Marine Georesources & Geotechnology

ISSN: 1064-119X (Print) 1521-0618 (Online) Journal homepage: http://www.tandfonline.com/loi/umgt20

Effect of embedment on the vertical capacity

of bucket foundation in loose saturated sand:
Physical modeling

Abdolhosain Haddad, Reza Amini & A. Barari

To cite this article: Abdolhosain Haddad, Reza Amini & A. Barari (2018): Effect of embedment
on the vertical capacity of bucket foundation in loose saturated sand: Physical modeling, Marine
Georesources & Geotechnology, DOI: 10.1080/1064119X.2018.1443354

To link to this article: https://doi.org/10.1080/1064119X.2018.1443354

Published online: 14 Mar 2018.

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MARINE GEORESOURCES & GEOTECHNOLOGY
https://doi.org/10.1080/1064119X.2018.1443354

none defined

Effect of embedment on the vertical capacity of bucket foundation in loose

saturated sand: Physical modeling
Abdolhosain Haddada , Reza Aminia , and A. Bararib
a
Department of Civil Engineering, Semnan University, Semnan, Iran; bDepartment of Civil Engineering, Aalborg University, Aalborg Ø, Denmark

ABSTRACT ARTICLE HISTORY

Bucket foundations have been widely used for a variety of offshore applications. The effects of skirt Received 29 July 2017
length on ultimate bearing capacity of bucket foundation have been studied and reported in published Accepted 16 February 2018
scientific papers. However, few studies have addressed the behavior of bucket foundations in loose KEYWORDS
saturated sand. In this paper, a series of experimental investigations were performed to determine the Embedment ratio; failure
bearing capacity of bucket foundation under uniaxial loading. The experiments were conducted on small- mechanism; skirt length;
scale foundations under vertical loading in loose saturated sand. It was found that increasing the skirt skirted foundation
length would enhance the bearing capacity of bucket foundation. As reflected in the present study,
bearing strength might be enhanced more than 5 times in loose saturated sand in comparison to surface
footing with equivalent diameter. Based on the experimental investigation, a depth factor was proposed
to approximate bearing capacity of bucket foundations in terms of those for surface footing and
embedment ratio. Moreover, the corresponding settlement of foundation at the failure load was found to
increase with skirt length.

1. Introduction 1.1. Bearing capacity of shallow foundations

By fast-growing demand for renewable energy and breaking Several classical methods have been developed to determine
the dependence on fossil fuels, strong political and economical the bearing capacity of foundations. Terzaghi (1943) suggested
scenarios emerged to develop the utilization of the offshore a simple analytical method to determine the bearing capacity
wind power. Wind energy is one of the most cost-effective of shallow foundation on dense sand subjected to vertical load.
sources of renewable energy that produce no greenhouse It was supposed that the collapse happens in consequence of
emissions and reduce fossil fuel consumption. sliding on a slip line, and the criterion would be satisfied with
The supportive structure of offshore wind turbine has a the soil mass. It is obvious that increasing the length of slip
significant effect on the total cost of the wind turbine. Several line would cause a greater bearing capacity. Usage of structural
foundation concepts are available for wind turbine including plate on circumference of foundation could increase the length
monopile foundation, gravity-based foundation, and bucket of the slip line and the bearing capacity.
foundation (Randolph and Gourvenec 2011). The bucket In spite of tremendous research on the bearing capacity of
foundation is a novel and innovative shallow foundation with shallow foundations, the capacity of bucket foundation is a
vertical plates that is also denoted as a skirted foundation or challenging topic, due to the embedment of foundation and
suction caisson. Bucket foundations are much easier to install the internal mechanisms due to the existence of deformable
in comparison to deep foundations and do not require plug (Barari and Ibsen 2012; Ibsen, Barari, and Larsen 2012).
expensive and heavy installation equipment (Houlsby and There is a lack of knowledge about behavior of bucket
Byrne 2000; Ibsen, Schakenda, and Nielsen 2004). foundation under uniaxial and general loading. Offshore
Skirted footing is widely used as an alternative to deep-pile shallow foundations’ design guidance is set out by the API
foundation for the offshore facility, e.g., offshore wind tur- (2000), Det Norske Veritas (DNV) (1992) and ISO:19901-4
bines. The skirts of bucket foundation strictly confine the soil (2003) among others. The existing solutions for offshore
inside the foundation and the soil almost acts as a rigid body, shallow foundation design, presented in the recommended
which can transfer superstructure load to soil at the bottom of practices, were developed from onshore design code, which
the skirt (Eid et al. 2013). Bucket foundations for jackets are based on the classical bearing capacity theory (Barari
or wind turbines have diameters up to 30 m and skirt length and Ibsen 2012). Bearing capacity and yield locus of bucket
to foundation diameter ratios d/D are typically in the range foundation under vertical and general loading have been
0.1–1 (Houlsby, Ibsen, and Byrne 2005; Tjelta 2015). In widely studied by several researchers in the past two decades
general, bucket foundations with embedment ratio (d/D) less (Bransby and Randolph 1999; Gourvenec 2008; Ibsen, Barari,
than unity are used for offshore facilities. Figure 1 shows full and Larsen 2012; Park, Park, and Yoo 2016). Such studies,
view and a cross section of a typical bucket foundation. based on 1 g physical and numerical modeling, have

