Circular Footings Research Articles

Behaviour of circular footings resting on a reinforced granular bed underlain by a single floating stone column

Behaviour of circular footings resting on a reinforced granular bed underlain by a single floating stone column

Numerical analysis of shape coefficients and bearing capacity factors of shallow foundations on heterogeneous soil

We often face heterogeneous foundation soils in geotechnics, which significantly influence shallow foundations' shape coefficients and bearing capacity factors. The evaluation of these factors introduces significant uncertainties in the thickness of the upper layer is comparable to the width of the rigid footing placed on the soil surface. This ambiguity depends on the geometry of the footing, the mechanical properties of the soil, and other geotechnical factors. Conducting thorough geotechnical studies and performing specific analyses are essential to accurately assess the effect of clay layering on the shape coefficients and bearing capacity factors of circular and square footings. A numerical analysis using the FLAC 2D and 3D software is carried out to evaluate the effect of the superposition of two undrained clay layers on the bearing capacity and shape factors of circular and square footings subjected to a static axial load. The aspects of homogeneous and heterogeneous shear strength profiles were addressed at various positions of the height of the first clay layer. It was found that the critical depth of the first clay layer necessary to optimize the bearing capacity of a foundation resting on stratified soil is 2, 1.5, and 1, respectively, for strip, square, and circular footings. The shape coefficient values range between 1.14 and 1.22 for square footings and between 0.98 and 1.64 for circular footings. The results are compared to previously published values in the literature.

Mitigating liquefaction risks for buildings on circular footings: a numerical modeling approach

Mitigating liquefaction risks for buildings on circular footings: a numerical modeling approach

Dimensioning equivalent of circular footing subjected to eccentric load with effective area approach

ABSTRACT Existence of moment or eccentricity is a common loading situation; thus, it is necessary to be totally aware of the circular footing bearing capacity subjected to eccentric load to design economically. This paper presents a design chart for transforming a circular footing under eccentric load into an equivalent rectangular footing, allowing the use of existing bearing capacity formulas. A new “effective area” is defined, and characterized by a uniform soil pressure distribution. Unlike previous methods, the paper fully describes the calculation process for this area. The results show significant differences in the dimensions of equivalent footings compared to older methods, especially in designs with low eccentricities, leading to higher bearing capacities. Additionally, the dimensions of the “contact area,” which fully interacts with the soil, are derived to ensure compliance with building codes. Finally, simple mathematical expressions for eccentricity reduction factors are provided for both drained and undrained conditions.

Ring Footing Bearing Capacity Erected on Dry Gypseous Soil

This study investigates the behavior of ring footing erected on gypseous soil and compares it with the circular footing, including conducting (24) experiments of loading ring footings, where the inner and external diameter ratio was (Din./Dout. = 0, 0.2, 0.3 and 0.4), resting on two types of Gypseous soil, for the circular footing the external diameter was (150mm) and thickness (15mm) made from solid steel. The results for study showed the ring footings were best than the circular footings. The ratio (Din./Dout. = 0.4) was beast for all ratios of (Df/D). Capacity of bearing increased when the ratio (Df/D) increase. Bearing capacity for high-gypsum content soil showed good results compared to the low-gypsum content soil. The first was high content of gypsum (63.42%) obtained from the Tikrit University, and the second was low content of gypsum (8.15%) from the Baiji area. The tests were doing inside box have dimensions (900×900×700 mm). The experiments were divided into twelve tests for dry gypsum soil condition with high gypsum content using density of (13.76 kN/m3), and twelve tests for dry soil with low gypsum content using density of (14.87 kN/m3). Experiments were conducted for different ratios (Df/D=0, 0.5, and 1).

