber reinforced concrete is used as a temporary or permanent lining on the rock wall of tunnels or the slope of roadways, so investigating the interaction behavior of concrete attached to the surrounding rock is of particular importance. In this article, using uniaxial compressive strength test, the strength behavior of sandstone/steel fiber reinforced concrete composite samples is investigated. To make composite samples, different percentages of steel fibers were used for the concrete part of the samples, and also the height of the concrete and rocky parts of the samples were considered variable. According to the obtained results, there is a moderate positive correlation between the uniaxial compressive strength and the percentage of steel fibers, in other words, by increasing the percentage of steel fibers, the strength of the composite sample increases. As the height of the concrete part of the samples increases, the uniaxial compressive strength decreases and there is a moderate negative correlation between the compressive strength and the height of the concrete part of the samples.The pattern of cracking before failure is diagonal in the concrete part and longitudinal cracks in the stone part. By reducing the height of the concrete part, the confinement of the concrete part between the upper rigid plate on one side and the rock part on the other side increases and the strength of the sample increases.

The particle size of granular soils have a great effect on their shear behavior. The purpose of this article is to investigate the shear behavior of granular soils with different particle sizes. The large-scale direct shear tests are conducted in three parts. The first part of the experiments is related to 4 types of granular soil with different particle size. The second part is related to the tests performed on composite samples and in the third part, the effect of a concrete block on the shear strength of granular soil is investigated. According to the results, as the particle size of the material increases, the push of the shear failure increases and the sample has a higher shear strength, in the same way, as the size of the particles increases, the friction angle of the materials and the dilation angle increases. The main finding of this article is that the materials located in the shear zone have a great impact on the strength of the sample. In composite samples, if the sand is compacted in the shear zone, although the top and bottom of the sample is gravel, the behavior and strength of the sample is close to that of pure sand. The thickness of the shear zone is dependent on the size of the particles, the thickness of the shear zone increases as the grain size increases. The concrete block in the shear zone increases the shear strength and internal friction angle of the sand sample.

Determining the directions and the values of in-situ stresses is of great importance as the most fundamental parameter needed to evaluate the borehole wall's stability. One of the methods for determining the directions and values of in-situ stresses is the borehole breakout phenomenon, which is developed by an increase in shear stress due to the concentration of compressive stress around the borehole and leads to the failure and collapse of the drilled borehole wall. In the present article, the width and depth of the failure were obtained by combining the stress relations around the borehole based on the theory of elasticity and through the Mogi-Coulomb failure criterion. Then, the minimum fluid pressure inside the borehole was evaluated to prevent damage to the borehole wall, and the effect of physical properties of materials, in situ stress ratio, and fluid pressure on the breakout dimensions was investigated. In the second section of this article, 215 breakout analyzes for different mechanical properties and in situ stresses were carried out for the selected sandstone. The objective of the present study is to evaluate the relationship between the width and depth of failure. The correlation coefficient between the width and depth of failure was equal to R=0.74 using simple linear regression. Moreover, the correlation coefficient's value was calculated to be R=0.82 based on the gene expression programming (GEP) method. It means that there is a moderate to strong correlation between these two parameters, and if the values of in situ stresses σ_h, σ_H to be obtained based on the breakout geometry, only the value of one of these stresses can be obtained due to the high correlation between width and depth of failure.

