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Behavior of circular skirted footing on gypseous soil subjected to water infiltration

  • Khawla A. Aljuari , Mohammed Y. Fattah EMAIL logo and Mohammed N. J. Alzaidy
Published/Copyright: January 3, 2023
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Journal of the Mechanical Behavior of Materials
From the journal Journal of the Mechanical Behavior of Materials Volume 32 Issue 1

Abstract

Skirted footings are used to increase the final carrying capacity of shallow foundations resting on unstable soil and to decrease settling by limiting the soil beneath them. Skirted footings are utilized as an alternative to pile driving in poor strength soils at the top layer, such as gypseous soil, to save project costs and time spent installing piles while maintaining excellent performance. The settling of circular skirted footings resting on gypseous soil subjected to loading, infiltration, and collapsing stages was investigated using numerical calculations in this research study to determine their stability under environmental loadings. Finite element analyses were carried out using the commercially available software GEO-STUDIO. The stage of gypseous soil and variable skirt depth to footing diameter ratios (d/D) were taken into consideration. The findings reveal that both the soil stage and the skirt embedment ratio have a substantial impact on the ultimate bearing capacity and the settlement of weak soil, with the skirt embedment ratio increasing resulting in superior skirted footing performance. Furthermore, the improvement in settlement for the loading stage is the smallest, whereas the value for the collapsing soil stage is the largest.

Keywords: gypseous soil; weak soil; skirted footing; settlement; finite element analysis

1 Introduction

Gypseous soils: gypseous soils are soils that collapse (settle with a lot of consolidation) when a certain amount of water is applied to them. Due to the collapse (excessive settlement) and low shear strength upon wetting, this soil is regarded one of the problematic soils. Gypseous soils can be found in dry and semi-arid regions all over the world, and gypsum deposits and rocks can be found all throughout Iraq. Gypseous soils are regarded to be extremely hazardous. It is unsaturated soil that undergoes essential particle rearrangement and is prone to distinct collapse, high volume change because it is considered highly soluble materials by nature, very soft soil with a distinct decrease in shear strength when exposed to water, causing serious damage to structures built on it. Gypseous soils cover around 20–30% of Iraq’s total land area, mainly in the western regions.

Skirted footings are suitable for a variety of offshore applications, including the oil and gas industry and structures where scour is a major concern. Skirted footings provide uplift bearing and load transmission beneath the surface without the need for driving piles; therefore, they are utilized as a replacement for deep footings; also, they save project cost and installation time while providing good performance.

Skirted footings are shallow footings with thin “skirts” around the perimeter that are embedded in the soil vertically to a depth d, resembling an inverted bucket with diameter B and depth D, as shown schematically in Figure 1. The vertical skirt under the foundation’s base limits the below-grade soil and offers soil bearing on the skirt direction, which aids the footing’s resistance to slide. In addition, as indicated in Figure 2, the soil works as a unit with the upper footing to transfer superstructure pressure to the soil practically at the skirt’s tip level. Skirt footings can be utilized with a variety of shallow footing designs, including square, rectangular, and circular footings. These footings are made to withstand lateral forces on particular structures caused by earthquakes, seismic forces, wind loads, water wave pressure, lateral earth pressure, and electricity transmission lines [1,2].

Figure 1 Schematic diagram of skirted footing [4].
Figure 1

Schematic diagram of skirted footing [4].

Figure 2 Soil confinement illustration inside skirt footing [5].
Figure 2

Soil confinement illustration inside skirt footing [5].

Many scholars have recently looked into the usage of a skirt as a soil enhancement technique. Skirted footings are used as an alternative to “pile foundations” in soils with weak upper layers, according to Watson and Randolph [3].

Yun and Bransby [6] used centrifuge model tests to investigate the reaction of skirted footings on loose sandy soil when subjected to a combination of vertical, horizontal, and flexural loads. They claimed that as compared to surface footing, the skirted footing’s horizontal carrying capacity was enhanced by up to four times. They also noticed that the mechanism of footing failure shifted from sliding to rotation.

Yun and Bransby [4] investigated the vertical bearing capacity of skirted foundations on normally consolidated-undrained soil using finite element models with various skirted embedment ratios. The findings were compared to skirted foundations that were placed on clayey soil centrifuge model trials. According to them, the capacity of a skirted foundation under vertical pressure can be estimated as if the footing is rigid and has an embedment depth equal to the skirt depth.