CONTACT Reza Amini r.amini@semnan.ac.ir Department of Civil Engineering, Semnan University, 19111-35131 Semnan, Iran.
© 2018 Taylor & Francis
2 A. HADDAD ET AL.

of the bearing capacity of bucket foundation to that of solid

foundation is approximately equal to 0.93 regardless of the
characteristics of sand and foundation size.
Park, Park, and Yoo (2016) performed a series of numerical
modelings to study the vertical capacity and the load transfer
mechanism of bucket foundations in sands. It was reported
that a significant arching occurred around the bucket
foundation, which increased horizontal stress and conse-
quently increased the shaft resistance (Qs). The Qs depends
Figure 1. Characteristics of a bucket foundation.
on d/D and friction angle of soil. Although Qs was calculated
for various friction angles, they did not clarify the contribution
demonstrated that inclusion of skirts increases the bearing of Qs in ultimate bearing capacity. Moreover, a shape-depth
capacity and reduces settlement of foundations resting on factor (Sq.dq) equation was proposed to calculate base capacity
granular soils (Villalobos 2006; Al-Aghbari and Dutta 2008; of bucket foundation (Qb). The Qb was dependent on friction
Eid et al. 2013; Barari et al. 2017). angle and d/D.
Since most often offshore seabed is covered by soft clay, Barari et al. (2017) performed a series of FE analyses to
most of the previous studies focused on the bearing capacity study the bearing capacity of bucket foundation in
of bucket foundations in clay (Bransby and Randolph 1999; cohesionless soil. They proposed depth factor relationships
Gourvenec 2008; Barari and Ibsen 2014). Bransby and to approximate the vertical capacity of bucket foundation in
Randolph (1999) conducted a series of finite element (FE) terms of the capacity of surface foundation and embedment
and upper bound analyses to investigate the effect of embed- ratio. The linear relationships are dependent on the embed-
ment depth on the size and shape of yield locus for skirted ment ratio (d/D) of the foundation. They also deduced that
strip foundation in clays. Some design charts and equations the bearing capacity of bucket foundation is slightly less than
were proposed to calculate the bearing capacity of skirted a solid foundation at the same embedment depth.
foundation under general loading. It was shown that the
bearing capacity of skirted foundation is less than that of an
1.2. Objective of the study
equivalent solid-embedded foundation. The difference
between the capacity of skirted foundation and solid Although the bearing capacity of shallow foundations has been
foundation was up to approximately 10%. a research topic for a long time and has been studied widely,
Barari and Ibsen (2014) performed a series of field tests and there are still very limited studies on the capacity of bucket
numerical analyses to investigate undrained vertical bearing foundation in sand. Most of the previous studies have been
capacity of bucket foundation in Baltic clay. They conducted conducted to investigate the behavior of bucket foundations
monotonic loading on various bucket foundations with differ- in medium to dense sands and there is limited research in
ent geometries and presented a quadratic equation to predict loose sand (Villalobos (2006) and Eid et al. (2009)). The work
vertical bearing capacity based on the embedment ratio. presented below focuses in the behavior of bucket foundation
Results showed that the skirt length has little effect on the in loose sand. The failure mode of the foundations in loose
bearing capacity of foundation resting on clay. sand is almost punching shear mode and finding the capacity
Villalobos (2006) performed some displacement-controlled of foundation is difficult. This is mainly due to the difficulty in
vertical loading tests of the bucket with varying embedment establishing a unique failure load. Moreover, due to inclusion
ratio on granular and cohesive soils. It was found that vertical of skirts, bucket foundations fail in a punching shear mode,
load increases with the bucket penetration in loose sand. and it is more difficult than shallow foundations to find the
A general failure occurred in dense sand, and a hardening bearing capacity of bucket foundation.
law was proposed for modeling of bucket behavior. In this paper, the combination of aforementioned difficult-
Al-Aghbari and Dutta (2008) investigated the behavior of a ies and the effects of skirt length on the bearing capacity are
square footing with a structural skirt on granular soil under investigated by small-scale bucket foundation. For this
vertical loading. The experimental results demonstrated that purpose, a series of experimental tests was performed on soil
structural skirt enhances the bearing capacity of footing and and foundation system to study the vertical capacity of bucket
decreases the settlement, which is dependent on the length foundations in loose saturated sand. A simple relationship,
of skirt. Moreover, an equation, which considered various which yields the vertical capacity of bucket foundation in
effective factors on settlement of footing, was proposed to terms of the embedment ratio (d/D) and bearing capacity of
predict settlement reduction. the surface footing, was proposed herein.
Eid et al. (2013) conducted a series of 3D FE analyses and
studied behavior of bucket foundation under vertical loading.
1.3. Ultimate vertical capacity depth factors
Ratios of bearing capacity and settlement of bucket foundation
to the surface foundation were proposed. The ratios were Byrne and Houlsby (1999) conducted a series of experimental
dependent on embedment ratio (d/D) of foundation and tests to study the behavior of suction caisson foundation on
independent of the friction angle. Results illustrated that the very dense and dry sand. Based on these tests, a general
agreement between numerical results and experimental tests bearing capacity formula was proposed to estimate the bearing
was weak. In addition, Eid et al. (2013) showed that the ratio capacity of suction caisson foundation that is also denoted as a
 MARINE GEORESOURCES & GEOTECHNOLOGY 3

