847
Experimental investigation of shell foundations
on dry sand
Adel Hanna and Mohamed Abdel-Rahman
Abstract: Shells are usually used as structural elements in buildings. In Germany they showed remarkable resistance to
the effects of bombing during World War II. About 1 decade later, the possibility of employing shells in foundation
engineering was explored. Surveys of the literature indicate that shell foundations have been employed effectively in
different parts of the world and were proven to provide an overall economical alternative to the conventional flat
foundations. However, the geotechnical design of these footings remained the same as for their respective flat ones.
Accordingly, the advantages of shell geometry in foundation engineering has not yet been explored in the design of
these footings. The objective of the present study is to examine the overall geotechnical behavior of three types of
shell foundations resting on sand under axial loading conditions, namely, triangular, conical, and pyramidal shells.
Furthermore, the resulting bearing capacities and settlements will be compared with conventional strip, circular, and
square flat foundations. The present paper presents an experimental study on nine foundation models tested on loose,
medium, and dense sand states. The influence of shell configuration and embedment depth on the ultimate bearing
capacity and settlement will be presented. The results of the present experimental investigation have shown the
admirable performance of shell foundations with respect to ultimate bearing capacity and settlement characteristics.
Shell foundations provide higher resistance to lateral loading as compared with flat ones, and thus they will perform
better in earthquake regions.
Key words: shell foundation, experimental investigation, bearing capacity, settlement, sand, geotechnical engineering.
Résumé : Des voiles sont couramment utilisés comme éléments structuraux dans des bâtiments. En Allemagne, ils ont
montré une remarquable résistance aux effets des bombardements au cours de la deuxième guerre mondiale. Environ
une décennie plus tard, l’on a exploité la possibilité d’utiliser des voiles dans les fondations. Des relevés de la
littérature indiquent que les voiles de fondations ont été utilisés efficacement dans différentes parties du monde
puisqu’il a été prouvé qu’ils fournissaient une alternative d’ensemble économique par rapport aux fondations planes
conventionnelles. Cependant, la conception géotechnique de ces semelles demeure la même que pour les fondations
planes respectives. En conséquence, les avantages de la géométrie des voiles utilisés dans les fondations n’ont pas
encore été explorés pour la conception de ces semelles. L’objectif de la présente étude est d’examiner le comportement
géotechnique global de trois types de voiles de fondations reposant sur le sable dans une condition de chargement
axial; nommément: triangulaire, conique, et pyramidal. De plus, les capacités portantes et les tassements résultants
seront comparés avec les fondations planes conventionnelles filantes, circulaires et carrées. Le présent article présente
une étude expérimentale de neuf modèles de fondations testés sur un sable dans des états dense, moyennement dense et
lâche. L’influence de la configuration du voile et de la profondeur d’enfouissement sur la capacité portante ultime et
sur le tassement sera présentée. Les résultats de la présente étude expérimentale ont démontré la performance
admirable des voiles de fondations en termes de capacité portante ultime et de caractéristiques de tassement. Les voiles
de fondations fournissent une résistance plus élevée au chargement latéral comparativement aux fondations planes, et
en conséquence, auront une meilleure performance dans les régions de tremblements de terre.
Mots clés : voile de fondation, étude expérimentale, capacité portante, tassement, sable, génie géotechnique.
[Traduit par la rédaction] Hanna and Abdel-Rahman 857
an experimental investigation on conical and hypar shell
footings to determine the contact pressure distribution as a
According to the literature, the research conducted on the function of the ultimate load. The conical and hypar shell
geotechnical behavior of shells as foundation elements has models were compared with circular and square flat models,
been considerably lagging behind that conducted on their respectively. The results indicated that the contact pressure
structural performance. Nicholls and Izadi (1968) performed near the perimeter of the shell was about 1.5 times the con-
tact pressure measured at the center. Furthermore, the ulti-
Received November 21, 1997. Accepted July 3, 1998. mate bearing capacity and the settlement of the shell were
significantly improved as compared with their conventional
A. Hanna. Department of Building, Civil, and Environmental
flat counterparts. Kurian and Varghese (1969), in a discus-
Engineering, Concordia University, 1455 Masonneuve
Boulevard West, Montréal, QC H3G 1M8, Canada. sion on this study, confirmed that the use of shell elements
M. Abdel-Rahman. Civil Engineering Section, BTC, Cairo, in rafts in place of the conventional flat elements was
Egypt. proven to be more economical.