In an experimental investigation, Saleh et al. [7] tested a one-sided skirted strip foundation model resting on sandy soil and subjected to varied eccentric inclined loads. The effects of changes in load eccentricity, load inclination angle, skirt length, and skirt side slope angle were studied. A numerical research was also carried out using the PLAXIS finite element software tool. It was found that using the skirt increased ultimate bearing capacity while also boosting bearing sliding resistance at high angles of load inclination due to the horizontal soil pressure exerted on the skirt’s side wall. They also discovered that as load eccentricity and inclination angle increased, load settling behavior increased. They also found that increasing the angle of inclination of the skirt increased the ultimate load-carrying capacity and decreased the “settlement.”

Understanding the consolidation mechanism for skirted footings is critical for estimating compression footing settlement estimates. Gourevence and Randolph [8] used small strain finite element studies using the ABAQUS software package to investigate the consolidation behavior beneath circular skirted footings. They looked at the effect of frictionless footings, rough skirt-soil interfaces, and skirt embedment ratios of less than 1.0 to mimic shallow footings. All of these variables, they found, have a considerable impact on the consolidation response.

EL Wakil [9] investigated the effect of a skirt circular foundation on sand layer bearing capacity. The skirt embedment ratio and relative density of sand were explored as variables. It has been suggested that the bearing capacity can be increased by up to 6 times. This improvement ratio is affected by the skirt depth to foundation diameter ratio as well as the relative density of the sand, with skirts being more useful in loose sand than in medium or dense sand. Golmoghani and Rowshanzamir [10] did a study in this area. They claimed that structural skirts could boost footing bearing capacity by up to 3.7 times when compared to footings with the same skirt depth.

Thakare and Shukla [1] investigated the performance of a rectangular skirted footing resting on a sand layer and subjected to lateral load in an experimental research. The number of skirts attached to the footing, the skirt embedment ratio, and the direction of applied load with the axis of the skirted footing have all been investigated. The results showed that increasing the skirt embedment ratio, the number of skirts attached to the footing, and the angle of inclination of the load with the horizontal can greatly improve the lateral load-carrying capacity of skirted footings.

The bearing capacity and settlement of circular skirted footings on weak clayey soil were investigated by Listyawan et al. [11]. Footing diameters and skirt embedment ratios of various sizes have been investigated. They discovered that the skirt reduces settlement significantly, with the higher the skirt embedment ratio, the lower the settlement. Furthermore, for a given settlement and diameter, the results revealed that as the skirt lengthens, the load sustained by the footing increases.

The carrying capacity of skirted footings on dry gypseous sandy soil was tested by Mahmood et al. [12]. Different skirt embedment ratios and relative densities of SW-SM gypseous soil were investigated to find the best skirt embedment ratio and relative density for highest bearing capacity. They came to the conclusion that the bearing capacity enhancement is a function of skirt embedment ratio and relative density and that increasing these parameters increases bearing capacity.

The majority of the previous research was limited to sandy soils and focused on structural skirted footings subjected to concentric or eccentric loads. Quantifying the influence of structural skirts on weak soaked gypseous soil has received little consideration. The objective of this research article is to investigate numerically the performance of circular skirted footing on gypseous soil exposed to infiltration subjected to concentric vertical load and different skirt embedment ratios. The analyses were done using commercially available GEO-STUDIO software program. The influence on bearing capacity and settlement response of an elastic soil has been analyzed, which has not been previously addressed by most of researchers in a systematic manner.

2 Finite element analysis

2.1 Geometry and properties of materials

In uniform undrained soil material, finite element analyses revealed entire settlement of two types of footings. Surface circular footings and circular skirted footings are the two forms. In most field applications, skirted footings with skirt depth to footing diameter ratios less than 1.0 are used; hence, different ratios of skirt depth to footing diameter (d/D = 0.2, 0.4, 0.6, and 1.0) are used to demonstrate the effect of different ratios of skirt depth to footing diameter. In the analyses, a ratio of skirt thickness to footing diameter (t/D) of 0.05 was assumed. Table 1 shows the index and engineering properties of Al-Jazirah soil at a depth of 2.0 m below the ground surface.

