A Study of the Relationship between the Stress State and Failure Mode of Concrete Specimens

An investigation of concrete specimen’s strength and its changing mechanism based on numerical simulation of the failure process of axis-stressed concrete specimens with different aspect ratios was described. .e state of internal stress and growth of crack of axis-stressed concrete specimens, as well as the changing mechanism of specimen strength under different ambient pressure values, were investigated. .e results revealed that specimen strength and failure surface decreased as the aspect ratio is increased. .e specimen strength is dependent on the state of internal stress and decreased with decreasing ambient pressure. Additionally, the failure mode shifted from shear failure to tensile failure gradually.


General Instructions
Previous studies have revealed that the strength of concrete is more than a material parameter.A variety of studies on the factors affecting the strength of concrete have been conducted to investigate the changing mechanism of this parameter.Widely studied globally [1][2][3], concrete can be regarded as a porous composite material consisting of cement mortar, fine aggregates, and coarse aggregates.e nonlinear-inelastic failure of compressed concrete is mainly caused by the growth of voids and microcracks.For industrial applications, the strength of concrete is usually enhanced by increasing the ambient pressure of single-axis compressible concrete, which can retard crack growth and axial compressive strength of concrete.To date, several triaxial tests of concrete have been reported [4][5][6][7][8][9].However, these studies focused on the strength of concrete in triaxial tests only and did not investigate the stress-strain relationship under different ambient pressures.Dong et al. [10][11][12][13][14][15][16][17] reported a study of the concrete compression at a fixed ambient pressure.
Among various factors affecting the strength of axisstressed concrete specimens, ambient pressure is one of the key factors.It is challenging to investigate the effect of aspect ratio of concrete strength using computed tomography (CT) due to the limitation of loading equipment.In this article, we prepared compressible concrete specimens with different aspect ratios and investigated the quantity and growth of cracks on these specimens based on numerical simulation.In this way, the strength, failure mode, and state of stress of axis-stressed concrete specimens under different ambient pressures were investigated.

Computational Mode Method
e numerical calculation in this article was based on random aggregate model establishing approach.e mixing ratio of concrete and parameters of different components are shown in Tables 1 and 2, respectively.e model size is shown in Table 3. Pre-1 to Pre-5 were compression numerical experiments.
e aspect ratios (κ) of different compression models were 1 : 1, 1 : 2, 1 : 4, 1 : 6, and 1 : 10. e numerical calculation was achieved using a double-brokenline model.In this model, Z-direction at the bottom was restrained, and the middle point was perfectly restrained.
e formation, growth, and coalescence of cracks were simulated, and step loading was applied for all models, with displacement control as the loading mode, as shown in Table 4. e study of the states of the concrete specimens with different aspect ratios under stress and failure test.

e States of the Concrete Specimens with Different Aspect
Ratios under Stress 2.1.1.Pre-1 Specimen.Figure 1 indicates that Pre-1 specimen with aspect ratio κ of 1 : 1 was flat.When the top of the specimen was under stress, confining pressure effect was generated perpendicularly to the stress.Along with the increased axis-stress, the microcracks which were in small angles with the axis-stress increased at a higher rate than the microcracks that were in large angles.As the axis-stress increased, the internal cracks formed were almost all parallel to the axis-stress.erefore, with the increased displacement load, the tension produced from confining pressure increased continuously, forming many intertwined cracks from top to bottom.Finally, the specimen was broken to small pieces.
2.1.2.Pre-2 Specimen.Figure 2 reveals that the concrete specimen exhibited shear-tension damage.is failure mode was similar to that of Pre-1 specimen.e difference is that   2 Advances in Civil Engineering fewer microcracks were formed.ese microcracks induced the subsequently broken of the specimen which resulted in small pieces in the longitudinal section until the complete destruction.As shown in Figure 2, Pre-1 specimen with aspect ratio κ of 1 : 1 was at.When the top of the specimen was under stress, con ning pressure e ect was formed perpendicularly to the stress.Along with the increased axisstress, the microcracks which were in small angles with the axis-stress increased at a higher rate than the microcracks in large angles.As the axis-stress increased, the internal cracks formed were almost all parallel to the axis-stress.erefore, with the increased displacement load, the tension produced from con ning pressure increased continuously, forming many intertwined cracks from top to bottom.Finally, the specimen was broken to small pieces.

