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Cloudy with a Chance Group

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Hakim Kornilov
Hakim Kornilov

F1 2011 Crack Pc Miler ##BEST##

FIGURE 2. Pre-stack depth migrated (PSDM) seismic profile, interpretation, and Vp model for the PSDM on line D6. (A) Uninterpreted PSDM profile. Locations of the helium isotope anomaly sites (Sano et al., 2014) are displayed: N3, N2, N1, and R. (B) Interpreted PSDM profile. The red star marks the hypocenter of the 2011 Tohoku mainshock (Mw9.0). Normal and reverse faults are denoted respectively by thin blue and red lines. A thin red line below site N3 in the middle slope region marks the SBP line depicted in Figure 3. It is noteworthy that landward-dipping normal faults (thick blue F1 and F2 below sites N3 and N2, respectively) and a potential shear zone (thick pink) develop in the middle slope region. Thin black, red, and blue dotted boxes are enlarged respectively in Figure 4, Figure 5, and Figure 7. (C)Vp model overlaid by the PSDM profile.

f1 2011 crack pc miler

FIGURE 6. P-wave tomographic image (Liu and Zhao, 2018) along the profile B (Figure 1). Fault interpretations (Figure 2B) on the PSDM profile of line D6 are shown in red box. The red star marks the hypocenter of the 2011 Tohoku mainshock (Mw9.0).

Citation: Park J-O, Tsuru T, Fujie G, Jamali Hondori E, Kagoshima T, Takahata N, Zhao D and Sano Y (2021) Seismic Reflection Images of Possible Mantle-Fluid Conduits and Basal Erosion in the 2011 Tohoku Earthquake Rupture Area. Front. Earth Sci. 9:687382. doi: 10.3389/feart.2021.687382

The limits on yield strength are required to ensure adequate ductility of a section and are related to the prescribed limit on concrete compressive strain of 0.003. The limits on yield strength also serve to control of crack widths at service loads. Crack width is a function of steel strain and consequently steel stress (Nawy 1968). Therefore, the stress in the steel reinforcement will always need to be limited to some extent in order to prevent cracking from affecting serviceability of the structure. However, with recent improvements to the properties of concrete, the ACI 318 limit of 552 MPa (80 ksi) and AASHTO limit of 517 MPa (75 ksi) on the steel reinforcement yield strength are believed to be unnecessarily conservative for new designs. Additionally, an argument can be made that if a higher strength reinforcing steel is used but not fully taken into account in design, there may be an inherent overstrength in the member that has not been properly incorporated in design.

When a reinforced concrete member is loaded gradually in pure tension, cracking of the concrete will take place in one or more places along the length of the member when the tensile stress in the concrete exceeds the tensile strength of the concrete. After cracking, the tensile stress in the concrete adjacent to the crack is relieved because of the slip that takes place between the concrete and reinforcement at this location. Away from the crack, tensile stress in the concrete between cracks is present because of the bond between the reinforcement and concrete. The distribution and magnitude of the bond stress along the reinforcement will determine the distribution of the concrete stress between cracks along the length of the member. As tension loading is increased, cracking will continue to take place until the stress in the concrete between cracks no longer exceeds the concrete tensile strength. This stage occurs due to excessive slip and the reduction of distance between cracks. Essentially, the distance between cracks becomes sufficiently small that the stress to cause concrete cracking can no longer be developed by the reinforcing steel present. When this condition is reached, the crack spacing reaches its minimum, but the crack widths will continue to increase as the tensile stress in the reinforcement increases (i.e., third stage cracking as described by Reis et al. 1964). Assuming this behavior to be valid and that second stage cracking is fully developed by ε s = 0.001 (Reis et al. 1964), it may be hypothesized that crack patterns in members having high strength reinforcing steel will not vary from those having conventional steel. Thus, only crack width, and not crack spacing, will be affected by utilizing the higher strength steel. The cracking behavior of reinforced concrete members in axial tension is similar to that of flexural members, except that the maximum crack width is larger than that predicted by the expressions for flexural members (Broms 1965a, b). The lack of strain gradient and restraint imposed by the compression zone of flexural members is probably the reason for the lower flexural crack width.