Table 1

Index and strength properties of Al-Jazirah soil [14]

Index properties Values Index properties Values
Natural water content (%) 20 Clay content (%) 14
Liquid limit (%) 60 Gypsum content (%) 41.33
Plastic limit (%) 36 Organic matter (%) 0.37
Plasticity index (%) 24 Total unit weight (kN/m3) 17.8
Specific gravity 2.68 Dry unit-weight (kN/m3) 14.8
Engineering properties Values
Effective cohesion (cʹ) (kN/m2) 10
Effective internal friction angle (ϕʹ) 30.11
Collapse index (%) 1.395

SIGMA/W is a versatile tool for simulating completely “connected analysis” of saturated and unsaturated swelling soil [13]. As a result, SIGMA/W can simply explore the volume change caused by gypseous soil. The material category of effective drained parameters with linear-elastic constitutive model was used for the starting condition of gypseous soil. The entirely coupled analysis is the effective-stress parameters of pore water pressure fluctuation under applied stresses, infiltration, and collapse phases, and the material is described by the elastic plastic constitutive model. The properties of the elastic plastic model are listed in Table 2. The shear strength parameters were determined from consolidated undrained triaxial test [14].

Table 2

Parameters for input of the FEM analysis of gypseous soil

Material Property Value
Initial state of gypseous soil (linear-elastic model) Effective elastic modulus (kPa) 40,000
Dry unit weight (kN/m3) 14.8
Poisson’s ratio 0.334
Loading stage (elastic-plastic model) Dry unit weight (kN/m3) 14.8
Poisson’s ratio 0.334
c′ (kPa) 100
ϕ° 40
Load response ratio 1.0
k-Saturation (m/day) 12.096
k-Function method Fredlund-Xing function
Maximum suction (kPa) 1 × 104
Minimum suction (kPa) 0.01
Number of points 20
Residual water content (m3/m3) 0.0
Infiltration and collapsing stages (elastic-plastic model) Effective elastic modulus (kPa) 20,000
Poisson’s ratio 0.334
Dry unit weight (kN/m3) 14.8
Effective cohesion 100
Effective angle of internal friction 40°
Concrete skirted footing Effective elastic modulus (kPa) 21,000,000
Poisson’s ratio 0.2

The soil was modeled as a single, homogeneous elastomer. Young’s modulus (E) and Poisson’s ratio (v) were considered to be constant and isotropic elastic parameters throughout the calculations, as well as isotropic hydraulic conductivity, i.e., a horizontal-to-vertical permeability ratio of 1.0. Because the value of Poisson’s ratio utilized in practical applications is between 0.1 and 0.5, a typical value of 0.334 was assumed in the analyses of this study, and Young’s modulus was considered to be 40,000 kPa. For concrete skirt footing, a unit weight of 24 kN/m3 was chosen. The soil’s effective cohesiveness and effective angle of internal friction were set at 100 kPa and 40°, respectively. The soil–water characteristic curve (SWCC) of the gypseous soil utilized in the analysis is shown in Figure 3. The SWCC is derived indirectly from the engineering features of the soil (liquid limit and grain size distribution). The hydraulic–conductivity curve for gypseous soil was computed indirectly using SWCC parameters and saturated hydraulic conductivities, utilizing the equation proposed by Fredlund and Xing [15] as shown in Figure 4:

(1) f ( h ) = m n α ( α h ) n − 1 [ 1 + ( α h ) n ] m + 1 ,

where m, n, and α are independent curve fitting parameters.

Figure 3 SWCC of gypseous soil.
Figure 3

SWCC of gypseous soil.

Figure 4 Hydraulic-conductivity curve of gypseous soil.
Figure 4

Hydraulic-conductivity curve of gypseous soil.

2.2 Boundary conditions

The type of boundary conditions to use in FEM is mostly determined by the actual loading conditions. The boundary conditions are divided into three categories by the SIGMA/W program: hydraulic, displacement, and rotation.

Three stages of modeling are used to mimic the field condition of circular footings with and without skirts that are subjected to applied stresses and designed on gypseous soil: loading, infiltration, and collapsing.

Stress/strain boundary conditions are used in finite element method stress analysis, and hydraulic boundary conditions are used in “finite element method” flow analysis. During the stress/strain analysis of the three phases, the vertical soil limits on the right and left sides of the model are only allowed to move in the vertical direction, while they are restrained in the horizontal direction. Rollers are put along the model’s right and left sides, as seen in Figure 5. As shown in Figure 5, the hinge boundary is used to describe this circumstance in which the bottom of the soil geometry is blocked in both horizontal and vertical dimensions. On the other hand, the top surface is left to move freely, and the footing was assumed a rigid material. The interaction was roughly assumed between the footing and soil.

