• Geomechanics and Engineering
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• 제18권4호
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• pp.391-406
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• 2019

The aim of this paper was to study the influence of the footing shape and the effect of the roughness of the foundation base on the bearing capacity of shallow foundations on rock masses. For this purpose the finite difference method was used to analyze the bearing capacity of various types and states of rock masses under the assumption of Hoek-Brown failure criterion, for both plane strain and axisymmetric model, and considering smooth and rough interface. The results were analyzed based on a sensitivity study of four varying parameters: foundation width, rock material constant (mo), uniaxial compressive strength and geological strength index. Knowing how each parameter influences the bearing capacity depending on the footing shape (circular vs strip footing) and the footing base interface roughness (smooth vs rough), two correlation factors were developed to estimate the percentage increase of the ultimate bearing capacity as a function of the footing shape and the roughness of the footing base interface.

• Coupled systems mechanics
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• 제13권3호
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• pp.201-217
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• 2024

This study aims to develop a new model to obtain the minimum area in circular isolated footings with eccentric column taking into account that the surface in contact with the ground works partially in compression, i.e., a part of the contact area of the footing is subject to compression and the other there is no pressure (pressure zero). The new model is formulated from a mathematical approach based on a minimum area, and it is developed by integration to obtain the axial load "P", moment around the X axis "M_x" and moment around the Y axis "M_y" in function of σ_max (available allowable soil pressure) R (radius of the circular footing), α (angle of inclination where the resultant moment appears), y₀ (distance from the center of the footing to the neutral axis measured on the axis where the resultant moment appears). The normal practice in structural engineering is to use the trial and error procedure to obtain the radius and area of the circular footing, and other engineers determine the radius and area of circular footing under biaxial bending supported on elastic soils, but considering a concentric column and the contact area with the ground works completely in compression. Three numerical problems are given to determine the lowest area for circular footings under biaxial bending. Example 1: Column concentric. Example 2: Column eccentric in the direction of the X axis to 1.50 m. Example 3: Column eccentric in the direction of the X axis to 1.50 m and in the direction of the Y axis to 1.50 m. The new model shows a great saving compared to the current model of 44.27% in Example 1, 50.90% in Example 2, 65.04% in Example 3. In this way, the new minimum area model for circular footings will be of great help to engineers when the column is located on the center or edge of the footing.

• Geomechanics and Engineering
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• 제38권1호
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• pp.93-106
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• 2024

The present paper investigates the spatial variability effect of soil property on the three-dimensional probabilistic characteristics of the bearing capacity factor (i.e., mean and coefficient of variation) of a circular footing resting on clayey soil where both mean and standard deviation of undrained shear strength increases with depth, keeping the coefficient of variation constant. The mean trend of undrained shear strength is defined by introducing the dimensionless strength gradient parameter. The finite difference method along with the random field and Monte Carlo simulation technique, is used to execute the numerical analyses. The lognormal distribution is chosen to generate random fields of the undrained shear strength. In the study, the potential failure of the structure is represented through the failure probability. The influences of different vertical scales of fluctuation, dimensionless strength gradient parameters, and coefficient of variation of undrained shear strength on the probabilistic characteristics of the bearing capacity factor and failure probability of the footing, along with the probability and cumulative density functions, are explored in this study. The variations of failure probability for different factors of safety corresponding to different parameters are also illustrated. The results are presented in non-dimensional form as they might be helpful to the practicing engineers dealing with this type of problem.

• Steel and Composite Structures
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• 제49권2호
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• pp.231-244
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• 2023

Many of the recent investigations in the field of geotechnical engineering focused on the bearing capacity theories of multilayered soil. A number of factors affect the bearing capacity of the soil, such as soil properties, applied overburden stress, soil layer thickness beneath the footing, and type of design analysis. An extensive number of finite element model (FEM) simulation was performed on a prototype slope with various abovementioned terms. Furthermore, several non-linear artificial intelligence (AI) models are developed, and the best possible neural network system is presented. The data set is from 3443 measured full-scale finite element modeling (FEM) results of a circular shallow footing analysis placed on layered cohesionless soil. The result is used for both training (75% selected randomly) and testing (25% selected randomly) the models. The results from the predicted models are evaluated and compared using different statistical indices (R² and RMSE) and the most accurate model BBO (R²=0.9481, RMSE=4.71878 for training and R²=0.94355, RMSE=5.1338 for testing) and TLBO (R²=0.948, RMSE=4.70822 for training and R²=0.94341, RMSE=5.13991 for testing) are presented as a simple, applicable formula.