The final crack pattern in a member is determined at the end of the second stage of cracking (Reis et al. 1964). Therefore, controlling the spacing and width of secondary cracks are most important to the overall performance of a member. Based on the early studies reported above, the following are the main factors involved in the control of the final crack pattern: (a) reinforcement stress, (b) the bond characteristics of reinforcement, (c) the distribution of reinforcement over the effective concrete area subject to tension, (d) the diameter of reinforcement, (e) the percentage of reinforcement, (f) the concrete cover over the reinforcement, and (g) the material properties of the concrete.

For Class 1 exposure (moderate exposure), the equation is calibrated, through γ d = 1, for a crack width of 0.43 mm (0.017 in.); for Class 2 exposure (severe exposure), γ d = 0.75. The de facto crack width (γ d ) is 0.43 mm.

In members having high-strength reinforcing bars, early studies showed that an increase in crack width is due to an increase in steel stress and, to a lesser extent, due to an increase in the curvature of the member. Thomas (1936) pointed out that an increase in the curvature at a constant steel stress tends to distribute the cracking rather than widening individual cracks. An increase in the steel stress affects the difference in the elongation between the reinforcing steel and concrete and causes additional slip to occur. This slip is the main cause of the increase in crack size. Slip occurs in the vicinity of a crack and extends to a point where the differential strain is zero. At that point the bond stress and resistance to slip reach maximum values and decrease toward the mid-point between cracks. The overall values of bond force decrease with an increase in load. This decrease is attributed to (a) the effects of the increase in transverse contraction of the reinforcing bar (i.e., Poisson effect) and (b) the deterioration of the concrete at the concrete-steel interface (Odman 1962). Therefore, the crack width increases while the crack spacing remains constant. If the load is increased further, the slip between concrete and reinforcement continues to increase. Due to the comparatively low values of concrete extensibility, the increase in crack width can be considered essentially equal to the accumulation of the slip between adjacent cracks.

The adopted equations for calculation of crack width and crack spacing are based on the use of conventional steel. However, concrete members reinforced with high strength steel reinforcement [having a yield strength, f y , greater than 690 MPa (100 ksi)] have different behavior due to the expected higher service loads. An empirical parametric procedure has been introduced for determination of crack opening (crack width and crack spacing) in a reinforced concrete prism. Effective parameters have been investigated and finally the result has been compared to the available experimental data.

In the case of using conventional steel bars in flexural members, it has been shown that during the second stage of cracking, when steel strains are usually greater than 0.0005, the presence of existing primary cracks affects the formation of secondary cracks under increasing moment. Away from a primary crack, stresses are transferred by bond from the reinforcement to the concrete. If enough force is transferred from the steel at the crack to the concrete away from the crack, the strains that are developed may exceed the strain capacity or the tensile strength of the concrete at a section and another crack will form perpendicular to the reinforcement. Theoretically, the section at which secondary crack formation occurs is midway between existing cracks. This mechanism continues until the tensile forces developed through bond transfer are insufficient to produce additional cracks. To compare and demonstrate the crack behavior of members reinforced with conventional steel bars and members reinforced with high-strength steel bars, a relatively complex material modeling in a simple direct tension model is used.

As shown in the Fig. 1, in a reinforced concrete member subjected to tension, T (or the tension zone in a flexural member), the reinforcement at both loaded ends (which may be interpreted as crack locations) sustains the total external force with the stress f so . At an arbitrary location between cracks, however, the tensile stress in the reinforcement is smaller than f so ; this difference is transferred to the concrete by bond along the transmission length, L 1 . From force equilibrium, therefore, the following relationship is valid at an arbitrary section located at distance, x.

Crack development in direct tension test. a Bond stress and resulting steel and concrete strain distribution before cracking. b No additional cracks have been developed after the first series of cracks at the tension load (T1).

If L1 is sufficiently long to transfer a cumulative tensile stress resulting in a concrete stress, f c , greater than ultimate tension capacity of concrete f cr , then cracks will form. At the same stress level, additional cracks will continue to develop until the distance between adjacent cracks is no longer adequate to transfer sufficient tension to develop a new crack.


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