Actually, after drilling a borehole, some materials would be eliminated from the original rock mass. The exhumed materials no longer can carry the stresses transferred to the rock surrounding the borehole. The process represents a stress concentration in the rock around the borehole. The so-called borehole breakout failure results from an enhancement in shear stress on the borehole wall because of the excavation-induced increase of the hoop stress surrounding the wall. Vertical borehole breakouts generated via un-equal horizontal in-situ stresses are usually focused in two opposed areas along the least horizontal in-situ stress. Excavation cause loss of balance stresses around the borehole and also cause compressive stress concentration on the walls. Changes in stresses around the borehole may cause formation damage. This status results in other modes of borehole instability such as collapsing of the wall due to shearing failure. Breakout phenomenon (collapsed walls under shear failure) will occur by increased shear stress at the borehole wall which by itself is due to an increase in hoop stress on the wall. In this paper, the goal is to compare four failure criteria including, Mohr-Coulomb, Hoek-Brown, Griffith and Fairhurst to estimate the depth and angular width of the borehole wall in damaged zone, where the stresses are heterogeneous. The results show that damaged zone, undamaged zone and boundary curve of failure around the borehole, can be obtained using the function of failure criteria (F) in σ1-σ3 plane. The more that the area under the curves of these criteria would be in σ1-σ3 plane, the less damaged zone will occur around the borehole.  For instance, the area under the curve for Griffith criteria in σ1-σ3 plane, is less than the area of other criteria. So damaged area in Griffith criteria is more than 3 other criteria. Angular width obtained from Hoek-Brown criterion, Mohr-Coulomb criterion and Fairhrust criterion (unlike Griffith) coincide, because these 3 criteria cut the σ1 axis with the same width in σ1-σ3 plane. Also, with the constant value for difference of in-situ stresses (σd=σH-σh), depth of the failure in minimum in-situ stress direction is more in Griffith and Fairhrust criteria in compare with 2 other criteria. By comparing the failure criteria, it has been observed that, with an increase in in-situ stresses ratio (σH/σh), the results of Griffith and Fairhrust criteria are more close to experimental results in compare with 2 other criteria (Hoek-Brown and Mohr-Coulomb).

The composition, texture and microstructure of rocks affect their physical and mechanical properties such as dry unit weight, porosity, p-wave velocity and Brazilian tensile strength. The aim of this study was to investigate the effect of mineralogy sandstone characteristics on physical and mechanical properties of sandstone in three groups with low mean quartz (less than 65%), moderate (65 to 80%) and high (more than 80% ) and 26 samples were collected from southern province of Zanjan city Then, a comprehensive program of rock mechanic tests are planned and mineralogical properties and engineering parameters such as dry unit weight, porosity, P-wave velocity and Brazilian tensile strength were determined and their relationship was investigated using linear regression analysis. The results show that the mineral composition is effective on the strength properties and increasing the quartz mineral content in the samples, two physical parameters of dry unit weight and P-wave velocity and a mechanical parameter Brazilian tensile strength increase. Also, due to the correlation between physical parameters, P-wave velocity can be predicted with appropriate approximation using porosity parameter for sandstone in studied regions and the results can be used in geomechanical studies.

By drilling borehole in the ground, the distribution of stress around it changes and stress concentration is created. If the shear stresses induced by in- situ stresses is more than rock strength, it causes a kind of failure around the borehole, which is called breakout. It has been observed that breakout failure zones are initiated and propagated in the direction of minimum in- situ stress. In this paper, by assumption of elasticit behavior of rock mass, the analytical 2D analysis of breakout failure using the Mohr-Coulomb and Hoek-Brown failure criteria is addressed and the failure zone is obtained by using these two criteria. According to the results of the mathematical model, the effective parameters in the depth and width of the breakout occurring around the borehole are depended on the mechanical properties of the materials in the medium as well as the amount and ratio of in- situ stresses. If the ratio of stresses is one, breakout failure will not occur. Also, with increasing the rock quality, the breakout depth decreases, and with decreasing rock strength and increasing the amount and ratio of stresses, the breakout area becomes larger.

It has been of great interest among the researchers to investigate the behavior of soil_geogrid interface. Due to the wide use of geogrids between different layers of soil; these investigations are very important. This paper shows the results of experimental tests on soil_geogrid interface. This study conducts a series of large scale direct shear tests to investigate the interface shear strength of granular soil with various degrees of compaction and various sizes of geogrid apertures. The shear stress versus shear displacement curves and peak shear strength are important for evaluating the results. The interactions between soil and geogrid may include the following mechanisms: 1) shear resistance between soil and the surface of the geogrids; 2) internal shear resistance of the soil in the opening area; and 3) passive resistance of the transverse ribs. The value of α was defined to evaluate the effect of geogrid on the shear strength of the soil which is the ratio of geogrid_soil shear strength to internal shear strength of soil. The results showed that a larger degree of compaction reduces the resistance in soil_geogrid interface and shear strength of soil_geogrid interface will be reduced further by reducing the distances of transverse ribs of geogrid.