Pre-3 Specimen.
Compared with Pre-1 and Pre-2 specimen, as displayed in Figure 3, the internal cracks formed on Pre-3 specimen were far less, and the damaged plane and the horizontal plane were at an angle, not along with the longitudinal direction, which was ascribed to shear failure.In this case, the cracks formed on the damaged plane which was oval and the so-called shear failed plane.e cracks in the damaged interface were x-shaped.
2.1.4.Pre-4 Specimen.As displayed in Figure 4, few cracks formed on Pre-4 specimen.e cracks went through the damaged plane which was in smaller angle with the cross section.And the damaged area with cracks went through was obviously less than that of pressure-1, pressure-2, and pressure-3.
2.1.5.Pre-5 Specimen.As displayed in Figure 5, the cracks in Pre-5 specimen were similar and extended straightly along their growth direction.Consequently, the damaged planes with cracks formed tended to be horizontal (-shaped).Besides, the damaged plane was similar to the round plane.

Analysis of the Stress-Strain Curve of the Concrete Specimen with Different Aspect Ratios
Figure 6 indicates that when the stress on Pre-1 specimen was below 28.326 MPa, the stress changed linearly with the strain.Afterwards, the slope of the stress-strain curve decreased, the interface units and the mortar units started   Advances in Civil Engineering damaging, and the damage of elasticity modulus damped.When the stress reached 29.96 MPa, the strain increased sharply.In this case, the units were damaged, the specimen strength stopped working, and the strain continued increasing until the failure of the specimen.
When the stress on Pre-2 specimen was below 20.066 MPa, the stress changed linearly with the strain.Afterwards, the slope of the stress-strain curve decreased, the interface units and the mortar units started damaging, and the damage of elasticity modulus damped.When the stress reached 21.23 MPa, the strain increased sharply.In this case, the units were damaged.en the stress reached its peak at 22.28 MPa, the specimen strength stopped working, and the strain continued increasing until the failure of the specimen.
When the stress on Pre-3 specimen was below 17.30 MPa, the stress changed almost linearly with the strain.Afterwards, the slope of the stress-strain curve decreased, and the interface units and the mortar units started damaging.Along with the damping of the damage of elasticity modulus, the strain increased sharply and the units were damaged.When the stress finally reached its peak at 18.41 MPa, the specimen strength ceased working and the strain continued increasing until the failure of the specimen.
When the stress on Pre-4 specimen was below 20.066 MPa, the stress changed approximately linearly with the strain.Afterwards, the slope of the stress-strain curve decreased, the interface units and the mortar units started damaging, and the damage of elasticity modulus damped.At this point, the strain increased sharply, and the units were damaged.When the stress reached the peak at 14.10 MPa, the specimen strength ceased working, and the strain continued increasing until the failure of the specimen.
e maximum stress of Pre-5 specimen obtained from stress-strain curve was 15.38 MPa.Before this point, the stress increased with increasing strain whereas, after this point, the stress dropped slowly with increasing strain.Along with enlarged loads, cracks were produced and grown, and the stress was released.Finally, the specimen was destroyed, and the stress was almost completely released.

Analysis of the Stress State of the Specimens with Different Aspect Ratios
e effect of confining pressure on strength was investigated via computational model.e study on multiphase concrete materials under stress was especially complicated; the relationships between the internal stresses generated on specimens were analyzed in this article.Herein, the central point on the middle cross section was studied.Under the same external force, the axial stress and cyclic stress are basically close to each other.Along with the enlarged aspect ratio of the specimen, the confining pressure decreased step by step.Among them, the confining pressure of Pre-1 specimen was the maximum; 72% of its axis-stress.Since the stresses in three directions were similar, many vertical and horizontal cracks appeared on Pre-1 specimen, resulting in multiple shear-failure planes and finally small broken pieces.e strain in the units which was stored during the generation and development of the cracks could be released along the cracks until the formation of the damaged planes.Pre-1 specimen was broken into small pieces with large exposed surfaces.Along with the enlarged aspect ratios, the rate of confining pressure to axis-stress decreased slowly.At mediate confining pressure, the failure angle of the shearfailure plane was 45 °.For Pre-5 specimen, the effect of confining pressure was negligible and the stress was on monopodium.Besides, the specimen was likely to be damaged along the cross section.In other words, with the increasing aspect ratio of the cylinder specimen, the vertical cracks interlinked with the horizontal cracks and the distribution of the cracks was from dense to sparse.Finally, the vertical cracks turned to horizontal and experienced shear failure and resulted in the development of horizontal cracks and the damage of the cross section.In the formation and development of the cracks, the more the cracks generated, the more the area was damaged.