Figure 5 Rollers and hinges boundary conditions assigned of circular skirted footing model.
Figure 5

Rollers and hinges boundary conditions assigned of circular skirted footing model.

During the analysis of application of the surface load, the surface load should be applied only during the first time step to allow excess pore-pressure to dissipate, and then, it should be numerically deleted for consecutive time steps. A surface load could not be imposed since SIGMA/W is based on an incremental formulation; thus, it was held during the dissipation step. A step function, such as the one shown in Figure 6, can keep this going. A 1 s time step is used. SIGMA/W retrieves the function values at time n(n − 1). As a result, the first time integration’s surface load is equal to the other time integration’s surface load, and the variation between them is zero. The vertical stress is gradually imparted in stages.

Figure 6 Typical finite element mesh for d/D = 1.0.
Figure 6

Typical finite element mesh for d/D = 1.0.

As a result, the surface load of the first time integration is equal to the surface load of the second time integration, and the difference between them is zero. Vertical stress is applied gradually in phases.

The base and side boundaries are thought to be impermeable to water flow, whereas the soil surface is believed to be permeable to flow. According to the limits proposed by Hillel [16], the rate of infiltration of sandy and silty soils ranges between 10.2 and 20.3 mm/h.

Therefore, the rate of infiltration of 10–20 mm/h = 0.24–0.48 m/day was chosen and dependent in this study.

2.3 Finite element mesh

The calculations were carried out using the finite element program SIGMA/W, which can be used to conduct stress and displacement evaluations of diverse earth structures, such as footings, embankments, excavations, and tunnels. As an example, Figure 6 shows the finite element mesh of the gypseous soil and skirted footing with d/D equal to 1.0. The model has a depth of 12 m and a width of 11 m. Both the gypseous soil and the circular skirting footing are represented by a consistent mesh size. Each element is 0.1 m in size. The eight-noded quadrilateral “isoparametric element” of rectangular grid of quads is the most appropriate picked element in the “finite element model.”

3 Results and discussion

3.1 Settlement variation

Two parameters have been considered consisting varying ratios of skirt depth to footing diameter d/D (0, 0.2, 0.4, 0.6, and 1.0) to study numerically their influence on settlement behavior of shallow footings. Three stages have been employed numerically in the program, which are loading, infiltration, and collapsing stages. Figure 7 shows the settlement–skirt ratio relationships that are plotted for the three stages mentioned under maximum and minimum rates of infiltration. It is obvious that the value of settlement is inversely proportional with skirt depth to the footing diameter ratio where the settlement of footing decreases linearly as the d/D ratio increases; this may be explained as, when d/D ratio increases the confining pressure at skirt tip level increases, so consequently elastic and plastic displacements of soil particles will be constrained. As well as, the longer drainage paths for water to dissipate due to the skirt tip level will retard the consolidation settlement. Also, the rough sides of skirted footing with the surrounding soil will cause a friction that reduces the settlement.

Figure 7 Correlation between settlement and skirt ratio.
Figure 7

Correlation between settlement and skirt ratio.

The correlations between settlement and width of footing for loading, infiltration, and collapsing stages at different skirt ratios are drawn in Figure 8a–c. It is worth mentioning here, the settlement of the soil is uniformly distributed along the width of footing under all the variables mentioned above, that is related to homogeneity of the soil, the load and water are uniformly distributed on the soil. Also, it can be seen that the value of settlement in loading stage is the smaller, where their values were 0.28 and 0.0 m for skirt depth to footing diameter ratio d/D 0 and 0.2–1.0, respectively. The value of settlement was intermediate for the infiltration stage, where their values were 0.28, 0.22, 0.19, 0.16, and 0.05 m for skirt depth to footing diameter ratio d/D 0, 0.2, 0.4, 0.6, and 1.0, respectively. While the values of settlement in collapsing stage were the larger, where their values were 0.56, 0.50, 0.47, 0.43, and 0.32 m for skirt depth to footing diameter ratio d/D 0, 0.2, 0.4, 0.6, and 1.0, respectively. This means that the percent of decrease in the settlement of the gypseous soil is 100, 82.1, and 42.86% when the depth of the skirt increased from 0 to 1 m during loading, infiltration, and collapsing stages, respectively.