depth factor. This formula was derived based on the bearing

capacity factors from Bolton and Lau (1993) to approximate
the vertical bearing capacity of bucket foundation.
VBucket d
¼ 1 þ 0:89 ð1Þ
VSurface D
where Vsurface is the vertical capacity of foundation with no
embedment, VBucket is the ultimate bearing capacity of bucket
foundation, d is the skirt length, and D is the diameter of
foundation. The depth factor defined as a linear function of
d/D, is highly dependent on relative density of soil. Based
on Terzaghi’s soil bearing capacity theory, bearing capacity
of foundation on cohesionless soil is expressed as Eq. (2):
� �� 2 � Figure 2. Variation of the fitting parameter (n) versus friction angle (φ).
1 0 � � pD
VFoundation ¼ c DNc þ qNq ð2Þ
2 4
linearly with the embedment depth. Following equations were
where VFoundation is the ultimate bearing capacity of an
proposed for loose to dense sand:
embedded foundation, γ0 is the effective unit soil weight, q is
the overburden pressure, and Nγ* and Nq* are the bearing ðVBucket =VSurf ÞDense sand ¼ 1 þ 2:5ðd=DÞ
capacity factors for circular foundation. Eid et al. (2013) and ðVBucket =VSurf ÞMedium Dense sand ¼ 1 þ 2:2ðd=DÞ ð5Þ
Barari et al. (2016) have reported that the vertical capacity of
bucket foundation is slightly less than the solid foundation ðVBucket =VSurf ÞLoose sand ¼ 1 þ 2ðd=DÞ
with equivalent embedment.
Barari et al. (2017) applied the limited settlement criterion
Therefore, the bearing capacity of bucket foundation takes
to determine bearing capcity of foundation. Based on this
into account the ultimate capacity of an embedded foundation
criterion, the load corresponding to settlement equal to
and the friction resistance of the skirts in soil. Unless the sig-
10%of foundation diameter would be considered as the
nificant contribution from base capacity, the friction resistance
ultimate bearing capacity. Although most of the shallow foun-
was shown to significantly decrease in small-scale models.
dations reached the ultimate bearing capacity at the ratio of
Therefore, this term can be ignored for current study and
settlement to width of less than 10%, this criterion would lead
the normalized bearing capacity of a bucket foundation can
to different capacities of foundation in loose to medium sand.
be expressed by:
! In the present research, it is assumed that shallow foundations
VBucket 2Nq� d in loose to medium sand reach the ultimate bearing capacity at
¼1þ : ð3Þ settlement/width up to 30% (Vesic´ (1975)). The fitting para-
VSurface Nc� D
meter in Eq. (5) for medium to dense sand have reasonable
Equation (3) shows that the capacity of bucket foundation agreement with therotical relationship which was proposed
is function of the embedment ratio (d/D) and the bearing by Eq. (3). However, the “n” value for loose sand in Eq. (5)
capacity of a surface footing. In addition, it is obvious that might be incorrect to estimate the bearing capacity of bucket
