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CHAPTER VI
STUDIES ON FUNICULAR SHELL MODELS
6.1 General
The effects of the shape of the contact surface on
the contact pressure distribution below shell foundations
are not well understood. The studies by Szechy (1965)
showed that a convex contact surface has a reduced
settlement when compared to flat surface, because of the
propagation of stresses to a larger zone below. Ciesielski
(1966) conducted photoe1astic tests on different shapes of
foundation base of structures and showed that the shells
having convex face in contact with the soil would distribute
the pressure more uniformly to the subsoil. It is to be,
therefore, expected that funicular shells with the convex
surface in contact with the foundation soil should have the
a~\antages mentioned above. Kurian and Jeyachandran (1972)
conducted tests on models of folded plates, one half of
hollow cylinders (split along its axis), cones and hypars
for two different rise to span ratios each on sand. They
reported that the bearing capacity of the foundation showed
a marked tendency to reduce when tested with concave faces
in contact with the soil and that marginal increases were
noticed when convex faces were in contact with the soil.
Another finding from the above study was that for both types
of contact surfaces, the settlements of shells were higher
than that for flat surfaces. Of the two types of contact
surfaces, the one with convex contact surface on the soil
showed less settlement than the concave contact surface. A
43
comparison of the pressure distribution below the shells
with concave face in contact with the soil and the flat
surface showed a concentration of stresses at the edges
whereas those with convex surface in contact with the soil
showed higher intensity of pressure at the centre. The
design of the centrally loaded shell foundations with
concave contact face based on uniform pressure distribution
thus becomes unsafe. In view of these findings it is
desirable to arrive at a suitable convexity of the funicular
shell so that the actual settlements of the shell foundation
do not significantly exceed those observed for flat contact
surfaces for efficiency. To arrive at the ideal depth/side
ratio (which is a measure of the curvature of the shell)
commensurate with the required rigidity it was decided to
conduct experiments with shells of varying depth/side ratios
and flat rigid raft models on sand bed in the laboratory and
in the field.
6.2 Models of Raft and Funicular Shells
The models of both raft and shells of 30cm square
and 2cm thicknesses were tested as foundations. Details of
the mould used for casting the raft model are given in
Fig.6.l. The dimensions of the edge beams of the raft and
the shell models were 4cm wide and 4cm deep. The models
were cast using a concrete mix of nominal volumetric
proportions of 1:2:4.
The model rafts were concreted with 6mm coarse
aggregate on a platform over which the outer form of the
44
edge beams were placed. After laying and compacting a layer
of concrete of lcrn thickness, the reinforcement mesh of 10
mm diameter mild steel bars at 7.5cm center to centre for
the raft slab and the reinforcement of a 10mm diameter mild
steel bar for the edge beam were placed over it. The slab
portion of the raft was then concreted completely.
Subsequently the inside form of the edge beam was placed to
facilitate its concreting. After the concreting was
completed, the model was allowed to set and cure for 3 days
in the mould. Later the form work was removed and the model
was cured in a water tank for 28 days before testing.
The funicular shell models were cast on moulds
prepared for casting shells of designed depth/side ratios.
The moulds were made by setting out the ordinates of the
shell on a wooden platform by driving nails on to it at grid
points (Fig.6.2), concreting WtS carried out to fill the
intermediate spaces between the nails and finishing the
curved surface thus obtained using fine cement plaster.
6.3 Casting of the Shell Models
The moulds were placed on a platform with thei~
convex faces up as shown in Fig.6.3a. Then the spacer
p1an k"s which act as the bottom forms of the edge beams,
were placed. The form \'/ork for the edge beams were placed
around the mould in such a way that the thicknesses of the
edge beams vie re kept the same. To ensure this, spacer
blocks of thicknesses equal to that of the edge beams were
placed i n between the form and the mould. Then the top
45
surface of the
were given a
removed from
mould and the inside of the edge beam forms,
thin coat of oil, so that the shells could be
it, after two or three days of concreting.
A layer of concrete of half the depth of the edge
beam of the shell was laid first and compacted properly by
tamping. Then the mild steel reinforcement of 6 mm diameter
bar (bent to the shape of a square such that it remained at
the centre of the edge beams of the shell) was placed
properly and the concrete was poured to form the edge beams
of the shell and the portion of the shell adjacent to them.