Can. Geotech. J. 35: 847–857 (1998) © 1998 NRC Canada
848 Can. Geotech. J. Vol. 35, 1998
Fig. 1. Sketch of the foundation models. Iyer and Rao (1970) reported a detailed experimental
study conducted on the feasibility of using a funicular shell
footing resting on sand as a replacement for a flat raft foun-
dation. The results showed that the bearing capacity of the
shell footing was considerably greater than that of the flat
footing of the same plan dimensions. Furthermore, under the
same applied load, the shell footing experienced lower set-
tlement than the flat one. These significant differences were
attributed to the effect of geometry and the stiffness of shell
elements.
Kurian and Mohan (1981) conducted an experimental
study in order to measure the contact pressure distribution
under different hyperbolic paraboloidal models at the elastic
and ultimate loading stages. The results indicated substantial
deviation from the linear distribution assumed in the current
design method.
Agarwal and Gupta (1983) conducted an experimental in-
vestigation on the soil–structure interaction of conical and
hypar shell models. The ultimate bearing capacity of the
shell models was reported to vary from 11 to 22% higher
than that of the flat ones. The increase in the ultimate bear-
ing capacity was attributed to the increase in the angle of
friction between the core soil under the shell models and the
soil below.
Hanna and Abdel-Rahman (1990) performed an experi-
mental investigation to study the ultimate bearing capacity
of triangular shell strip footings on sand. The results indi-
cated that triangular shell footings provide a higher bearing
capacity and produce less settlement under the same loading
conditions as compared with the strip flat ones.
Three types of shell foundations were used in the present
investigation, namely, triangular strip, conical, and pyrami-
dal shells, which simulate the plane strain, axisymmetrical,
and three-dimensional conditions, respectively. A detailed
description of this investigation is presented by Abdel-
Rahman (1996). To examine the effect of shell rises on the
their performance, the rise-to-half-width ratio (a/b) was
Fig. 2. Overall view of foundation models.
© 1998 NRC Canada
Hanna and Abdel-Rahman 849
Fig. 3. Sketch of experimental setup.
taken as 1/2 and 1, as this represents a practical range for glued to the base of each model to simulate a rough surface
construction purposes. Strip, circular, and square flat mod- condition. An overall view of the nine foundation models is
els, with the same plan dimensions, were tested, and the re- shown in Fig. 2. An experimental setup was organized to
sults were compared with the triangular strip, conical, and perform the testing program. Load–settlement data was re-
pyramidal shell models, respectively. The dimensions of all corded up to failure by means of a load cell and a linear
models in plan were kept the same for comparison purposes varying displacement transducer (LVDT).
(square area of 160 mm × 160 mm for the plane-strain and
three-dimensional models, and for the axisymmetrical model
the diameter was 160 mm). Figure 1 shows the geometrical
configuration of these models. The models were fabricated An overall sketch of the experimental setup is illustrated
from high-quality stainless Atlas Alloys (Type 6061-T651) in Fig. 3. Two testing tanks were used in this investigation.
using the Computer Numerical Control “CNC” Vertical A Plexiglas tank was used for testing the plane strain models
Milling Machine (Mazak VQC-15/40). To avoid using any and also for conducting special loading tests using colored
bolts or welds in the structure of these models, each model layered sand. A steel tank was used for testing the
was fabricated from a single piece of alloy. Sand paper was axisymmetrical and three-dimensional setup models. The
© 1998 NRC Canada
850 Can. Geotech. J. Vol. 35, 1998
Table 1. Experimental testing program.