Fatigue and monotonically-loaded reinforced concrete specimens subjected to partial area loading

The degradation of concrete structures is often due to the continuous application of compressive fatigue loads. Understanding of concrete behaviour in different environmental conditions and under especial fatigue loading arrangements, particularly in cases where the loaded area is smaller than loaded element, herein referred to as partially loaded area, is of utmost importance to make a realistic prediction of the concrete fatigue life for a reliable design of civil engineering infrastructure. This paper focuses on investigating the fatigue performance of reinforced concrete specimens subjected to partially loaded areas, considering the influences of steel fibres, reinforcement arrangement, and the environmental factor of water submergence. A typical example of a partially loaded concrete component subjected to fatigue loading is circular spread footings used as concrete foundations for typical wind turbines. In these types of elements, the compressive strength of the concrete can be enhanced due to the confinement provided by way of lateral restraint stemming from surrounding concrete and reinforcement. However, design codes primarily address static loading and lack specific criteria for fatigue loading in these partially loaded regions. To address this research gap, results from a comprehensive experimental study, which in total included 111 concrete specimens subjected to monotonic loading and 25 specimens tested under cyclic loading, were used to study this problem. The investigation aimed to evaluate the effects of steel fibres and reinforcement arrangement on both static and fatigue capacity. Additionally, the impact of submerging concrete structures in water on their fatigue performance was examined, revealing a decrease in their fatigue life. The experimental results demonstrated that the presence of steel fibres and splitting reinforcement significantly increased both static and fatigue capacity. Most current design codes neglect the environmental factor of water submergence, leading to reduced fatigue capacity in concrete structures. Consequently, the validity of the design codes DNV-OS-C502 and fib Model Code 2010 was evaluated, and a new environmental factor for partially loaded areas subjected to cyclic loading is proposed. To evaluate the experimental results and understand the mechanical response, nonlinear finite element analyses were conducted using a smeared-crack continuum modelling procedure coupled with high cycle fatigue material models to assess its applicability for estimating fatigue performance of partially loaded reinforced concrete elements. It was found that a plane stress modelling procedure was capable of estimating fatigue capacity for dry concrete components, however, overestimated the fatigue capacity of wet concrete components.

Experimental Investigation of Bearing Capacity of Circular and Ring Footings on Geogrid-Reinforced Cohesionless Soils

Abstract This experimental investigation describes an extensive series of reduced laboratory scale tests, conducted on circular and ring footing models rested on a geogrid reinforced cohesionless soil. The study examined the impact of several factors at different relative sand densities, such as the inner to the outer diameter ratio of the ring footing, the number of geogrid reinforcements, the depth of the initial reinforcement, and the vertical spacing between the geogrids, as well as the geogrid stiffness. The results indicated that the optimum diameter ratio of ring footings resting on loose or medium-dense cohesionless soil is 0.40 at which the maximum bearing capacity is reached, leading in a cost-effective design of the footings, while for the dense soil, a diameter ratio of 0.45 is the optimal ratio. Also, the results indicated that the optimum number of reinforcement layers which after the bearing capacity improvement can be considered negligible is three layers for the circular footing and four layers for the ring footing model. To achieve the maximum increase in bearing capacity, the study identifies optimal values for the depth of the first geogrid reinforcement layer and the vertical spacing between reinforcements, which apply to circular and ring footing. While the stiffness of the reinforcement has a significant effect on the bearing capacity, this effect is not proportional.

Undrained Bearing Capacity of Circular and Square Footings above Centric and Eccentric Three-Dimensional Cavities

Undrained Bearing Capacity of Circular and Square Footings above Centric and Eccentric Three-Dimensional Cavities

Bearing capacity evaluation of embedded circular footing considering presence of an overload adjacent

The bearing capacity of axially loaded embedded foundations has been widely studied using analytical and numerical methods. However, there are many discrepancies in the literature results regarding the bearing capacity factors and depth factors of circular embedded footings proposed by different authors. Terzaghi's hypothesis has been used to assess the bearing capacity of shallow foundations and several analytical solutions have been proposed for computing bearing capacity factors, even though a superposition of individual contributions may lead to some error in the computed bearing capacity. This assumption has sometimes been criticized as being more conservative. This article aims to study two problems; The first part is focuses on the numerical evaluation of the superposition hypothesis in the calculation of the bearing capacity for rough circular foundations embedded in sand. In this section, the bearing capacity factors contributing to the conventional solution have been evaluated and superposition errors are indicated and compared with those found by different authors. The latter part of the work is devoted to studying the depth effect on the estimation of the bearing capacity of a rough circular footing embedded in the sand considering presence of an overload adjacent. For both analyses, the finite-difference code Flac2d (FLAC 2007) was used to reach the bearing capacity for embedded circular footings, the ground friction angles are between 25° and 40° and a depth ratio Df/D varies from 0.1 to 2. The calculation results are presented in tables and graphs and compared to previously published results available in the literature.

