This paper presents the numerical results of concrete footing-soil foundation seismic interaction mechanism. The concrete footing has been made with two different shapes, but with the equal volume of concrete material. The concrete footing-soil foundation has been analyzed using nonlinear finite elements, with the fixed-base state. The simulated near-fault ground motions have been applied to the concrete footing-soil foundation. The problem has been formulated based on the settlement controlled analysis. The local geotechnical conditions of all configurations have been analyzed. The numerical analysis results indicate that the shape of a concrete footing alters seismic response, revises inertial interaction, enhances damping ratio, improves load carry capacity, modifies cyclic differential settlement, revises failure patterns, minimizes nonlinear deformation, and changes cyclic strain energy dissipation. The novelty of this research work is the strain energy has more been dissipated with artistic concrete footing design.

A number of the buildings have been collapsed due to improper soil-footing interaction; it has occurred when dynamic or seismic forces have been applied to them. The improvement of soil-footing seismic interaction mechanism is an art in geotechnical earthquake engineering design and needs to select appropriate footing shape to enhance the safety of the structure.

There are many experimental, numerical, and theoretical research studies which mainly focus on differential settlement and bearing capacity of the soil when the soil has been subjected to simulated seismic loading, liquefaction, and landslide. The outcome of these research studies has been realizing failure mitigation of soil foundation and introducing different methods for improving soil foundation stability [

In the previous studies, many investigations have been made in understanding the differential settlement of soil, when the soil has been subjected to dynamic loading [

The nonlinear deformation develops due to six components of stresses applied to a body element; the six components of stresses are

Two types of distortions arise: (i) direct strain

The strain matrix is

The rotation matrix is

Consequently, the complete distortion of a volume element may be expressed as the sum of corresponding strains and rotations in the matrix form [

The concrete footing-soil foundation has been modeled using nonlinear finite elements, with the fixed-base state. The soil foundation is 1.8 ∗ 1.8 ∗ 0.9 (m). The concrete footing for configuration-1 and configuration-2 are 0.6 ∗ 0.6 ∗ 0.4 (m) and 0.4 ∗ 0.9 ∗ 0.4 (m), respectively. For both models, the concrete foundation of 0.2 ∗ 0.2 ∗ 0.2 (m) is installed on center of concrete footing. The soil foundation-concrete footing seismic interaction has been evaluated. The concrete footing configuration is with two different shapes and equal volume. In the numerical analysis, the typical mesh has been used. The concrete footing is placed on a horizontal surface of the soil foundation; it is shown in Figures

Soil models. (a) Configuration-1. (b) Configuration-2.

Concrete footing-soil configurations. (a) Configuration-1. (b) Configuration-2.

Acceleration history of Norcia Earthquake [

Acceleration history of Norcia Earthquake [

Mechanical properties of materials [

Materials | Modulus elasticity, |
Poisson’s ratio, ( |
Friction angle, |
Dilatancy angle, |
Cohesion, |
Unit weight, ^{3}) |
Ref |
---|---|---|---|---|---|---|---|