Foundation Surface footings Embedded footings
model Test No. (D/B = 0) Test No. (D/B = 0.75)
Plane strain
Strip flat model 1, 2, 3 Loose, medium, 4, 5, 6 Loose, medium,
and dense sand and dense sand
Triangular (1) 7, 8, 9 Loose, medium, 10, 11, 12 Loose, medium,
shell model and dense sand and dense sand
Triangular (2) 13, 14, 15 Loose, medium, 16, 17, 18 Loose, medium,
shell model and dense sand and dense sand
Axisymmetrical
Circular flat 19, 20, 21 Loose, medium, 22, 23, 24 Loose, medium,
model and dense sand and dense sand
Conical (1) shell 25, 26, 27 Loose, medium, 28, 29, 30 Loose, medium,
model and dense sand and dense sand
Conical (2) shell 31, 32, 33 Loose, medium, 34, 35, 36 Loose, medium,
model and dense sand and dense sand
Three-dimensional
Square flat 37, 38, 39 Loose, medium, 40, 41, 42 Loose, medium,
model and dense sand and dense sand
Pyramidal (1) 43, 44, 45 Loose, medium, 46, 47, 48 Loose, medium,
shell model and dense sand and dense sand
Pyramidal (2) 49, 50, 51 Loose, medium, 52, 53, 54 Loose, medium,
shell model and dense sand and dense sand
Table 2. Physical and mechanical characteristics of sand in the spectively. The tank walls were braced with four steel angles
Plexiglas tank. (L 50 × 50 × 5 mm), located at mid-height, to prevent buck-
ling of the walls during testing.
Sand Unit weight, Angle of shearing Relative density,
The loading system was composed of a gear box device,
state γ (kN/m3) resistance, φ (°) Dr (%)
which generated a downward displacement at a constant rate
Loose 16.4 33 20 of 2 mm/min. This displacement was transformed into a
Medium 17.6 37 54 force through a steel arm positioned at the centre of the
Dense 18.4 40 77 foundation model. A load cell of 5000 lbs capacity
(22.24 kN) was connected to the gear box to measure the ap-
plied load. An LVDT was mounted on the gear box device
to record the movement of the footing during testing.
Table 3. Physical and mechanical characteristics of sand in the To document the data collected from each loading test, the
steel tank. electrical measuring devices (load cell and LVDT) were con-
Sand Unit weight, Angle of shearing Relative density, nected to an HP Data Acquisition System, which registered
state γ (kN/m3) resistance, φ (°) Dr (%) voltage changes. A computer program was developed to
Loose 16.5 34 22 convert these voltage readings into loads and displacements
Medium 17.7 38 57 utilizing a calibration factor for each individual device.
Dense 18.5 41 79 Throughout the testing program, a routine calibration of all
electrical measuring devices was performed.
first tank was made of two Plexiglas walls of 1 in. thickness A total of 54 loading tests were performed on the above-
(25.40 mm). The base and the sides were made of wooden mentioned foundation models and sand states. Surface foot-
sheets of 2 in. thickness (50.80 mm). The tank had internal ings (D/B = 0, where D is the depth of embedment and B is
dimensions of 800 × 165 × 640 mm for length, width, and the footing width) and embedded footings at an embedment
depth, respectively. The Plexiglas walls were thick enough ratio of D/B = 0.75 were tested. Table 1 summarizes the test-
to prevent or to minimize buckling of walls during testing. ing program. Several loading tests using different sand states
To assure a plane strain condition, the tank width was cho- were performed before the reported testing program had be-
sen to be almost equal to the width of the strip models (a gun, to check the repeatability of the results. During this
difference of 5 mm). The second tank was made of steel stage, it was proven that the selected testing procedure pro-
plates of 6.50 mm thick. The tank had internal dimensions duced homogenous results and that the repeatability of the
of 1000 × 1000 × 1250 mm for length, width, and depth, re- results was quite satisfactory.
© 1998 NRC Canada
Hanna and Abdel-Rahman 851
Table 4. Ultimate load (Qu) and settlement (δu) for plane strain Fig. 4. Typical load–settlement curves (surface plane strain
conditions. models on medium sand).