Then, 2cm size cubical wooden blocks were placed on top of
the mould at salient points on the top of the mould and
concrete poured over the mould such that the top level of
the concrete was in flush with the top of the wooden blocks.
Thus the thickness of the shell was made 2 em. The concrete
was tamped well with a trowel. the wooden blocks were
removed and the gaps refilled with concrete properly. The
concrete was allowed to set and cure on the mould for 3
days. Afterwards, the shells were removed from the mould by
lowering the edge beams against the mould and were cured in
a water tank for 28 days before testing, Funicular shell
models and raft model are shown in Fig.6.3b. For control of
concrete mix, concrete ~ubes were cast and tested from each
batch of concrete with which the shells were made.
6.4 Laboratory Tests
The laboratory test bed of sand consisted of a
7.5m x 5m (24 ft. x 16 ft.) size and 5m (16 ft) deep sand
46
bed and the self straining loading frame of 200t capacity
described earlier. The aim of the experiments with the
model was to find the effect of depth/side ratio of the
contact surface with the soil on settlement and pressure
distribution below the shell models. The grain size
distribution of the sand was as given in Fig.6.4. For the
sake of uniformity and consistency of test results, the sand
bed in the laboratory was compacted to a density of
1.63gm/cc. After every test, the test bed was recompacted
to the same density to ensure same initial conditions for
all the tests. For soil pressure measurements a hydraulic
type pressure cells were used.
After compacting the sand to the required level in
the test bed, the pressure cells were embedded in the test
bed, taking care to see that proper contact between the
cells and the sand below was ensured. For this, fine sea
sand was spread over the compacted sand bed for 3mm
thickness above which the cells were placed. Then fine sand
was spread over the cell for a thickness of 3mm above which
the sand was compacted to such a thickness that would give a
sand cushion of 7.5cm (3 inches) between the pressure cell·
and the apex of the model funicular shells with their convex
faces in contact with the soil. The central load applied by
jacking against the loading frame was distributed over the
edge beams of the shells and raft. using a system of load
distributors as shown in Fig.6.5. Settlements measurements
were done at the centre of the shell. at the corner and at
the centre of the edge beam of the shell using dial gauges
47
to read up to an accuracy of O.Olmm. Loads were applied in
increments of 40kg at a time. The initial readings of the
dial gauges and of the pressure shells embedded centrally
below the shell model were taken before application of the
first increment of load. After each increment of load the
final readings of dial gauges and pressure cells were taken.
The maximum load applied was 700kg. The test was repeated
with shell models of various depth/side ratios and the model
raft. The load settlement graph for the shells are given in
Fig.6.10 and pressure vs depth/side ratio in Fig.6.12.
6.5 Field Tests on Raft Model and Funicular Shell Model
Field tests on raft model and funicular shell
models were conducted at Monkompu. Kuttanad, Kerala State.
about 160km away from Trivandrum. The soil profile at the
site is shown in Fig.6.6.
The site was typical of a reclaimed area that
consists of on an average 1.8m deep fill over compressible
deposits of fine sandy loam. clay loam, clay and silt. over
the low lying water logged paddy field. The fill consists
of fine alluvial silty sand excavated from the beds of·
adjoining canals and river and dumped at the site above 50
years' back. The typical grain size distribution of the fill
is given in ~ig.6.7. The top 15 to 30cm thick fill is
desiccated. A test pit 1.8m x 1.8m size and 100 cm in depth
was excavated for the field tests of the models. To ensure
control of quality of concrete, the casting of the shells
was done in the Laboratory at the College of Engineering.
48
Trivandrum. The shells and all testing equiprnents were
transported to site. The loads were applied by jacking
against a built up RSJ 30cm x 30cm loaded at its ends by
sand bags. A schematic diagram of the loading setup used
is shown in fig.6.8 •. Fig.6.9 shows a typical test in
progress.