• Advances in Computational Design
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• 제4권3호
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• pp.273-294
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• 2019

In this paper is presented the minimum cost (optimal design) for reinforced concrete circular isolated footings based on an analytic model. This model considers a load and two moments in directions of the X and Y axes, and the pressure has a variation linear, these are the effects that act on the footing. The minimum cost (optimal design) and the Maple program are shown in Flowcharts. Two numerical experiments are shown to obtain the minimum cost design of the two materials that are used for a circular footing supporting an axial load and moments in two directions in accordance to the code of the ACI (American Concrete Institute), and it is compared against the current design (uniform pressure). Also, the same examples are developed through the normal procedure to verify the minimum cost (optimal design) presented in this document, i.e., the equations of moment, bending shear and punching shear are used to check the thickness, and after, the steel areas of the footing are obtained, and it is compared against the current design (uniform pressure). Results section show that the optimal design is more accurate and more economical than to any other model. Therefore, it is concluded that the optimized design model presented in this paper should be used to obtain the minimum cost design for the circular isolated footings.

• Geomechanics and Engineering
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• 제35권1호
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• pp.41-54
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• 2023

The use of a skirt, a vertical projection attached to the footing, is a recently developed method to increase the bearing capacity of soils and reduce foundation settlements. Most of the studies were focused on vertical skirted circular footings resting on clay while neglecting the rigidity and inclination of skirts. This study employs finite element limit analysis to investigate the bearing capacity enhancement of flexible and rigid inclined skirts in cohesionless soils. The results indicate that the bearing capacity initially improves with an increase in the skirt inclination but subsequently decreases for both flexible and rigid skirts. However, the rigid skirt exhibits more apparent optimum skirt inclination and bearing capacity enhancement than the flexible one, owing to differences in their failure mechanisms. Furthermore, the bearing capacity of the inclined skirted foundation increases with the skirt length, footing depth, and internal friction angle of the soil. In the case of rigid skirts, the bearing capacity increases linearly with skirt length, while for flexible skirts, it reaches a stable value at a certain skirt length. The efficiency of the flexible footing reduces as the footing depth and soil internal friction angle increase. Conversely, the efficiency of the rigid skirt decreases only with an increase in the depth of the footing. The paper also presents a detailed analysis of various failure patterns, highlighting the behaviour of inclined skirted footings. Additionally, nonlinear regression equations are provided to quantify and predict the bearing capacity enhancement with the inclined skirts.

• Earthquakes and Structures
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• 제7권6호
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• pp.1001-1024
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• 2014

The size of spread footings was found to be unnecessarily large from some actual engineering practices constructed in Taiwan, due to the strict design provisions related to footing uplift. According to the earlier design code in Taiwan, the footing uplift involving separation of footing from subsoil was permitted to be only up to one-half of the foundation base area, as the applied moment reaches the value of plastic moment capacity of the column. The reason for this provision was that rocking of spread footings was not a favorable mechanism. However, recent research has indicated that rocking itself may not be detrimental to seismic performance and, in fact, may act as a form of seismic isolation mechanism. In order to clarify the effects of the relative strength between column and foundation on the rocking behavior of a column, six circular reinforced concrete (RC) columns were designed and constructed and a series of rocking experiments were performed. During the tests, columns rested on a rubber pad to allow rocking to take place. Experimental variables included the dimensions of the footings, the strength and ductility capacity of the columns and the intensity of the applied earthquake. Experimental data for the six circular RC columns subjected to quasi-static and pseudo-dynamic loading are presented. Results of each cyclic loading test are compared against the benchmark test with fixed-base conditions. By comparing the experimental responses of the specimens with different design details, a key parameter of rocking behavior related to footing size and column strength is identified. For a properly designed column with the parameter higher than 1, the beneficial effects of rocking in reducing ductility and the strength demand of columns is verified.