the capacity increases with embedment ratio (d/D). Based on foundation in loose sand.
Eq. (3), an analytical value for fitting parameter “n” Table 1 provides a variety of fitting parameters “n” for sand
2Nq� with different relative densities. There are significant differ-
(n ¼ Nc� ) can be proposed as a function of soil friction angle.
ences between the values of fitting parameter “n,” which
Therefore, the “n” value was derived for a variety of soil fric- depends on various parameters such as friction angle of soil
tion angles (φ) based on analytical relations (Figure 2). It is and the criteria to determine the bearing capacity of foun-
clear that the fitting parameter is a function of friction angle dation. However, there is no exact value of parameter “n”
and it decreases with increasing the friction angle. for similar friction angles. The discrepancy between different
Because of the bearing capacity factors proposed by Bolton approaches may also be attributed to the fact that the influence
and Lau (1993) are incorrect for foundations with a rough of the skirt friction on the uniaxial bearing capacity of skirted
base, Ibsen, Barari, and Larsen (2012) proposed Eq. (4) based footings is not noticeable for small-scale tests in the laboratory
on a recommended expression of Nγ. The fitting parameter “n” and may not be too sensitive to the slight changes in the
was calculated with a friction angle of 48°, which was derived interface roughness.
by backanalysis of the experiments from Byrne and Houlsby Table 1 presents the values of fitting parameter based on
(1999). Theoretical and experimental methods from the literature. It
VBucket d can be found that the fitting parameter “n” increases with
¼ 1 þ 2:1 ð4Þ reduction of soil relative density. The higher values of n show
VSurf D
that the bucket foundation has a better performance to
Barari et al. (2017) proposed, based on FE analyses, a suite enhance the capacity of foundation in loose sand in compari-
of empirical depth factors for dense, medium dense, and loose son to dense sand. It is important to note that Eq. (3) has been
sands. It was reported that the bearing capacity increases derived for an embedded solid foundation (Eid et al. 2013;
4 A. HADDAD ET AL.

Table 1. Fitting parameter (n) for vertical bearing capacity of the embedded
foundation in sand.
Relative density
Reference Modeling of sand (%) N
Meyerhof (1963) Therotical 80 1.37
55 1.79
35 2.10
Hansen (1970) Therotical 80 4.42
55 5.15
35 5.69
Martin (2005) Therotical 85 3.02
55 4.31
35 4.91
Byrne and Houlsby (1999) Physical >80 0.89
Villalobos (2006) Physical 83 2.14
47 3.00
40 4.00
Eid et al. (2009) Physical 71 1.15
57 1.70
44 2.55
Ibsen, Barari, and Physical >80 2.10
Larsen (2012)
Barari et al. (2017) Numeical-Physical 80 2.50
55 2.20
40 2.00
Figure 3. Experimental setup used for loading tests.