6.6 Details of Testing
The test bed was levelled properly and the
pressure cell was embedded carefully in a groove cut into
the bed to its size at the centre of the test bed. Proper
contact between the soil and the cell was ensured by
spreading a layer of sea sand of 3mm thickness in the groove
and placing the pressure cell carefully. The initial
readings of the pressure cell were taken. A thin layer of
sea sand {3mm thick} was laid over the pressure cell over
which medium river sand was spread and compacted to the
desired density 1.65gm/cc such that there was a sand cushion
of 7.5cm (3 inches) in between the test model and the top of
the cell. The raft model was placed centrally over the cell
and the load distribution set up arranged so that the
centrally applied reaction load was distributed as a
uniformly distributed load on the edge beams of the model.
The readings of settlements and pressures corresponding to
every increment of load of 40kg from 0 to 560kg were
measured. Loading was limited to 560kg as pilot tests
conducted showed that loading beyond 600kg produced larger
values of settlements.
49
The settlement readings at the corner at the
centre of the edge beanls and at the centre of the model raft
were almost same thereby showing that the foundation element
behaved rigidly in the chosen loading range. The raft model
was replaced by shell models of various depth/side ratios as
in the case of laboratory tests and were tested. The load
settlement graph for the models of raft and shells are shown
in Fig.6.11.
The graph of soil pressure Vs. depth/span ratios
of shells is shown in Fig.6.12.
6.7 Analysis of Test Results
From the load settlement graphs obtained from
laboratory and field tests, it was seen that minimum
settlements were obtained for the flat bottomed raft model
and that with increase in curvature of the contact surface,
the settlements also were found to increase. The maximum
settlements were observed in the case of funicular shell
model with depth/side ratio of 1/2 in each set of
experiments, namely in the laboratory and in the field. Of
these two, t~e settlements observed for the laboratory tests'
were more than those observed for field tests for any given
load. This phenomenon is due to differences in soil
condition in the field and the laboratory. The lack of
confinement of the cohesionless sand in the case of
laboratory sand bed corresponds to a greater settlement
whereas with a cohesive soil in the field, there is a
greater restraint laterally. From the contact pressure
50
distribution studies t it was seen that the soil pressure
were minimum for the raft model with slight increase in the
case of shell with depth/side ratio 1/10. As the depth/side
ratio increased (ie. curvature of the contact surface
increased) the soil pressures were also observed to be
increasing progressively for any given load and the maximum
values of soil pressure were observed for the shell with
maximum curvature in the laboratory and in the field. The
increase in soil pressures might have contributed to higher
settlements under shells of higher curvature.
Therefore t it is concluded that the depth/side
ratio has an important bearing on the behaviour of the
funicular shell element as a foundation structure. The
performance of the shell model with depth/side ratio of 1/10
was very close to that of the raft model. From the
variation of the behaviour with depth/side ratio t it is seen
that the shell with least depth/side ratio consistent with
the required rigidity for the shell is considered to be the
ideal one for use as a foundation element. This will enable
the shell to behave as closely as a rigid raft without the
disadvantage of increasing thickness and reinforcement.
Thereforetfor prototype funicular shells used for studies in
the laboratory and in the field a depth of 7.35cm for a side
of 100cm was chosen to give the required strength and
rigidity.
51
FIG.6.1 MOULD FOR RAFT MODEL
FiG.6 .2 METHOD OF SETTING THE ORDlNATESOF A TYPICl~l" SHELL MODEL
52
FIG. 6· 3a. MOULDS FOR CASTING FUNICULAR SHELL
FIG. 6· 3 b. RAFT MODEL AND FUNICULAR SHELL
MODELS OF DEPTH I SPAN RATIOS OF
1/10, 1/6 , 1/4, 1/3 AND 1/2
53
I---r-r---~
'"~
"'\\r\\\
\I\.