Although hydraulic fracturing has many applications, but breakdown pressure from hydraulic fracturing process is very important, since this pressure is related to the in situ stresses. In hydraulic fracturing fluid over time, injected into a borehole until it reaches to the limit such that tensile fractures occur in the wellbore wall. At the moment of occurrence of fracture, fluid pressure within the wellbore, said the breakdown pressure that is equivalent to the peak point of the pressure-time curve. There are simple and classic relations that related breakdown pressure to the in situ stresses. Estimation of in-situ stresses is a major challenge in Geomechanic. In this paper, the finite difference modeling of hydraulic fracturing will be discussed. Modeling is base on two-dimensional plane strain assumptions. The purpose of the modeling is to study on parameters affecting the breakdown pressure, parameters that do not exist in the classical relations but affect the breakdown pressure. After validation of the model and in accordance with the results of this paper breakdown pressure not only is related to the in-situ stresses and rock tensile strength but also wellbore radius and pre-existing cracks in the wall of the wellbore are parameters that involved in hydraulic fracturing and breakdown pressure. For isotropic in situ stresses variation of wellbore radius dont effect on the breakdown pressure but for non-isotropic in situ stresses with increasing wellbore radius breakdown pressure decreases and with increasing deviatoric stresses (difference between in situ stresses), the rate of breakdown pressure reduction increases.

Investigation of the effect of angle and geotextile position on the sand resistance parameters is the aim of this experiment. The behaviors of the tested samples were analyzed by the direct shear tests results and charts derived from it. In this study, three positions, including vertical, horizontal and oblique, were studied. Each of these items also has other arrangements. In total, 17 different arrangements were tested under three overload stresses. The type of soil is have lower initial shear sand. The results show that soil reinforced horizontal arrangements stiffness. Also, they have softer behavior. In vertical arrangements, the shear strength increases with increasing number of layers. Shear strength in oblique arrangement with two layers is greater than the vertical arrangement with two layers. For example, for stress of 2 kg per square centimeter, in arrangement with two-layer vertical and double-layer, there are oblique 23 and 33 percent increases in resistance. In oblique arrangement, the less the position angle relative to the horizon is, the more the shear strength will be. Using reinforcement elements in improving geotechnical properties of soil has been considered by a human for many years. In recent years, many improvements have been made in the field of improving poor soils and reinforcing them. Soil reinforcement has been used as an effective method to improve the soil layers in order to increase the bearing capacity and reduce the settlement. In oblique arrangement, the results showed that if the direction of moving geotextile is in line with that of cutting, then we can observe an increase in the rate of resistance; if the direction of moving is in opposite direction with shearing direction, then we can observe a decrease in the rate of resistance. The results of vertical arrangement showed that by increasing geotextile layers, the rate of resistance increased. The results of the test showed that in horizontal arrangement, the rate of flexibility decreased and not significant difference in the rate of resistance was seen. The results of the study on different samples showed that using geotextile almost in all the conditions caused an increase in the rate of flexibility and resistance.

In this paper 3D and full tunnel modeling with considering step by step excavation and installation of lining, will be discussed. Full 3D modeling of tunnel by finite element method (FEM) can be ideally represents the behavior of longitudinal and transverse ground settlement by progress of excavation and installation of lining. Results of numerical analysis showed good agreement with empirical formulations for longitudinal settlement. It is also seen that the effect of boundary condition of the model, there are up to five times the diameter of the tunnel and then reaches its maximum and steady-state condition. With increasing the tunnel depth, ground surface settlement decreases before the tunnel face and increases after the tunnel face. Also according to the results, settlement longitudinal curves of different depths intersect in the tunnel face, which means ground surface settlements in the tunnel face are the same for different depths. In the other section of the paper transverse settlement curve obtained by 2D analysis compared with the corresponding trough from 3D analysis, by comparing these two profiles area, can be reached to the stress release factor, that is one of the key parameters in the 2D analysis.

Based on the extensive studies which have been done, undoubtedly, the role of the wave velocity data of rocks in hydrocarbon reservoir evaluation is absolutely vital. Within, it is important to study the wave velocities in the Dolomites, which often make up one of the best parts of hydrocarbon reservoirs in the carbonate system. Certainly, the texture of rocks, mineralogical composition, grain size, percent of quartz in rocks, and many microstructure properties affect the Engineering and Physical Behavior of rocks. According with previous studies and to better understanding this relationship, a comprehensive program of tests on the three categories of dolomite with fine, medium and coarse grained were designed. In this paper, the results related to the measurement of compressive (Vp) and shear wave velocity (Vs) for 32 samples are given. According to the results, with increasing in grain size, density of rock decreases. The compressive and shear wave velocity for fine grain and coarse grain samples were found to be %9 and %12 lower, respectively, than those for the medium grain samples. The results showed that for fine, medium and coarse grain samples; moreover, the ratio of Vp/Vs is 1.78, 1.81, and 1.77 respectively. It was also observed that the dynamic Young›s modulus for the medium grain samples approximately 15% of the fine grain samples and approximately 27% of the coarse grain samples is more. In addition, it was found that a significant change does not occur in Poisson›s ratio of the studied rocks with an increase in grain size.