Surface footings Embedded footings
(D/B = 0) (D/B = 0.75)
φ (°) Qu (N) δu (mm) Qu (N) δu (mm)
Strip flat footing
33 2 081 12.4 4 813 17.8
37 4 613 19.7 9 278 24.6
40 8 572 21.8 15 875 31.4
Triangular (1) shell footing
33 2 477 13.1 5 321 16.5
37 5 241 17.1 10 036 22.3
40 9 567 19.3 16 880 29.9
Triangular (2) shell footing
33 2 811 14.1 5 699 16.2
37 5 816 18.1 10 666 22.2
40 10 336 20.0 17 837 29.5
Table 5. Ultimate load (Qu) and settlement (δu) for
axisymmetrical conditions.
Surface footings Embedded footings
(D/B = 0) (D/B = 0.75)
φ (°) Qu (N) δu (mm) Qu (N) δu (mm)
Circular flat model
34 1794 11.6 4 673 17.2
38 3727 17.1 8 638 25.3
41 6780 21.1 14 557 32.6
Conical (1) shell model
34 2153 11.1 5 215 17.7
38 4287 16.6 9 444 26.2
41 7730 20.5 15 665 33.1
Conical (2) shell model
34 2457 12.1 5 619 17.4 A mixture of well graded sand was obtained from five dif-
38 4816 16.7 10 122 25.4 ferent gradations of 99.9% high silica sand imported from
41 8414 20.8 16 731 33.5 the United States of America. The sand mixture consisted of
a percentage passing by weight from mesh Nos.
10:16:24:40:140 = 2:1:3:2:2. Based on the Unified Soil
Table 6. Ultimate load (Qu) and settlement (δu) for three- Classification System, the tested sand was classified as well
dimensional conditions. graded, with a uniformity coefficient of Cu = 9.50, a coeffi-
cient of curvature Cc = 2.13, and an average specific gravity
Surface footings Embedded footings (Gs) of 2.68.
(D/B = 0) (D/B = 0.75) The sand states used in the present investigation are loose,
φ (°) Qu (N) δu (mm) Qu (N) δu (mm) medium, and dense. A sand placing technique was devel-
Square flat model oped and calibrated before testing to ensure the
34 2 370 12.1 6 103 17.4 reproducibility of a predetermined unit weight in the testing
38 4 959 16.6 11 273 26.7 tanks. This technique was achieved by placing the sand in
41 9 035 22.5 19 018 32.1 layers and applying mechanical compaction by means of an
Pyramidal (1) shell model air pressure hammer using constant air pressure. By chang-
34 2 854 11.3 6 790 17.2 ing the duration of compaction, as an external controlled
38 5 686 16.0 12 304 25.9 factor in the compaction process, different unit weights of
41 10 179 23.0 20 391 30.4 the sand were produced.
Pyramidal (2) shell model In the Plexiglas tank, three layers of 160 mm thickness
34 3 272 11.0 7 318 16.8 each were poured and then subjected to an air pressure of
38 6 351 16.7 13 173 26.2 40 psi (276 kPa), and in the steel tank, four layers of
41 11 111 23.9 21 708 32.1 160 mm thickness each were poured and then subjected to
air pressure of 37 psi (255 kPa). Direct shear box tests were
performed on sand samples of unit weights of 16.0, 17.0,
© 1998 NRC Canada
852 Can. Geotech. J. Vol. 35, 1998
Fig. 5. Ultimate loads (Qu) for plane strain condition. Fig. 6. Ultimate loads (Qu) for axisymmetrical condition.
Table 7. Shell gain factor, η (%).