Barari et al. 2017). Due to the internal mechanism of soil in length, 0.9 m wide, and 0.9 m high was prepared (Figure 3).
inside, the capacity of bucket foundation differs from an The container was made of steel and a plexiglass sheet was
embedded solid foundation and it must be corrected for a installed on one side of it for visual observation of soil
bucket foundation. deformation during loading.
The bucket foundations were modeled by open-ended steel
1.4. Scale effect cylinder with diameter (D) of 10 and 20 cm, which had a
5-mm-thick top plate and 2-mm-thick skirt. In view of the
Due to the difficulties associated with loading full-scale foun- results, it is clear that the model foundations can be considered
dation, small-scale models have been utilized to study the as practically infinitely rigid. Due to the stiffness of the foun-
behavior of foundation under vertical and general loading. dations, deflection of the plates is too little to affect the bearing
Although, most of the bearing capacity factors of foundation capacity of bucket foundations. The range of skirt depth to
have been derived from small-scale models, it was shown that foundation diameter ratio (d/D) was selected between 0 and
the results of small-scale foundation were higher than theoreti- 1.0 to represent a range encountered in the field. The founda-
cal equations. Therefore, it could not be utilized to design tions had a roughness between steel and sand. A hydraulic jack
prototype foundation without any reduction. This observation was utilized to apply vertical loads. The load was measured by
has been referred as scale effect. Sources of scale effect include a load cell, which was fixed between the hydraulic jack and the
two important factors. The first factor is the dependence of the foundation. In addition, to measure displacement of the
mechanical properties of sand on stress level (Zhu, Clark, and foundation, two LVDTs with an accuracy of 0.01 mm were
Phillips 2001; Cerato and Lutenegger 2007) and the second installed on the top of the foundation. A schematic view of
factor is mostly relevant to the particle size effect (Tatsuoka the experimental setup is demonstrated in Figure 4. Depth
et al. 1997). and length of the inside box were 80 and 120 cm, respectively,
Scale effect can be significant in testing foundation models which are sufficient for foundation loading with 20 cm
and the small-scale model may not develop sand confinement diameter.
similar to that generated by full-scale foundation. In this study,
settlement and bearing capacity of bucket foundations were
investigated by small-scale foundations and the corresponding 2.1. Soil properties
values were compared with theoretical solutions, not with the The chosen sand for the experiments was from Babolsar city,
measured values for full-scale foundations. In addition, this northern Iran. Babolsar sand covers a vast area in the southern
study is focused on the effects of the skirt on the behavior of coast of Caspian Sea. Properties of Babolsar sand have been
bucket foundation in loose saturated sand. Therefore, such well documented in previous studies (Noorzad and Amini
effects were presented using bearing capacity ratio and depth 2014; Jafarian, Haddad, and Mehrzad 2016). It is classified as
factor. poorly graded sand (SP) based on Unified Soil Classification
System (USCS). Figure 5 shows the grading curve of Babolsar
sand.
2. Experimental setup
The sand specific gravity and minimum and maximum
To investigate the depth factor of bucket foundation in void ratios were measured to be 2.73, 0.54, and 0.73, respect-
loose saturated sand, some experiments were conducted ively. The water pluviation method (Lagioia, Sanzeni, and
on foundation models. Therefore, a soil container of 1.2 m Colleselli 2006; Wood, Yamamuro, and Lade 2008) was used
 MARINE GEORESOURCES & GEOTECHNOLOGY 5

Figure 4. Schematic view of experimental setup (dimensions in cm).

to prepare model sand deposit inside the container. The chosen four times greater than the bucket diameter. Results
desired relative density of sand was planned to be prepared indicated that the height does not affect ultimate bearing of
at a relative density of about 35% through water pluviation the bucket. After soil deposition, surface circular foundation
method. To control the relative density of soil model, volume was installed by placing the foundation on the soil surface.
and weight of each layer were measured. The container was Previous researchers have utilized an external load to install
filled with water and then the dry sand was poured inside bucket foundations in laboratory to study the behavior of
the container using a sand rainer to achieve loose density. This foundations under vertical and general loading (Villalobos
procedure of deposition is similar to soil sedimentation in nat- 2006; Eid et al. 2009; Ibsen, Larsen, and Barari 2014). Eid
ure and creates a uniform sand model. et al. (2009) investigated the effect of pushing the bucket on
the changing relative density. The comparison was made
between the capacity of bucket foundations, which were
2.2. Test procedure pushed into a preprepared soil and the capacity of some tests
where the bucket foundations were first placed and then the
The model tests included bucket foundations with different sand was poured between and around them. The findings
diameters and skirt lengths. All tests were performed in showed that the differences of capacities of small-scale bucket
saturated sand with low relative density (35∼40%). Table 2 foundation were less than 4%.
summarizes details of the tests. To omit any effects of the The bucket foundation was placed at the center of the box
rigid-bottom box, the height of deposed soil in the box was and pressure was exerted on the top of the plate with a
hydraulic jack. An air screw was mounted on the top of each
bucket foundation; therefore, the water and existing air inside
the bucket were pushed out. The bucket was carefully installed
to minimize disturbance of the soil around the foundation
before loading (Figure 6). During foundation installation

Table 2. Characteristics of the experiments.