Ground response curve is a component of convergence-confinement method in rock support interaction analysis which is used for determining the displacement around tunnels excavated by New Austrian Tunneling Method. Analytical solution of the ground response curve is based on the assumption of isotropic in-situ stress field and is applicable for deep tunnels. Today, urban tunnels mainly excavated in shallow levels and often under anisotropic in-situ stress field. In this paper, for 2D models with geometry and specific environmental characteristics, the response curves for different depths and different in-situ stress ratios, are determined in two ways: 1) By analytical solution and using anisotropic stress field equivalent to an isotropic stress field. 2) Numerical solution. The results of these analyzes were compared with together and range of application of analytical solution of the ground response curve is determined. Based on the results, tunnel wall displacement is mainly influenced by the ratio of the initial in-situ stresses in comparison of tunnel depth. The results showed that crown and floor numerical displacements deviate more from analytical solution than the wall displacement. The only displacement that can be accurately obtained from the analytical solution for the shallow tunnel is the displacement of the tunnel wall under isotropic stress. In the case of isotropic stress field, the results given by the analytical solution agree with the numerical ones at depths higher than 14 times radius of the tunnel. The difference between numerical and analytical solutions becomes higher while increasing the initial in-situ stress ratio, even for deep tunnels.

In this study, to determine a dolomitization model for the Soltanieh Formation a suitable outcrop 35 km southwest of Zanjan city has been studied. The Soltanieh Formation with a total thickness of 985 m sharply laid on the shales and sandstones of the Bayandor Formation and was covered by shales and red-sandstones of the Barut Formation. Distribution and extension of the dolomite layers in the Soltanieh Formation, is parallel with the sedimentary layers and bedding and also has considerable lateral extension. Abundant relict of blue-green algae (stromatolites) and nodules and bands of cherts, have been recognized into the dolomitic layers of the Soltanieh Formation. Based on fieldwork, petrography and geochemistry evidences (ICP-OES and XRD), four different types of dolomite have been distinguished in Soltanieh Formation. These dolomites include: (1) fine crystalline dolomites or dolomicrite; (2) subhedral, dense and medium crystalline dolomite; (3) subhedral to anhedral coarse crystalline dolomite and finally (4) pore-filling dolomite cements. In the studied dolomites of Soltanieh Formation, saddle dolomite were not observed. The results of this research indicate that these dolomites have been formed in shallow to relatively deep diagenetic environments by moderately saline marine fluids (mean Na 435 ppm), via seepage reflux of evaporate seawater into the Soltanieh Formation platform in the study area. Low Sr values (mean 47 ppm) and relatively high Fe (mean 3088 ppm) and Mn values (mean 453 ppm) in coarse crystalline dolomites, likely indicate increase in dolomite crystal size and recrystallization process during the burial. The very low Ba concentration (mean 12 ppm) and the absence of saddle dolomite into the dolomitic sequences of the Soltanieh Formation, indicates ineffectiveness of hydrothermal fluids acting during dolomitization process of the Soltanieh Formation carbonates into the study area.