(A) Plain strain
Angle of shearing resistance (φ°)
Surface footings (D/B = 0) Embedded footings (D/B = 0.75)
33 37 40 33 37 40
Triangular (1) 19.0 13.6 11.6 10.6 8.2 6.3
Triangular (2) 35.1 26.1 20.6 18.46 15.0 12.4
(B) Axisymmetrical and three dimensional
Angle of shearing resistance (φ°)
Surface footings (D/B = 0) Embedded footings (D/B = 0.75)
34 38 41 34 38 41
Conical (1) 20.0 15.0 14.0 11.6 9.3 7.6
Conical (2) 37.0 29.2 24.1 20.2 17.2 14.9
Pyramidal (1) 20.4 14.7 12.7 11.3 9.2 7.2
Pyramidal (2) 38.1 28.1 23.0 20.0 16.9 14.1
18.0, and 19.0 kN/m3. Tables 2 and 3 summarize the physi- voir, located above the testing tank. The sand was poured
cal and mechanical characteristics of the sand used in this into the tank through a funnel assembly, which was moved
investigation. by hand in a consistent manner over the testing tank to
achieve uniform sand distribution. When the sand surface
reached the top of the first layer (160 mm), the compaction
The sand mixture was prepared to the prescribed grada- was then applied using the air-pressure hammer. The air
tion and pumped up by a vacuum machine to the sand reser- pressure was set at constant and the compaction duration
© 1998 NRC Canada
Hanna and Abdel-Rahman 853
Table 8. Settlement factor (Fδ) at ultimate load (x 10-3).
(A) Plain strain
Angle of shearing resistance (φ°)
Surface footings (D/B = 0) Embedded footings (D/B = 0.75)
33 37 40 33 37 40
Strip 2.5 1.9 1.2 1.6 1.2 0.9
Triangular (1) 2.2 1.5 1.0 1.3 1.0 0.8
Triangular (2) 2.1 1.4 0.9 1.2 0.9 0.8
(B) Axisymmetrical and three dimensional
Angle of shearing resistance (φ°)
Surface footings (D/B = 0) Embedded footings (D/B = 0.75)
34 38 41 34 38 41
Circular 2.1 1.6 1.2 1.2 1.1 0.8
Conical (1) 1.7 1.4 1.0 1.1 1.0 0.8
Conical (2) 1.6 1.2 0.9 1.0 0.9 0.8
Pyramidal (1) 1.7 1.3 1.1 1.1 1.0 0.7
Pyramidal (2) 1.4 1.2 1.0 1.0 0.9 0.7
Fig. 7. Ultimate loads (Qu) for three-dimensional setup Fig. 8. Settlement factor (Fd) for plane strain condition.
condition.
was applied according to the required sand state. Spreading surface for the axisymmetrical and three-dimensional setup
and compaction processes were repeated for other sand lay- models, the shell model was filled up with a precalculated
ers until the foundation level was reached. volume of sand according to the required unit weight.
For surface loading tests, i.e., at D/B = 0, the flat model The sand filling process of a shell model was done by
was placed at the center of the testing tank, then the load ap- placing a thin steel plate on the bottom of the shell model
plication was started. To prepare the soil core under the shell and transferred to its location at the center of the tank. The
© 1998 NRC Canada
854 Can. Geotech. J. Vol. 35, 1998
Fig. 9. Settlement factor (Fd) for axisymmetrical condition. Fig. 10. Settlement factor (Fd) for three-dimensional setup
condition.
steel plate was then removed from underneath the shell, and
good care was taken to insure full contact between the sand
and the shell surface. In addition, the top part of the shell
model was removed and additional sand was poured to com-
pensate for what might have been lost during the removal The load–settlement data were recorded and plotted for
process of the steel plate. each loading test. Figure 4 shows typical load–settlement
curves for a surface strip shell footing on medium sand. The
For the triangular shell strip models, the sand was poured ultimate load (Qu) is defined as the point of maximum load
through three holes located at the top portion of the model, obtained from the load–settlement (Q–δ) curve, at which the
and by looking through the sides of the Plexiglas tank, full load starts to decrease while the settlement continues to in-
contact between the sand and shell surface was achieved. crease. The values of the ultimate load (Qu) and the corre-
For embedded footing tests, i.e., at D/B = 0.75, the sand sponding settlement (δ u ) obtained from the present
spreading continued until the upper surface of sand was experimental investigation are presented in Tables 4, 5, and
reached, and then the compaction was applied carefully at 6 for the plane strain, axisymmetrical, and the three-
the top surface outside the area of the foundation model. dimensional setup conditions, respectively.