A numerical study on effect of liquefaction on ring footings during 2001 Bhuj earthquake at Kutch (Gujarat), India

Liquefaction, the temporary loss of strength in saturated sand causing it to behave like a liquid, leads to devastating consequences, including the settling, tilting, or collapsing of structures built on loose, saturated soil. The 2001 Bhuj earthquake witnessed extensive liquefaction in regions such as the Great Rann of Kutch, Banni Plains, Kandla, and Gulf of Kutch, resulting in substantial damage to various infrastructures, including bridges, docks, buildings, embankments, and dams. This study employs a finite element approach to analyse the behaviour of shallow foundations on liquefying subsoil in Kutch during the 2001 earthquake. The investigation focuses on ring footings with inner radii of 0.25 m, 0.5 m, and 0.75 m, as well as an outer radius of 1 m, alongside a circular foundation with a 1 m radius. Notably, the ring footing with a radius ratio of 0.5 exhibits the least settlement under static loads, underscoring that liquefaction-induced settlement for ring footings is significantly less than that for circular footings.

Drained Bearing Capacity of Skirted Circular and Ring Footings with Varying Depths of Skirts

Drained Bearing Capacity of Skirted Circular and Ring Footings with Varying Depths of Skirts

Prediction of Damping Ratio and Shear Modulus of Saturated Clay Soil under Rotating Machine

Developing countries' industrial growth necessitates innovative machine foundation design and resilient infrastructure. Meanwhile, soil properties play a significant role in the satisfactory design of machine foundations. The paper presents an experimental work to determine accurately the damping ratio and shear modulus by equations. The paper studies the effect of different parameters (embedded depth of foundation, shape of footing, and changing operating frequency of machine) on the damping ratio and shear modulus of saturated clay soil. Moreover, mathematical expressions are derived from statistical analysis to predict the damping ratio for rectangular and circular footing on saturated clay. The physical model results reveal that the damping ratio inside the soil will be increased with an increase in the depth of the point inside the soil for all cases. The damping ratio tends to decrease with an increase in operating frequency. The maximum damping ratio has occurred below a rectangular foundation with a 16.6 Hz operating frequency in saturated clay. The damping ratio is a function of many factors, such as embedment depth, degree of saturation, shape of foundation, and operation frequency of the machine.

Mathematical Modeling for the Optimal Cost Design of Circular Isolated Footings with Eccentric Column

This article shows a model for the design of circular isolated footings and the column placed anywhere in the footing under minimum cost criteria. Some designs for obtaining the diameter, effective depth, and steel areas of the footing under biaxial bending assume the maximum and uniform pressure at the bottom of the footing supported on elastic soils. All these works consider the column placed at the center of the footing. Three numerical problems are given (each problem presents four variants) to determine the lowest cost to design the circular footings under biaxial bending. Problem 1: Column without eccentricity. Problem 2: Column with eccentricity in the direction of the X axis of one quarter of the diameter of the footing. Problem 3: Column placed at the end furthest from the center of the footing on the X axis. The results are verified by the balance of moments, one-way shear or shear and two-way shear or punching. The new model shows a saving of 17.92% in the contact area with soil and of 31.15% in cost compared to the model proposed by other authors. In this way, the proposed minimum cost design model for circular footings will be of great help for the design when the column is placed on the center or edge of the footing.