Figure 8 Settlement of soil with width of footing during different stages and skirt ratios.
Figure 8

Settlement of soil with width of footing during different stages and skirt ratios.

The behavior of settlement is also obvious in Figure 9, which represents the relationship between settlement–time as a function of skirt depth to footing diameter ratio for the three stages mentioned previously. It is obvious that the settlement of the footings reduces with increasing skirt embedment ratio, this can be explained by the contribution of the friction parameter along the skirts, which will carry a portion of the applied load on the footings, which increases with increasing skirt depth leading to a reduction in contact pressure. As a result, the distribution of excess pore pressure below skirt tip level is going to reduce with increasing skirt depth, so the consolidation settlement durations are increasingly prolonged. Moreover, it is important to note that in the actual situation the stiffness of soil is increased with increasing depth; therefore, the settlement will reduce with increasing the skirt depth. Also, when the soil became saturated, the water acts as a lubricated material which reduces the friction between the skirt side and the surrounding soil and between the soil particles together. These results have achieved good agreement with numerous researchers [9,11,12,17].

Figure 9 Settlement with time during different stages and skirt ratios.
Figure 9

Settlement with time during different stages and skirt ratios.

Figure 10a and b shows the relationship between settlement with depth under footing as a function of skirt depth to footing diameter ratio d/D. The analyses have been done for two points, the first one located under the center of the footing, while the second point located at the edge of the footing adjacent to the skirt, to observe the behavior of settlement and the possibility for the differential settlement under the footing to be occur. It can be seen that the settlement reduced with increasing depth under footing from zero until to dissipate at a depth of 12 m, and the settlement values are almost the same for the two studied points, which means that the settlement is uniform under the footing and there is no differential settlement.

Figure 10 Settlement with depth after collapsing stage with different skirt ratio. (a) Below the center of footing. (b) Adjacent to the skirt.
Figure 10

Settlement with depth after collapsing stage with different skirt ratio. (a) Below the center of footing. (b) Adjacent to the skirt.

Mahmood et al. [18] found that when the initial degree of saturation increased, the collapse potential reduced dramatically. One of the primary parameters regulating the collapse behavior of unsaturated soil is the initial degree of saturation. As the saturation level rises, more gypsum dissolves, and the unit weight rises. As a result, the void ratio is reduced, and the risk of collapse is reduced. The skirted footing enhances the load–settlement behavior of the footing by increasing bearing capacity while reducing settlement. The bearing capacity of a skirted footing increases by 1.92–2.27 times, depending on the surface and geometrical parameters of the skirt, as well as gypseous soil characteristics. It is not suggested to compact the soil below the footing to increase the relative density. According to Fattah et al. [19], for the same gypsum content under high stress, the collapse potential increases with time as the relative density increases. When dry soil is compacted at a higher relative density, the strain is much reduced. When the relative density goes from 40 to 60% for an extended period of time, there is a drop. The saturated samples behaved in the other way; when saturated soil is compacted at a higher relative density, the strain increases.

4 Conclusions

A series of finite element analyses were conducted to indicate the settlement behavior of the circular skirted footing on weak gypseous soil subjected to different soil stages. The results were compared numerically with the surface raft footing. Notable agreement of finite element analyses results has been obtained with numerous researches related to skirted footings. From the numerical solution results analyzed above, the following conclusions can be made:

  • Skirted footings have a significant influence in reducing the settlement. The value of settlement is inversely proportional to the skirt depth to footing diameter ratio. As the skirt depth to footing diameter ratio increases, settlement value will reduce and better performance is achieved for skirted footings.

  • The soil stage has a significant influence in the settlement behavior. For loading stage, the settlement was the lowest, whereas its value was the biggest for collapsing soil stage

  • The settlement values were the same under the footing. In other words, it was homogeneous under the skirted footing and there is no differential settlement noticed.

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: Authors state no conflict of interest.

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Received: 2022-04-05
Revised: 2022-06-02
Accepted: 2022-08-23
Published Online: 2023-01-03

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/jmbm-2022-0252
Keywords for this article
gypseous soil; weak soil; skirted footing; settlement; finite element analysis
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