Case Diameter, D (cm) Skirt length, d (cm) d/D Relative density, %
1 10 0 0 35∼40
2 10 5 0.5 35∼40
3 10 10 1 35∼40
4 20 0 0 35∼40
5 20 10 0.5 35∼40
Figure 5. Grain size distribution of Babolsar sand. 6 20 20 1 35∼40
6 A. HADDAD ET AL.

Figure 6. Installation of the bucket foundation.

procedure, no heave and no sand boiling around foundation

were observed. This may be attributed to low ratio of skirt
depth to diameter of models and the relatively small thickness
Figure 7. Load–settlement curves of bucket foundation: (a) D ¼ 10 cm and
of skirt. (b) D ¼ 20 cm.
After installing the bucket, LVDTs and load cell were
placed on the top of the bucket, and it was subjected to vertical
loading by a hydraulic jack. A data logger recorded displace- was defined as a point where the slope of load–settlement
ment and load values. In each test, the model foundation curve becomes constant. Figure 8 shows the result of an
was incrementally loaded to the maximum load. To control experimental test as an example of load–settlement curve to
the loading speed, the foundations were loaded under a determine the bearing capacity based on the proposed method
constant velocity of penetration 0.05 mm/s. by Vesic (1973). Bearing capacity and corresponding settle-
ment at failure load (S) of the experimental tests are presented
in Table 3. Moreover, in Table 3, the capacity of foundation at
2.3. Experimental results a settlement equal to 10% of the footing diameter was pre-
To study the effect of embedment ratio and skirt length on the sented. Obviously, the capacity at a certain settlement (0.1D)
ultimate capacity of bucket foundation under vertical load in is less than the capacity of foundation and was found by Vesic
loose saturated sand, a series of 1 g tests were conducted on criterion.
bucket foundations. The typical load–settlement curves for Previous studies have reported that the bearing capacity of
surface footings and bucket foundations, with foundation bucket foundation under vertical loading is slightly less than
diameter of 10 and 20 cm, are shown in Figure 7. The results solid foundation with equivalent embedment depth (Eid
demonstrated that inclusion of skirts enhances bearing et al. 2013; Barari et al. 2017). Therefore, a comparison was
capacity of the bucket foundation in loose sand. An increase
in embedment ratio (d/D) increases bearing capacity, and
due to soil confinement, the skirts decrease the settlement of
bucket foundation. All tests of this study failed in punching
shear mode, which was defined by Vesic (1973), and no bulg-
ing of soil was observed around the foundations. The trend of
these curves indicates the behavior of a foundation on loose
sand. Consequently, there is no peak load in load–settlement
curve of foundation to determine the ultimate bearing capacity
and the foundation failed without any peak–base resistance in
load–settlement curve.
Vesic (1973) described the minimum slope failure load cri-
teria to determine the bearing capacity of shallow foundation
in loose sand. According to this criterion, ultimate bearing
capacity is defined as a point of load–settlement curve where
its slope reaches zero or becomes steady. In all the tests of this Figure 8. An example for the determination of bearing capacity of surface
study, a peak load was never observed, and bearing capacity footing (case 4).
 MARINE GEORESOURCES & GEOTECHNOLOGY 7

Table 3. Bearing capacity and failure settlement of bucket foundations.

Limited settlement
criterion of 0.1D The minimum slope failure load criteria
Bearing Bearing Settlement at
Case capacity (N) capacity (N) failure (mm) S/B
1 155 95 4 0.04
2 258 360 21 0.21
3 361 535 25 0.25
4 990 820 12 0.06
5 1450 2794 52 0.26
6 2397 4103 52 0.26