Experimental Investigation of the Behavior of Ring and Circular Footings on Geogrid Reinforced Layered Soil Strata

Experimental Investigation of the Behavior of Ring and Circular Footings on Geogrid Reinforced Layered Soil Strata

Bearing capacity of circular footings on multi-layered sand-waste tire shreds reinforced with geogrids

The presence of waste tires poses an environmental challenge as they occupy a significant amount of land and are expensive to dispose in landfills. However, reusing waste tires can address this issue when waste tires are used in geotechnical applications. To determine the viability of this approach, laboratory-scale tests were conducted to investigate load-bearing capacity of circular footings on sand-tire shred (STS) mixtures with shredded waste tire contents of 5%–15% by weight and three different widths of shreds. The investigation focused on analyzing the thickness of layers composed of STS mixtures, the soil cap, and the impact of geogrids on bearing capacity. The results indicate that a specific mixture of sand and tire shreds provides the highest footing-bearing capacity. In addition, the optimal shred content and size were found to be 10% by weight and 2 cm × 10 cm, respectively. Furthermore, for a given tire shred width, a particular length provides the largest bearing capacity. The results agree well with that of previous research conducted by the first author and his colleagues in direct shear and California bearing ratio (CBR) tests. The primary finding of this research is that the use of two-layered STS mixtures reinforced by geogrids significantly enhances the bearing capacity.

Bearing Capacity of Skirted Ring Footing on Dense Sand Overlying Loose Sand

Introduction: The ultimate bearing capacity of an unskirted/skirted ring foundation on dense sand overlying loose sand is estimated using finite element analysis in this study. Methods: The range of thickness ratio (thickness of top dense sand layer divided by external diameter of ring) was kept between 0.25 and 1.5. The friction angle of the upper dense and bottom loose sand layers was maintained between 40° and 44° and 30° and 34°, respectively. In the case of skirted ring footing, the skirts are attached at the inner edge, outer edge, and both the edges, respectively. Results: According to the results, the bearing capacity increases with an increase in either the friction angle of upper dense and lower loose sand layers or the thickness ratio. A double-skirted ring footing was observed to provide the greatest bearing capacity, followed by footing with skirts attached at the outer and inner edges, respectively. Conclusion: To sum up, the bearing capacity of the ring footing was higher than the circular footing for the given friction angle of the top and bottom layer and thickness ratio.

Hardening plasticity formulation for drained behavior of circular foot-ings

Upon moving the offshore wind energy sector to deeper waters, there is an increased demand towards developing more complex foundation solutions, in particular suction caisson foundations as single or jacket supported on multiple foundations. Broadly, foundations for offshore wind turbines need to be able to withstand a variety of load combinations throughlout their lifetime.
 This contribution is devoted to a comprehensive review of the performance of circular surface and shallow foundations under combined loading (VHM), and how this can principlally be understood in a theoretical framework in the context of plasticity theory [1-2]. Initially, the associated and non-associated plasticity in offshore foundation design is discussed. The plastic potential function for a non-associated plasticity framework, with the aid of two association factors and is as follows:
 where indicates the apex of the potential surface; is eccentricity parameter; and represent the uppermost size of the yield surface along the vertical loading coordinate; and are curvature factors.
 Assuming , two potential surfaces with and > ( ) have similar shapes despite having different intersection points with the V axis, a clear indication that associated flow is the governing plastic flow mechanism in radial plane (Fig.1).
 Contrarily, the plastic potential surface for surface foundations was plotted for two different association factor values ( i. e., while all else remains unchanged. The two cases shown in Fig. 2 are for two different values of . Thus, according to Eq. (1) and Fig. 2, the normality condition is no longer relevant in the radial plane. Further, The hardening law for circular surface footings can be described by the following expression [3], in which the post-peak softening behavior is modeled by a factor :
 where indicates the apex of the potential surface; is eccentricity parameter; and represent the uppermost size of the yield surface along the vertical loading coordinate; and are curvature factors.
 Assuming , two potential surfaces with and > ( ) have similar shapes despite having different intersection points with the V axis, a clear indication that associated flow is the governing plastic flow mechanism in radial plane (Fig.1).
 Contrarily, the plastic potential surface for surface foundations was plotted for two different association factor values ( i. e., while all else remains unchanged. The two cases shown in Fig. 2 are for two different values of . Thus, according to Eq. (1) and Fig. 2, the normality condition is no longer relevant in the radial plane. Further, The hardening law for circular surface footings can be described by the following expression [3], in which the post-peak softening behavior is modeled by a factor :
 The above hardening law describes the relationship between vertical loading and plastic settlement, where = at the infinity amount of plastic settlement ( is the post-peak vertical loading and is peak bearing capacity), The denotes initial plastic stiffness, and are plastic settlement and plastic settlement at maximum load, respectively (Fig. 3).
 Although the studies on surface footings yielded values lower than unity (a clear indication of the prevailing post-peak softening behavior), this key trend is not confirmed in shallow foundations according to FE push-over analyses and scaled model tests [4].
 In current study, multiple FE push-over analyses were carried out to establish a new hardening law for a multi-pod system. The validation procedure was detailed in [5-6]. As a consequence, = 1.99 and 1.85 and = 12700 and 11400 corresponding to the embedment ratios 0.5 and 1 were determined, respectively. Furthermore, the initial plastic stiffness was found significantly higher than that of surface footings [7]. Finally, the hardening law and plastic potential surface turned out to be inherently complex, because both involve several parameters that need to be calibrated (i.e., depending strongly on foundation type and soil strength). Thus, special care should be taken when assessing the skirted foundation responses on different loading planes.