The States of the Concrete
Specimens under Pull e maximum tensile strain failure criterion is applied to simulate the tensile process of concrete specimens with displacement control loading.e uniform load is applied on the top surface of the model, and the loading step is divided into nine steps; the displacement load is shown in Table 4.
From Figure 7, concrete specimen tensile action, the stress perpendicular to the tensile stress concentrated easily in the crack tip and crack along its edge began to expand and kept the development in the crack plane.Along with the expansion of the crack, the stress concentration around was also increasing; hence, the development of the crack was not stable, and it extended to the edge of concrete specimens, until the specimen cracking damage.erefore, the crack shows transverse distribution, perpendicular to the direction of tensile stress, and the crack develops from a main crack until it is destroyed.e failure surface occurs in the cross section of the specimen.
Figure 8 indicates that when stress was less than 5.31 MPa, change in stress with strain was linear, followed by reduction in the change of stress with strain curve slope; damage of part of the interface units and mortar occurred, the elastic modulus was damaged, specimen internal microcracks appeared, and the internal cracks of the specimen rapidly expanded.When the stress reached 7.88 MPa,  Advances in Civil Engineering maximum stress, strain was gradually increased.As the crack in the specimen gradually converged and versed, a big crack was formed, stress was rapidly reduced at the same time, damage occurs in the part of the unit, and specimen strength began to fail.As the strain continued to increase, stress stability reduced slowly.

The States of the Concrete Specimens under
Bending Simple e damage evolution of concrete cube can be seen in Figure 9.In the cube concrete three-point bending test, the maximum bending moment on the cross section is the dangerous point which is farthest from the neutral axis in the uniaxial stress state, the damaged part is the middle part of the cube, the surface tension is one of the largest, and the edge stress of the central section achieves the maximum rst.Gradually with the increase of load, cracks extended upward in the longitudinal and cross section of the cube, the e ective area of the middle section gradually decreases, and the strength of specimens When accumulated to a certain degree of the crack damage, specimens are damaged.
Bending simple displacement and stress of the specimens are shown, abscissa for concrete beam specimen edge point on the vertical displacement v divided by the relative displacement of beam height h after (v/h) and the longitudinal axis of the nite element calculation of concrete specimen under the edge point X to the normal stress.When the displacement of the specimens is 0.617 v/h × 10 -4 before, beam specimens for elastic load, and with the increase of applying displacement when the specimen displacement is 0.84509 v/h × 10 -4 , the stress peak value of the specimen is 6.56 MPa. e specimen cracks are initiated along the lower edge of the section, and the stress decreases with the increase in the displacement.As the displacement continues to increase, the stress decreases signi cantly.If there is no change in stress with the increase in the displacement, the slope of the stress and displacement curve is almost horizontal, the specimens are damaged, and the concrete beam specimen section is the surface of destruction.

Conclusions
Numerical simulation was applied to study the performances of concrete specimens with di erent aspect ratios under continuously increased stress.Along with the increasing stresses, the cracks formed and developed and eventually resulted in the failure of the specimens.e growth direction and the amount of the cracks determined the strength of the specimens, whereas the internal stress determined the development of the cracks.With the increasing aspect ratio, the e ect of the con ning pressure on the strength of the specimen decreased, and the e ect of the constitutive property on the strength enlarged.e strength of the concrete specimens varied with varying con ning pressures, which means that the strength was a ected by the internal stress.e con ning pressure decreased with increasing aspect ratios, and the angle between the damaged plane and the principal stress plane reduced with increasing axis-stress.e specimen was broken into small pieces and  Advances in Civil Engineering many shear-failure planes.In this case, the confining pressure, the axis-stress, and the strength of the specimen all reached the maximum.Afterwards, the damaged planes reduced, and the angle between the damaged planes and the cross section also reduced.e change in failure mode was due to decreased internal confining pressure.Along with increased stress, the ability to resist axis-stress weakened as well, resulting in decreased strength the specimen.

Figure 1 :
Figure 1: e damaged specimen and damaged cross section of Pre-1.Figure2: e damaged specimen and damaged cross section of Pre-2.

Figure 2 :
Figure 1: e damaged specimen and damaged cross section of Pre-1.Figure2: e damaged specimen and damaged cross section of Pre-2.

Figure 3 :
Figure 3: e damaged specimen and damaged cross section of Pre-3.

Figure 4 :
Figure 4: e damaged specimen and damaged cross section of Pre-4.

Figure 5 :Figure 6 :
Figure 5: e damaged specimen and damaged cross section of Pre-5.

Figure 9 :
Figure 9: e damage element diagram of the bending specimen.

Table 1 :
e proportion of concrete mixture in Dagang Mountain.

Table 4 :
Displacement control loading step.