made between the failure load values from the performed tests
in this study and the estimated values by some popular meth-
ods such as done by Meyerhof 1963; Hansen 1970; Martin Figure 9. Variations of ratio of settlement to foundation width (s/D) versus
embedment ratio (d/D).
2005. The Meyerhof’s (1963) and Hansen’s (1970) methods
are based on limit equilibrium theory with some differences
in the assumption of slip surfaces and loading conditions.
2.4. Development of depth factor in loose material
Martin (2005) used method of characteristics to calculate
the bearing capacity of strip and circular foundations. It The results of the experimental tests and the existing solution
should be noted that the mentioned methods are proposed of bearing capacity for foundation in loose sand are normal-
for embedded foundations and may be modified for bucket ized to the capacity of surface foundations. The normalized
foundation. bearing capacities as a function of the embedment ratio
However, the results in Table 4 show that due to the (d/D) are shown in Figure 10. These curves show a
assumptions of each method, there is a large discrepancy reasonably good agreement between this experiment and the
between the methods of capacity calculation. Significantly, literature. Expectedly, the relation between bearing
the capacity of foundation based on Vesic criterion which is capacity and d/D ratio is linear and depends on the value of
close to the value was calculated by classical methods. More- d/D ratio.
over, the ultimate capacity of foundation in experimental tests As mentioned in the previous section, there is a reasonable
was found by Vesic criterion which shows a good agreement relation between the bearing capacity and embedment ratio
with the capacity was reported by Martin (2005). (d/D) that is called depth factor. The vertical bearing capacity
Villalobos (2006) has mentioned that the soil inside the ratio (VBucket/VSurface) of foundations versus embedment ratio
bucket foundation could be either rigid or flexible. In fact, (d/D) is presented in Figure 11. Based on the experimental
assuming flexible soil inside the bucket is closer to real con- results for loose saturated sand, a linear relationship can be
ditions. In spite of assuming flexible soil, it has been shown represented by Eq. (6):
that assuming rigid soil for bucket foundation under pure
vertical loading does not have any dramatic effect on the VBucket d
¼ 1 þ 4:49: ð6Þ
results (Villalobos 2006; Eid et al. 2013; Barari et al. 2016). VSurface D
Surface footing failed under vertical load at the settlement
ratio of s/D ¼ 4∼6%, where S is settlement of the foundation. A comparison was made between the proposed Eq. (6) and
In contrast to surface footing, bucket foundation failed at a the experimental results of previous studies for depth factor
larger settlement (almost 21∼26% of D). This can be explained was proposed by Byrne and Houlsby (1999), Eid et al.
by the internal failure mechanism of bucket foundation. (2009), and Villalobos (2006) for various friction angles. The
Due to increasing the confining pressure of the soil that comparison is presented in Figure 11. Figure 11 proves that
surrounded the bucket foundation and failure line length, the depth factor is greater than 1 and increases with the
the corresponding settlement of bucket foundation at failure decreasing value of friction angle (φ). The proposed
was larger than surface footing. Figure 9 displays ratio of values of “n” by Eid et al. (2009) is almost half of those
settlement to foundation diameter versus embedment ratio values proposed by Villalobos (2006). The value of “n” in this
(d/D). study for loose sand is slightly more than that proposed by
Barari et al. (2016) and less than that of Villalobos (2006)
and that calculated by Martin (2005) for embedded
Table 4. Comparison between measured and calculated bearing capacities. foundation.
Calculated capacity (N) Based on the experimental results, the values of fitting para-
Measured
Foundation capacity Meyerhof Hansen Martin meter “n” in depth factor for dense to medium-dense sand
diameter (cm) d/D (N) (1963) (1970) (2005) vary from 0.89 to 3. It is seen that the fitting parameter “n”
10 0 95 119 51 94 for loose sand in Figure 11 is significantly higher than that
0.5 360 244 196 341 value for depth factor in medium to dense sand. In other
1 535 369 341 554
20 0 820 954 407 748 words, the effect of skirt on bearing capacity of the
0.5 2794 2167 1759 2725 foundations in loose sand is significantly more than that for
1 4103 3562 3431 4433 foundations in dense sand.
8 A. HADDAD ET AL.

Figure 10. NorMalized bearing capacity versus embedment ratio: (a) D ¼ 10 cm and (b) D ¼ 20 cm.

Figure 11. Vertical capacity factor based on embedment ratio.

3. Conclusion References
The main purpose of this work is to investigate the vertical Al-Aghbari, M. Y., and R. K. Dutta. 2008. Performance of square footing
bearing capacity of bucket foundation loose saturated sand. with structural skirt resting on sand. Geomechanics and Geoengineering
Accordingly, a series of experimental investigations were 540 3 (4):271–77. doi:10.1080/17486020802509393.
American Petroleum Institute (API). 2000. Recommended practice for
conducted on small-scale foundation in loose sand. An
planning, designing and constructing fixed offshore platforms.
experimental setup was used to determine vertical capacity of Washington, DC: API RP 2A.
bucket foundation with different diameters and skirt depths. Barari, A and L. B. Ibsen. 2014. Vertical capacity of bucket foundations in
Results of this study showed that the skirts around foundation undrained soil. Journal of Civil Engineering and Management 20 (3):
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