One of tunneling methods is cut and cover method, in which the excavation start from the ground surface and deep in the ground, then a concrete box is made as a tunnel. Thus in this method, the cross section of the tunnel is not circular but rectangular. The aim of this paper is seismic analysis of rectangular tunnels. For a special accelerogram, tunnel geometry, depth of overburden and ground conditions, are the three main factors affecting the dynamic behavior of the tunnels. By numerical methods, and by assuming the plane strain condition, models of this type of tunnels were analyzed. According to the results, the maximum internal forces that are generated in the tunnel lining and the stress concentration are at the corners of the cross section of rectangular tunnel. In seismic mode, the internal forces of concrete lining are several times of static mode. In this situation, the ground surface settlement profiles are asymmetric and the settlement is greater than the static mode. In tunnels with large width, in 2D cases, if a column be placed in the middle of span, the ground settlement, bending moment and shear forces is decreased in comparison with 1 span tunnel with the same dimension

Modeling of fluid-driven fractures, arguably one of the most challenging computational problems in geoengineering, has been the subject of numerous investigations. The thrust of these efforts has been directed, however, towards the mechanics of deep hydraulic cracks, with subsurface hydraulic fractures receiving comparatively little attention. Nonetheless, there are numerous circumstances when the propagation of a fluid driven fracture in a solid medium is influenced by the presence of a free surface: remediation of contaminated soils, excavation of hard rock by injection of fluids, preconditioning and cave inducement in mining, waste disposal, and fracture propagation in dams. Furthermore, there are also spectacular examples of geological processes that involve near-surface magma-driven fractures. Investigations have addressed various aspects of the problem, both analytically and numerically, for some further references. It is, however, only recently that there has been a rigorous effort to study the parametric dependence of a fluid-driven fracture and the corresponding different limiting regimes. An explicit solution for fracture propagation in the toughness-dominated regime has been constructed by Garagash [Engineering Fracture Mechanics, 2006], when the energy dissipated in the viscous fluid flow inside the fracture is negligibly small compared to the energy expended in fracturing the solid medium. It was also shown that the established method of asymptotic expansion in small parameters is equally applicable to study other small effects (e.g., fluid inertia) on the otherwise toughness-dominated solution. This paper represents an analytical method for solving the problem of plane-strain hydraulic fracture propagating in an impermeable brittle rock under large toughness and axisymmetric conditions. The flow of incompressible fluid in the fracture is unidirectional and laminar. Fracture propagation is described in the framework of linear elastic fracture mechanics (LEFM). The fracture is fully fluid-filled at all times. This problem has been examined by Garagash [Engineering Fracture Mechanics, 2006] without considering the interaction effect of inertia and viscosity parameters. In this work, the net pressure in the fracture, the crack opening, and the fracture half-length are obtained from the perturbation solution considering this interaction effect on the otherwise toughness-dominated solution. The results are compared with analytical reference solutions.

Underground structures like tunnels are important elements of transportation, network, and service, which due to being surrounded by the ground and withstanding in situ stresses show different seismic behavior in comparison of surface structures. This paper presents analytical solutions for seismic and static loads in circular tunnels, and then they have been used to evaluate internal forces of lining for a section of Bangkok’s urban tunnel. The problem is solved using numerical analysis of finite difference for both horizontal and vertical acceleration coefficients and the results compared with analytical solutions results. According to the results by increasing the horizontal seismic acceleration, the axial force and bending moment increases. And with increasing the depth of tunnel, the forces of lining increases but vertical acceleration of earth has small effect on stresses. For the in- situ stress coefficient it has been seen that as the ratio is further more away from the number one, the created stress increases in the lining.

Using of reinforcement elements in improving geotechnical properties of soil has been considered by a human for many years. In recent years, many improvements have been made in the field of improving poor soils and reinforcing them. Soil reinforcement is used as an effective method to improve the soil layers in order to increase the bearing capacity and reduce the settlement. Soil-bag system is one of the new polymer products. That can be used as a soil reinforcing element in various projects. Soil-bag system was developed in order to increase the bearing capacity of the soil and reduce its settlement. The kind of filling materials mostly depends on the application of soil-bag system and availability of materials. The most important characteristic implemented into the structure of soil-bag system is tension strength of the polymer implemented in the bag. Bags implemented into soil-bag system are generally built of polyethylene or polypropylene polymers. When soil-bag system undergoes vertical loading, tension force produced into the bag cover causes to increase vertical force (N), consequently, this causes to increase the force between soil particles (= soil friction coefficient and F=.N). Earth reinforcement using of soil-bag system causes to increase bearing capacity and it causes to minimize transformation of foundation bed influenced by the imposed load. The results of simple pressure test on the foundation reinforcement with soil-bag system by Yongfu Xu show that when soil-bag system is exposed on external load, it exhibits high strength which a fundamental portion of this strength is resulted from tension force generated in the cover of polymeric bag. Of other characteristics of soil bags, the absorption of vibrations resulted from traffic load can be addressed.
In this study, the bed soil models in reinforced and non-reinforced conditions have been investigated using numerical method. Numerical studies have been done in three dimensional cases using finite element method (Abaqus). In this method sand and polypropylene polymer bag behavior were defined by using Mohr-coulomb and Elastic- Perfect Plastic models. Also, the effects of soil-bag system in increasing the bearing capacity and reducing settlement were evaluated. Another resistance-based parameters of soil-bag system which was examined in this research, is the effect of internal friction angle of soil on the bearing capacity of soil-bag system. Regarding the results of numerical method, it is observed that the maximum tension concentration in the above-mentioned model is placed in the corners of polymeric bag. The results show that the more is the friction angle between soils particles, the resistance of soil-bag system will also be increased against the external loading. There are proper matching between the results obtained from numerical studies and field studies done by other researchers. The results show that the bearing capacity of reinforced bed is almost 2 times bigger than the non-reinforcement bed.