Effect of eccentric loads on the behavior of circular footing with/without skirts resting on sand soil

The stability of circular footings under eccentric vertical loads is a significant problem in geotechnical engineering. Therefore, this paper shows the results of experimental tests carried out on an eccentrically loaded circular foundation on sand soil. The focus of this research is on examining how eccentric loads affect the behavior of circular footings on sand soil, both with and without skirts. Various load eccentricities (e) equals zero, 2.50, 5.00, 7.50, 10.00, 12.50, 15.00, 17.50 and 20.00 mm are used. In addition to, a 60 mm-diameter circular foundation and sand with an 85% relative density (Dr) are used in this experimental study. To study the effect of changing the skirts depth on the load-settlement response skirts with different depths (h) = 60 mm, 150 mm, 240 mm are used for vertical reinforcement. In comparison to the unreinforced condition, test findings show an improvement in ultimate bearing capacity. When the skirts are positioned at the ideal embedment depth L/D = 4, it is found that the circular footing's load-settlement behavior is enhanced by 92% and 93% in case of using (e/D) ratio = 0.125 and 0.25 compared to the unreinforced case.

A comparison of experimental and computational methods for circular footing response on lime-treated geotextile reinforced silty sand

A comparison of experimental and computational methods for circular footing response on lime-treated geotextile reinforced silty sand

BEARING CAPACITY OF SHALLOW FOOTINGS RESTING ON DUNE SAND

As a result of the growth of economic, demographic and building activities in Iraq, that necessitates carrying out geotechnical investigations for the dune sand to study behavior of footings resting on these soils. To determine these properties and to assess the suitability of these materials for resting shallow foundation on it, an extensive laboratory testing program was carried out. Chemical tests were carried out to evaluate any possible effects of the mineralogical composition of the soil on behavior of foundation rested on dune sands.Collapse tests were also conducted to trace any collapse potential. Loading tests were carried out for optimum water content and different shapes of footing. Loading test recommends manufacturing of steel box and footing models with different shapes and dimensions. The results indicated that, Affek dune sand is predominantly fine sand with non-plastic fines.Because the content of sulphate (as SO3) is only 0.05%, and the alkalinity of dune sand, which reduces the corrosion potential, ordinary Portland cement can be used in concrete foundation construction in/on dune sands. The results of collapsing tests showed that Affek dune sand exhibit a slight to moderate potential depending on stress level. Due to Soaking by water, the reduction in bearing capacity of optimum state was about 45%. The bearing capacity of square footing was greater than those of the circular and rectangular footings.