abaqus帮助文档之地震相应计算分析(2)

show the contour plots of the tensile damage variable, DAMAGET (or ), on the left, and the stiffness degradation variable, SDEG (or d), on the right. The tensile damage variable is a nondecreasing quantity associated with tensile failure of the material. On the other hand, the stiffness degradation variable can increase or decrease, reflecting the stiffness recovery effects associated with the opening/closing of cracks. Thus, assuming that there is no compressive damage (), the combination and at a given material point represents an open crack, whereas and represents a closed crack.

At time , damage has initiated at two locations: at the base of the dam on the upstream face and in the region near the stress concentration where the slope on the downstream face changes.

When the dam displaces toward the downstream direction at time , the damage at the base leads to the formation of a localized crack-like band of damaged elements. This crack propagates into the dam along the dam–foundation boundary. The nucleation of this crack is induced by the stress concentration in this area due to the infinitely rigid foundation. At this time, some partial tensile damage is also observed on several elements along the upstream face.

During the next large excursion in the upstream direction, at time , a localized band of damaged elements forms near the downstream change of slope. As this downstream crack propagates toward the upstream direction, it curves down due to the rocking motion of the top block of the dam. The crack at the base of the dam is closed at time by the compressive stresses in this region. This is easily verified by looking at the contour plot of SDEG at time , which clearly shows that the stiffness is recovered on this region, indicating that the crack is closed.

When the load is reversed, corresponding to the next excursion in the downstream direction at time , the downstream crack closes and the stiffness is recovered on that region. At this time tensile damage localizes on several elements along the upstream face, leading to the formation of a horizontal crack that propagates toward the downstream crack.

As the upper block of the dam oscillates back and forth during the remainder of the earthquake, the upstream and downstream cracks close and open in an alternate fashion. The dam retains its overall structural stability since both cracks are never under tensile stress during the earthquake. The distribution of tensile damage at the end of the earthquake is shown in Figure 2.1.15–8, at time . The contour plot of the stiffness degradation variable indicates that, except at the vicinity of the crack tips, all cracks are closed under compressive stresses and most of the stiffness is recovered. No compressive failure is observed during the simulation. The damage patterns predicted by Abaqus are consistent with those reported by other investigators. Abaqus/Explicit results

Figure 2.1.15–9 shows the distribution of tensile damage at the end of the Abaqus/Explicit simulation. Two major cracks develop during the earthquake, one at the base of the dam and the other at the downstream change of slope. If we compare these results with those from the analysis in Abaqus/Standard (see Figure 2.1.15–8 at time ), we find that Abaqus/Standard predicted additional damage localization zones on the upstream face of the dam. The differences between the results are due to the effect of the dam–reservoir hydrodynamic interactions, which are included in the Abaqus/Standard simulation via an added-mass user element and are ignored in Abaqus/Explicit. This is easily verified by running an Abaqus/Standard analysis without the added-mass user element. The results from this analysis, shown in Figure 2.1.15–10, are consistent with the Abaqus/Explicit results in Figure 2.1.15–9 and confirm that additional damage to the upstream wall occurs when the hydrodynamic interactions are taken into account.

Input files

Abaqus/Standard input files

1、Frequency analysis of the Koyna dam. *HEADING

KOYNA DAM: NATURAL FREQUENCY EXTRACTION Units - n, m, sec

*PREPRINT, MODEL=YES *NODE

1 , 0.00, 0.00 21, 70.00, 0.00 2401, 0.00, 66.50 2421, 19.25, 66.50 3601, 0.00, 91.75 3621, 16.17, 91.75 3801, 0.00, 103.00 3821, 14.80, 103.00 *NGEN, NSET=NBASE 1, 21

*NGEN, NSET=NMID 2401, 2421

*NGEN, NSET=NWL 3601, 3621

*NGEN, NSET=NTOP 3801, 3821

*NFILL, BIAS=1.05

NBASE, NMID, 24, 100 *NFILL, BIAS=0.92 NMID, NWL, 12, 100 *NFILL

NWL, NTOP, 2, 100

*ELEMENT, TYPE=CPS4R 1, 1, 2, 102, 101

*ELGEN, ELSET=DAM 1, 20, 1, 1, 38, 100, 100

*ELSET, ELSET=WDAM, GENERATE 1, 3501, 100

*SOLID SECTION, ELSET=DAM, MATERIAL=CONCRETE 1.0,

*MATERIAL, NAME=CONCRETE *ELASTIC

3.1027E+10, 0.2 *DENSITY 2643.0

*CONCRETE DAMAGED PLASTICITY