After the testing tank was prepared, the Data Acquisition The load–settlement data are summarized and presented in
System was initialized and checks on all the electrical mea- Figs. 5, 6, and 7 as curves of the ultimate load (Qu) versus
suring devices were performed to insure all connections. Af- the angle of shearing resistance (φ) for the plane strain,
ter the checking stage was completed, the load application axisymmetrical, and three-dimensional setup conditions, re-
stage was started. Vertical load and settlement were automat- spectively. It can be observed from these curves that the ulti-
ically recorded during testing. The loading tests were contin- mate load (Qu) increases with the increase of the angle of
ued beyond the failure point, i.e., when the settlement was shearing resistance (φ). Also, it can be seen that shell foot-
increasing rapidly while the loads were either decreasing or ings have higher ultimate loads than conventional flat ones.
remaining almost constant. It should be mentioned here that The ultimate load (Qu) increases as the depth of embedment
primarily tests were conducted to check the repeatability of increases for flat as well as shell footings. The relationship
the sand state and the measured values. between the ultimate load (Qu) and the angle of shearing re-
© 1998 NRC Canada
Hanna and Abdel-Rahman 855
Fig. 11. Strip flat model at ultimate stage.
Fig. 12. Triangular (1) shell model at ultimate stage.
sistance (φ) has a similar trend for the three-dimensional where η is the shell gain factor; Qus is the ultimate load of
setup conditions. the shell footing; and Quf is the ultimate load of flat footing.
The increase in the ultimate load of a shell footing as Table 7 presents the calculated shell gain factors (η) de-
compared to its flat counterpart is recognized in the present duced from the present experimental investigation. In gen-
investigation as the shell gain factor (η). It is defined in eral, it can be concluded from Table 7 that shell efficiency
eq. [1] as the ratio between the difference in the ultimate factor (η) decreases with the increase in the angle of shear-
loads of shell and flat footings over the ultimate load of the ing resistance (φ), i.e., the effect of shell configuration di-
flat footing: minishes when the soil becomes denser. Moreover, the shell
gain factor (η) reduces remarkably for the tests conducted on
Qus − Quf
[1] η= the embedded footings as compared to surface footing tests.
Quf This trend holds true for all the shell footings at any sand
© 1998 NRC Canada
856 Can. Geotech. J. Vol. 35, 1998
Fig. 13. Triangular (2) shell model at ultimate stage.
state. Also, it can be noted that the shell gain factors (η) for
the conical and pyramidal footings are higher than that of
the triangular ones. The comparison between the conical and To predict the shape of the rupture surface for flat and
pyramidal footings shows that the factors (η) for the conical shell footings, special loading tests were conducted for the
footings are slightly higher than that of the pyramidal ones plane strain condition. The strip flat and the two triangular
for all tests except the ones conducted on surface shell foot- shell footings were tested in a Plexiglas tank using colored
ings on loose sand. loose sand layers. The results were captured by time limit
To examine the settlement characteristics of shell footings exposure photographs throughout the loading process. Fig-
as compared to their conventional flat counterparts, a ures 11, 12, and 13 show the test at the ultimate stage for the
nondimensional settlement factor (Fδ) was introduced. The strip flat, triangular (1), and triangular (2) shell models, re-
settlement factor (Fδ) was calculated at the ultimate load spectively. The observed rupture surfaces were idealized to
(Qu) to reflect the settlement characteristics of the footings formulate the theoretical model for the bearing capacity of
throughout the loading process. The settlement factor (Fδ) is shell foundations, which is beyond the scope of this paper
presented in eq. [2]. It should be noted that a lower value of (Abdel-Rahman and Hanna 1997). It can be noticed that the
the settlement factor (Fδ) indicates better settlement charac- wedge of the rupture surface for the triangular (1) shell foot-
teristics. ing is deeper than that for the flat footing and shallower than
that for the triangular (2) shell footing, which indicates that
δu γAh the shell footings have a higher bearing capacity than the
[2] Fδ =
Qu flat one and that the bearing capacity is proportional to the
shell angle.
where δ u is the settlement at ultimate load; γ is the soil unit
weight; Ah is the area of the footing in horizontal projection;
and Qu is the ultimate load.
