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