The theory used in the nonlinear solution is called CDP and is outlined in the theoretical background [4]. The material model is a part of the ABAQUS library for concrete simulation.
The simulation was terminated when the model reached its maximum bearing capacity, subsequently transitioning to the plastic state and the post-critical state, as observed on the load-deformation curve. No, predefined stop criteria were applied in this case, as in CSFM.
Assumptions and attributes of the model:
- Utilizes concepts of isotropic damaged elasticity in conjunction with isotropic tensile and compressive plasticity to characterize the inelastic behavior of concrete.
- It is designed for applications in which concrete is subjected to monotonic, cyclic, and/or dynamic loading under low confining pressures.
- Consists of the combination of non-associated multi-hardening plasticity and scalar (isotropic) damaged elasticity to accurately describe the irreversible damage that occur during the fracturing process.
- Compression softening and tension stiffening are employed under assumptions of perfect bonding for reinforcement bars modeled independently.
- Total number of nodes 46003
- Total number of elements 37892
- 27600 linear hexahedral element C3D8 - full integration, element deletion-on
- 10192 linear line elements T3D2
- Mesh size - 50 mm on the concrete and reinforcements
- The interlayer between compression-only constraints representing soil and concrete footing strip provides information about the contact status and contact stress.
- A thin layer of 10 mm with modulus elasticity 1000 MPa to emulate an interlayer for the results outputs from soil pressure.
34) Mode + reinforcements, mesh
Material models for Concrete-Damage-Plasticity
The evolution of the material model under compression exhibits softening after reaching 20 MPa, while in tension, it exhibits a value of 0.2 MPa, which approximately simulates zero tensile strength. This precise zero value results in the model diverging.
35) Material models for concrete in compression, tension, and reinforcement
Concrete-Damage-Plasticity - Low-Stiffness-Soil (LSS)(GMNA)
The ultimate loading force imparted to the model was recorded at -2029 kN. The minimum (compressive) strain observed was -0.04, located at the intersection of the column and footing. Conversely, the maximum (tensile) strain was identified on the bottom face of the footing, measuring 0.105. Excessive compressive strains have been assessed as the primary failure mechanism, characterized by concrete crushing.
36)Maximal applied force, Minimal principal stress
37)Minimal plastic strain, Maximal plastic strain
38)Damage in tension, Damage in compression
Regarding the reinforcement capacity, the analysis was terminated at a plastic strain of 6% on the rebars, corresponding to a Von-Mises stress of 439 MPa. The longitudinal bars, transverse horizontal stirrups, and shear legs of the stirrups are utilized within the hardening plastic branch of the diagram. A simultaneous failure of both longitudinal and shear reinforcement is observed. This interaction results in a combined failure mechanism, where the longitudinal bars experience bending, the stirrups undergo tension due to transverse bending, and the vertical legs of the stirrups, subjected to shear forces within the concrete, experience axial tensile rupture.
39)Stress in reinforcements
40)Nonlinear deflections
41)Contact area and contact stress
Concrete-Damage-Plasticity - High-Stiffness-Soil (HSS)(GMNA)
The ultimate loading force exerted on the model was documented at -4181 kN. The minimum (compressive) strain observed was -0.0175, which represents approximately a 56% reduction compared to the values recorded in LSS. A noteworthy change was identified in the location of this strain, shifting to the bottom face of the footing rather than the interface between the column and footing. This shift is primarily attributed to the predominance of vertical stress, which resulted in the peak strain relocating. Concurrently, the maximum (tensile) strain was observed on the bottom face of the footing, measuring 0.0451.
The reduction in strain values can be attributed to the increased stiffness of the soil, confinement phenomena, and reduced deformation relative to LSS. Furthermore, the confined stress within the concrete reached a value of -166 MPa. The confined strain highlighted the post-critical behavior of concrete, including compression softening and concrete crushing.
42)Maximal applied force, Minimal principal stress
43)Minimal plastic strain, Maximal plastic strain
44)Damage in tension, Damage in compression
The concentration of stress is predominantly centralized beneath the column area, resulting in elevated contact stress 3.41 MPa and a significant gradient of shear. This condition increases the likelihood of punching shear failure. The longitudinal reinforcement bars and stirrups play a pivotal role in accommodating plastic behavior. The localized stress induces yielding in the immediate vicinity of the column area on the footing strip. The tensile forces in the reinforcement bars, arising from the bending of the footing in both directions, combined with the shear force traction captured by the vertical legs of the stirrups, contribute to the manifestation of plasticity. The primary mode of failure is characterized by tension-induced stress along the reinforcement bars.
45)Stress in reinforcements
46)Nonlinear deflections
47)Contact area and contact stress