Soil | 120 | 0.35 | 53 | 21 | 0.01 | 22.68 | [ |

Concrete | 49195 | 0.24 | — | — | — | 24.405 | [ |

Enhancement geometry of a concrete footing considerably changes soil-footing seismic interaction mechanism, and this process leads to develop a new concept for the satisfactory seismic design of a concrete footing. The morphology of concrete footing influences on the shear strain travel paths and seismic energy distribution. The meaningful relationships have been observed between simulated near-fault ground-shaking and energy dissipation mechanism at each configuration. The characteristics of seismic waves are altered as it is facing different simulated geomorphological conditions. The seismic wave dispersion modifies damping ratio and governs nonlinear deformation patterns of soil foundation and footing-soil seismic interaction mechanism. However, the morphology of concrete footing significantly affects the amplitude of earthquake ground motions; it may be known as “geomorphological conditions effect” in concrete footing-soil foundation seismic design. The numerical analysis results have confirmed that the geomorphological condition influence to strain energy dissipation, and this process leads to developing nonlinear deformation patterns and differential settlement with the specific shape at each configuration, and subsequently, it is understood that the geomorphological conditions are important in the distribution of earthquake damage. The flexible soil foundation area-to-ridge concrete footing area interaction is responsible for the failure mechanism of soil foundation at each configuration. However, the design of concrete footing shape at each configuration is important in the stability of concrete footing and soil foundation as well. The modified shape of concrete footing leads to change in the concrete footing center of gravity and shape of cyclic load distribution; this phenomenon results in the modification of concrete footing-soil foundation seismic interaction mechanism and seismic load response. And on the other hand, the geomorphological conditions and morphology of concrete footing are responsible for developing characteristics of strain paths, and the strain path is a factor in developing a differential settlement, failure mechanism, deformation, and bearing capacity. The seismic site response is highly variable with respect to concrete footing morphology, while the volume of used concrete is equal in both configurations, and cost effectiveness of the project is considered with seismic design of concrete footing. The geotechnical condition is another factor in ground motion behavior prediction. The geomorphological condition affects the seismic response of an infrastructure. It can suggest beyond the theoretical seismic design; it requires to numerically simulate the influence of geomorphological conditions to predict seismic stability of the infrastructure. The near-fault ground motions change strain energy dissipation via travel path of seismic wave propagation. The hysteretic behavior of soil significantly affects the concrete footing seismic response. This process affects concrete footing and soil foundation inertial interaction and leads to stress response of the soil foundation. Cyclic seismic load response has been developed due to concrete footing morphology, and it is shown in Figures

Seismic load (kPa) vs cyclic displacement (mm) at the base of a concrete footing, configuration-1.

Seismic load (kPa) vs cyclic displacement (mm) at the base of a concrete footing, configuration-2.

Seismic load (kPa) vs cyclic strain at the base of a concrete footing, configuration-1.

Seismic load (kPa) vs cyclic strain at the base of a concrete footing, configuration-2.

The stress third invariant behavior is depicted in Figures

Cyclic stress invariant at the base of the concrete footing. (a) Configuration-1. (b) Configuration-2.

Cyclic stress invariant at the base of the soil foundation. (a) Configuration-1. (b) Configuration-2.

Cyclic stress invariant for configurations 1 and 2. (a) Configuration-1. (b) Configuration-2.

3D cyclic stress invariant of soil at the base of soil foundation, using matrix for numerical simulation. (a) Configuration-1. (b) Configuration-2.

Figures

Color map surface projection techniques are used in matrix analysis to simulate results of ABAQUS software, which is reported in cyclic stress invariant. According to Figure

The minimum strain energy density allows the influence of the T-stress on the mixed modes I/II fracture strength [

The different types of loads can store elastic energy before damage, and this energy storage accelerates and develops damage mechanism [

The nonlinear finite elements are applied in the analysis of concrete footing-soil seismic interaction mechanism. The concrete footing is built up with two different shapes and equal volume. The simulated near-fault ground motions have been applied to each configuration. In the present study, the following aims have been achieved:

It has been found that the concrete footing-soil interaction and morphology of differential settlement have been changed with respect to the shape of the concrete footing.

The local geotechnical conditions have been modified ground-shaking characteristics. The anomalous damage distributions may not derive with the select appropriate shape of a concrete footing, considering local site conditions.

The morphology of concrete footing affects the seismic energy travel paths, and meaningful relationships have been observed between simulated near-fault ground-shaking and energy dissipation mechanism. The strain energy has more been dissipated with artistic concrete footing design.

The shape of concrete footing governs hysteretic soil damping and inertial interaction; these processes have occurred based on kinematic interaction of concrete footing-soil foundation characteristics.

The higher strain energy concentration has been observed at the base of the configuration-1, with respect to the magnitude and shape of the seismic loading response. The differential settlement is significantly minimized in configuration-2.

The cyclic strain causes plastic cyclic deformation, with respect to the shape of concrete footing and related to increment of stress. According to the numerical results, this approach supports in forecasting the seismic stability of concrete footing.

No data were used to support this study.

The authors declare that they have no conflicts of interest.

The support by the Major Projects of Natural Science Research in Jiangsu Colleges and Universities (grant no. 17KJA560001), the Science and Technology Planning Project of Jiangsu Province (grant no. BY2016061-29), the Jiangsu Province Six Talent Peak High-Level Talent Project (grant no. JZ-011), and the New Wall Materials and Development of Bulk Cement Projects of Jiangsu Economic and Information Commission (grant no. 2017-21) is greatly acknowledged.