The calculated settlement factors (Fδ) deduced from the
present experimental investigation are given in Table 8. In The geotechnical behavior of shell foundations was inves-
general, for any footing, the settlement factor (Fδ) decreases tigated and compared to their conventional flat counterparts.
for denser sand. The comparison between the surface and An experimental investigation was carried out on nine foun-
embedded footings shows that the settlement factor (Fδ) de- dation models, which represent plane strain, axisymmetrical,
creases remarkably for the embedded footings, especially in and three-dimensional setup loading conditions. Based on
loose sand. The comparison between shell and flat footings the results of the present investigation, the following conclu-
for any given sand state indicates that shell footings possess sions can be drawn:
a lower settlement factor (Fδ), which demonstrates better (1) The ultimate bearing capacity of shell foundations is
settlement characteristics for shell footings. The relation- higher than that of their conventional flat counterparts with
ships between the settlement factor (Fδ) and the angle of the same plan dimensions.
shearing resistance (φ) are presented in Figs. 8, 9, and 10 for (2) For a given shell foundation, the ultimate bearing ca-
the plane strain, axisymmetrical, and three-dimensional pacity increases with an increase in the shell angle (θ). An
setup conditions, respectively. increase of 19° of the shell angle (θ) led to an increase in the
© 1998 NRC Canada
Hanna and Abdel-Rahman 857
ultimate bearing capacity of 8 to 15% depending on the sand
state.
(3) A shell gain factor (η) was introduced to represent the Abdel-Rahman, M.M. 1996. Geotechnical behavior of shell foun-
dations. Ph.D. thesis, Department of Civil Engineering, Con-
increase in the ultimate load of shell foundations as com-
cordia University, Montréal, Que.
pared to their flat counterparts. The shell gain factor (η) de-
Abdel-Rahman, M.M., and Hanna, A.M. 1997. Theoretical model
creases for a higher angle of shearing resistance (φ), i.e., the for bearing capacity of shell foundation. Proceedings of the In-
effect of shell configuration reduces with an increase in soil ternational Conference on Soil Mechanics and Foundation Engi-
strength. The shell gain factor (η) decreases for the embed- neering, Hamburg, Germany.
ded shell footings as compared with surface ones. Agarwal, K.B., and Gupta, R.N. 1983. Soil structure interaction in
(4) A nondimensional settlement factor (Fδ) was intro- shell foundations. Proceedings of the International Workshop on
duced to examine the settlement characteristics of shell Soil Structure Interaction, University of Roorkee, India, Vol. 1,
foundations against their conventional flat counterparts. The pp. 110–112.
results of the calculated settlement factor (Fδ) deduced from Hanna, A.M., and Abdel-Rahman, M.M. 1990. Ultimate bearing
the present experimental investigation demonstrate that shell capacity of triangular shell strip footings on sand. Journal of
foundations have better settlement characteristics than the Goetechnical Engineering, ASCE, 116(12): 1851–1863.
conventional flat ones. Iyer, T.S., and Rao, N.R. 1970. Model studies on funicular shells
(5) To monitor the movement of the sand particles during as rafts on sands. Proceedings, Symposium on Shallow Founda-
loading, special tests were conducted using colored sand lay- tions, Bombay, India, Vol. 1, pp. 149–156.
ers in a Plexiglas tank. The results deduced from these tests Kurian, N.P., and Mohan, C.S. 1981. Contact pressures under shell
demonstrate that the rupture surfaces for the triangular shell foundations. Proceedings of the 10th International Conference
footings are deeper than those for the flat one, which leads on Soil Mechanics and Foundation Engineering, Stockholm,
to the increase in the ultimate load for the shell footings. Sweden, Vol. 2, pp. 15–168.
Kurian, N.P., and Varghese, P.C. 1969. Discussion of “Design and
testing of cone and hypar footings,” by D.L. Nicholls, and M.V.
Izadi. Journal of Soil Mechanics and Foundation Engineering,
ASCE, 95(SM1): 415–416.
The financial support from the Natural Sciences and Engi- Nicholls, R.L., and Izadi, M.V. 1968. Design and testing of cone
neering Research Council of Canada (NSERC) is gratefully and hypar footings. Journal of Soil Mechanics and Foundation
acknowledged. Engineering, ASCE, 94(SM1): 47–72.
© 1998 NRC Canada