Static analysis of slope stability using limit equilibrium method has been studied and different methods have been presented. But in the earthquake it is seen that the slopes undergo with a wide slips. Thus investigation of seismic stability of slopes has special important. In this paper by using numerical method, slopes with different heights and angles were seismic analysis by applying Tabas earthquake accelerogram. According to the results it is seen that during the earthquake and with increasing the time, a plastic zone at the foot of the slope is created and began to propagate into the middle and the crown of slope. Plastic zone created in seismic analysis is deeper and larger than the static analysis and it is because of the large inertia forces that are applied by the earthquake. Also with increasing the height of slopes, areas in which it occurs plastic shear strain increases but at the same time they slip.

Result of an underground tunnel designation is determining the static and seismic forces generated in the tunnel lining. For calculating of these forces in static and quasi- static mode¡ several relationships have been presented that briefly in this article is cited. Then for two tunnels with circular and square sections¡ numerical- seismic analysis were done and the results are compared with each other. According to the results¡ the axial force created in the circular tunnel lining in static and seismic conditions¡ is greater than those in square tunnels¡ but bending moment and shear force in square tunnel are larger than those for the circular tunnel. The resulting forces of seismic analysis of circular tunnel averagely are 12 times of static analysis and for the square tunnel are 6 times of the static analysis. Ground surface settlement profile in static mode is symmetric¡ and settlements above the square tunnel are greater than those for circular tunnel. Ground surface settlement profile is asymmetric in seismic condition¡ but the settlement values are almost identical for both sections of the tunnel.
Keywords:

The first phenomenon related to tunneling especially in urban area¡ is ground surface settlement. For estimating the settlement trough there are two empirical methods and analytical solutions¡ also¡ in recent years with the development of numerical method¡ this method has been added to the other two methods. This paper discusses the comparison between the proposed methods and critique of the first two methods. Hence¡ for obtaining the settlement trough with three analytic methods¡ the models of an urban tunnel was built under the plane strain condition. By comparison settlement troughs¡ it can be seen that except some particular cases the troughs provided by the first two methods are far from the numerical methods. It''s because of the first two methods are not considered all the effective parameters on the surface settlement ground¡ whereas¡ the numerical method are considered¡ thus the numerical method has a relatively accurate estimate of settlement trough. Therefore¡ the numerical method can be a good alternative for the first two methods.

By excavation of a tunnel in a rock mass, the stresses in the medium redistributed and base on theses new stresses a plastic zone created in the tunnel periphery. Ground reaction curve and radius of plastic zone are two important parameters in the design of tunnels lining and are key components of convergence- confinement method. Analytical relationships assuming isotropic stress field around the tunnel to determine these two parameters have already been proposed. In this paper, two-dimensional numerical analysis assuming plane strain conditions are conducted on circular tunnels. In contrast to analytical models, the weight of the rock mass as well as non-isotropic stress conditions considered and their effect on the ground reaction curve, the radius of the plastic zone and stress distribution around the tunnel is investigated. In accordance with the results obtained for the tunnel wall for a given lining pressure, with increasing horizontal stress ratio, the amount of pressure required to create plastic zone (critical pressure) and the radius of the plastic zone decreases. In the crown of the tunnel, with increasing the horizontal stresses, critical pressure and the radius of the plastic zone increases, and resistance of the crown against the plastic deformations decreases.