• Earthquakes and Structures
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• 제14권4호
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• pp.323-336
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• 2018

Machine foundations with impact loads are common powerful sources of industrial vibrations. These foundations are generally transferring vertical dynamic loads to the soil and generate ground vibrations which may harmfully affect the surrounding structures or buildings. Dynamic effects range from severe trouble of working conditions for some sensitive instruments or devices to visible structural damage. This work includes an experimental study on the behavior of dry dense sand under the action of a single impulsive load. The objective of this research is to predict the dry sand response under impact loads. Emphasis will be made on attenuation of waves induced by impact loads through the soil. The research also includes studying the effect of footing embedment, and footing area on the soil behavior and its dynamic response. Different falling masses from different heights were conducted using the falling weight deflectometer (FWD) to provide the single pulse energy. The responses of different soils were evaluated at different locations (vertically below the impact plate and horizontally away from it). These responses include; displacements, velocities, and accelerations that are developed due to the impact acting at top and different depths within the soil using the falling weight deflectometer (FWD) and accelerometers (ARH-500A Waterproof, and Low capacity Acceleration Transducer) that are embedded in the soil in addition to soil pressure gauges. It was concluded that increasing the footing embedment depth results in increase in the amplitude of the force-time history by about 10-30% due to increase in the degree of confinement. This is accompanied by a decrease in the displacement response of the soil by about 40-50% due to increase in the overburden pressure when the embedment depth increased which leads to increasing the stiffness of sandy soil. There is also increase in the natural frequency of the soil-foundation system by about 20-45%. For surface foundation, the foundation is free to oscillate in vertical, horizontal and rocking modes. But, when embedding a footing, the surrounding soil restricts oscillation due to confinement which leads to increasing the natural frequency. Moreover, the soil density increases with depth because of compaction, which makes the soil behave as a solid medium. Increasing the footing embedment depth results in an increase in the damping ratio by about 50-150% due to the increase of soil density as D/B increases, hence the soil tends to behave as a solid medium which activates both viscous and strain damping.

• Coupled systems mechanics
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• 제13권4호
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• pp.311-335
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• 2024

This work aims to show a model to estimate the minimum cost (Thickness and area of steel in X and Y directions) for design a circular isolated footing with eccentric column that considers that the surface in contact with the ground works partially under compression. The formulation is shown by integration to find the moments, the bending shears and the punching shear using the pressure volume under the footing. Some researchers show the minimum cost design for circular isolated footings for an eccentric column assuming that the contact area works completely in compression, others consider the contact surface with the ground working partially in compression for a column in the center of the base. Three numerical examples are developed to obtain the complete design, which are: Example 1 for a column in the center of the base,Example 2 for a column at a distance of 1.50 m from the center of the base in the X direction, Example 3 for a column at a distance of 1.50 m from the center of the base in both directions. Also, a comparison of the new model against the model proposed by other authors is presented. The comparison shows that the new model generates a great saving of up to 43.74% for minimum area and 48.44% for minimum cost design in a column located in the center of the base, and when the column is located at a distance of radius/2 starting from the center of the base in the X direction generates great savings of up to 45.24% for minimum area and 31.80% for minimum cost design. Therefore, it is advisable to use the model presented in this study.

• Geomechanics and Engineering
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• 제27권5호
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• pp.419-431
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• 2021

Construction of retaining walls with geocell has been gaining in popularity because of its easy and fast installation compared to conventional methods. In this study, model tests were conducted by constructing the geocell retaining wall (GRW) at a constant height (i.e., 90 cm) and using aggregate as an infill material at four different configurations and two different surface angles. In these tests, a circular footing was placed behind the walls at different lateral distances from the wall surface and loaded monotonically. Subsequent to this vertical loading being applied to the footing, horizontal displacements on the GRW surface were measured at three different points. The performance of Type 4 GRW exceeded the other three types of GRW, with the highest lateral displacement occurring in Type 4 GRW at approximately 0.67 % of wall height. In addition, the results of these tests were compared with theoretical approaches widely accepted in the literature. The stress levels reached beneath the footing were found to be compatible with theoretical results.