~~ r--
100
908070a::
~60
LL 50
wL.O19;::f 30
aJ 20uffi ,a0.. 0
5.04.0 3.0 2.0 1.0 05 OJ 0.15 0.1
GRAIN SIZE in mm
FIG.6.l.GRAIN SIZE OlSTRIBUTION CURVE OF SAND
IN THE LABORATORY TES T BED
54
-JACK
, ,,-----RSJ Piece C
( ,r- RSJ Pieces B
==-----'---'--~==-----l..-...L.-.J'---------!.=---___;
I--tt---RSJ Pieces ATeak wood
II1 J -Raft model
Elevat"lon
, ,RSJ Piece C
PlanFIG.6.5DETAILS OF ARRANGEMENT FOR
LOAD DISTRIBUTION ALONG EDGES OF RAFT
RSJ Pieces 'B'
~~---
55
Grey sof t clay
Clay loam
yW.T. Sandy loam
r-----o-.Ground level/ Desiccated soil
-
J-r
DEPTH,ma1
2
3
'-+
5
6
7
8
FIG.6.6S0IL PROFILE AT TEST SITE
56
----,"\
~
~\
[.............~r-- --..~i'- -.-----..
U1-.J
100
r 90
180
f5 70~60U-
w 50~ 40I-Z 30w020a:::~ 10
o0·4 0·2 0·1 0·06 0·04 002
GRAIN SIZE, mm0.01 0.006 0.002 0.001
F1G.6.7 GRAIN SIZE DISTRIBUTION GRAPH OF TYPICAL FILL SOIL AT TEST SITE ..
MANCOMPU 1 KUTTANAD
........Proving ring
~-a-..".......{._-- Sand bags ------+}:-~:J.._,r__;
J--Rolled steel joist
~;:;4: )---+ Load distri butingRaft model :..:: .... :.... :::... ',:'.':.":': .:.:::-:::.:,..:.;.; arrangement -5Z.- GWL
Pressure Cell~ Sand layer 7.62cm thick
FIG.68SCHEMATIC DIAGRAM OF LOADING SETUP
58
FIG. 6.9 A TEST ON MODEL SHELL IN THE FIELD
59
04 0.8 1.2 1.6 2.0 24 2.8 ~2 3.4 36SETTLEMENTkm) ~
FlG6.10.LOAD SETTLEMENT GRAPHS OF TESTS ON RAFT
MODEL AND SHELL MODELS IN THE LABORATORY
60
480
400
560 ; ----r-------r-----,.---,-----fJ1tc -----It-~-__I/ , .....
./~" /,1 .,'
.~1' I /41 ./~..
/, ".'/,,' ¥.,., .---+----1----1-----+ /'," ". ....• ---+--",0
'.N,;:~,/<~....... //'/' ."" .." /0I'~' .',' ~.' .' " ."./
~'.I".~..,.... -..a........---1----I./ ;' . /-
J,/...... /', ...' /"
" )t....,.. ".0II' /,•• , /.~ ,".0'3 201-----f----+-- ~'..r.,-- t1,./',---t---t------l
y..... ,,/"~ ./ -':f . "a./ /1/
,!.~ ,,-I.~··· /
240 .I~" /------------1---+--. -/ll
#-~"I /"on ,l/ v 0 0 Raft slab'-' . p
~ /1/// ~-·-·-teShell with depth/span=1/10~160 '~"/ 1/6'-' 1--- I> _----... // // // //-a % -o . <; _._._.-.A /J /1 // /1 =1/4
-.J 0 II
80 i{? ,......_...-..~ I 1 IJ 1/ , / =1/3-/1 0- - -11 1/ 11 11 11 =1/2
11
o 0.1 0.2 OJ 0.4 0.5 a.6 0·7Settlement (em)
Fl G6.11 LOA 0 SE TTLEMENT GRAPHS OF rES TSON RAF T AND SHELL MODELS IN THE
~IELD
61
0.9 r----.---.------,----.--/-",P
~E ,/~ LABORATORY TESTl. 7' /IF O:8 /~~ .'0
~t )~~ IO.71------+---+-
L--r-·/-. 0 -----+-----f
~ /.~. FIELDw /.~ TEST
~ O.6,;71Y I
~Q.
0.5 '---_------'--__._--'--_---'--_-----L--_----'
o 1/10 1/6 1/4 1/3 1/2DEPTH TO SPAN RATIO OF SHELL
>-
FIG.6.12.PRESSURE vs DEPTH TO SPAN RATIO GRAPH FOR
A LOA 0 OF 480 kg DURING LOAD TES TS ON
MODEL RAFT AND SHELLS IN THE LABORATORY
AND FIELD
62
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