ShotcretePunch-loaded shotcrete I iningson hard rock

Jonas Holmgren

Swedish Rock Mechanics ResearchFoundation - BeFo

!t l.bl aV

Pu nc h-loaded s hotcreteliningson hard rockJonas Holmgren

Swedish Rock Mechanics ResearchFoundation - BeFo

Stockholm 1979

Holmsren J 1979. PUNCH-LOADED SHOTCRFÍE LININGS ON HARD

ROCK. Dissertotion, Royol lnstitute of Technology, Stockholm, Sweden,

ABSTRACT

Lorge scole punch lood tests on plone ond orch-shoped shotcrete loyers

interocling wîrh gronite blocks ore presented.

Tests were mode on plone unreinforced loyers of differenl thickness. Tests

were qlso mqde on plone loyers with dîfferent omounts of reinforcement

interocting with rock bolts in different woys.

Arch shoped shotcrete loyers were tested both with ond without end sup-

ports.

The lood-deformotion curve for reinforcement bqrs of different kinds em-

bedded in concrete wos invesligofed. The some kind of tests were mode

on strips of reinforcement nets embedded in shotcrete,

Colculotions were mode for o rough esf imote of the influence on the cor-

rying copocity of o two-dimensionol extension of the sholcrete loyers.

Colculotions were olso mode for rough estimotes of the oction of reinforc-

ed shotcrele bolh ot o service stoge ond ot locol cove in.

Finite element colculotions were mode of the stote of stress in the rock-

shotcrete interfoce neor o ioint ot different loodings.

A lìterolure survey is presented together with o discussíon of shotcrete

design.

Key words: Tests, shoÌcrete, reinforcement, rock bolts, odhesion, corrying

copocity, lood-deformotion curve, finìte element cqlculotions, design.

PREFACE

ln 1972 discussions oboul the interqction of shotcrete ond rock were

held between the Swedish Rock Mechonics Reseorch Foundotion (BeFo)

represented by S Biurström ond the Royol Swedish Fortificotions Ad-

ministrolion (FortF) represented by E Abrohomsson, W v Essen, T Hohn

ond H Sundquist.

At the time being BeFo olreody hod put shotcrete on their reseorch

progrom, The theme rock reinforcement olso interested FortF, which

builds o lot of militory plonts in rock coverns. Therefore ii wos no-

turql to stort o cooperotive pro[ect on lhe behoviour ond corrying co-

pocity of shotcrele linings between BeFo ond FortF lhrough its Reseorch

Deportment.

Thonks to the obsence of bureoucrocy in these two orgonizolions lhe

proiect wos stqrted very quickly - the Author become employed port-

lime by BeFo os o reseqrch officer in Jonuory 1973, o reference group

wqs set up ol lhe some time ond the first fests were mode ìn the spring

of 1973.

From the beginning the reference group consisted of E Abrohomsson, T

Hohn, H Sundquist, oll FortF, S G A Bergmon, Consultont, S Biurström,

BeFo qnd C Alberts, Stobilotor AB. Loter on B Broms, Royol lnst of

Technology (KTH), ond S Söllström, Swedish Stote Power Boord were

ossocioted lo the reference group. When leoving the Boord S Sallstrc;m

wos reploced by 5 Jonsson, olso of the Boord.

Lorge.-scole shotcrete tests were performed of the Test Siotion of FortF,

where on excellent work wos done by the stoff. The most involved in

this proiect were F Adolfsson ond PNilsson.

The tests on concrele-embedded reinforcement bors were performed ot

the Reseorch lnst of Norionol Defence (FOA) by J Eriksson ond E

\'Vernqvist. The test specimens were monufoctured by B Korlström ond

T Woll, both KTH, who olso ossisted ot the tests ond their evoluqlion'

The input doto for the finite element colculotions were prepored by

P-O Sundquist, FortF. M Viklund, FortF, contributed with remorks

on rhe linguistic usoge ond the reference list.

Through the yeors o lot of voluoble help with typing ond drowing

wos received from P Alm, C Ericson, I Jöderberg, G Lennesledt,

oll FortF ond E Ask, B Ahlgren, bofh KTH.

lwish to express my deep grotitude to oll these persons mentioned

qbove for their support ond portícipotion in the proiect.

lolso wish to express my thonks to K Lindgren, KTH. Without be-

ing ossocioted with the proiect he hos olwoys been willing to discuss

equipment problems ond reloted questions.

This proiect hos given me o lot more friends thon those mentioned

obove, ond I wîsh to thonk them oll for whot they hove toughl me

obout shotcrele qnd tunnelling works.

Finolly I wish to thonk my teocher, Professor H Nylonder, KTH,

for his kind support ond for whot he hos tought me during the yeors

within the field of building stotics.

Stockholm, Morch 1979

Jonos Holmgren

DISSERTATION

This dissertotion consists of o survey ond fhe fol lowing three porls:

(A) Holmgren J "Plone shotcrele loyers subiected to punch loods". Royol

Swedish Fortificotions Adm, Reseorch Dept, Report l2l :4, Stockholm

175, speciol edition 79-02-01 .

(B) Holmgren J "Deformotioner hos ingiutno ormeringsstönger". (Deformo-

tions of concrete-embedded reinforcement bors). Royol lnst of Techno-

logy, Div of Building Stotics, Bull no ll4, Stockholn 1f75.

(C) Holmgren J "Curved shotcrete loyers subiected to punch loods". Royol

Swedish Forfificolions ,Adm, Reseorch Dept, Report l2l :5, Stockholm

179. (Published only in the present thesis).

Sholcrete linings on hord rock o survey

óy

Jonos Holmgren

CONTENTS

l. Nüapuq-aN

2. DESIGN BASED ON EXP

2.1 CASE HISTORIES

2.2 DESIGN BASED ON ROCK CLASSIFICATION

3. DESTGN BASED ON l4EAs_U8EM_ENII

3.I SOFT-ROCKTUNNELING

3.2 HARD-ROCK TUNNELING

4, DESIGN BASED ON IIQçK IVIQÞ-EIS

4,1 INTRODUCTION

4.2 THEORETICAL BLOCK MODELS

4.3 LARGE SCALE TESTS

4,4 ANALYTICAL TREATMENT OF BLOCK MODELS BASED ON

TESTS RESULTS

5. çoNç!$laNs

6. REF ERENC ES

N_Ieap!q!_aN

This thesis deols wilh some ospects on the use of shotcrete os o meons

of supporting surfoces of hord rock mosses. ln this survey o short litero-

ture review will be given, where the investigotions reported in the

thesis will be looked upon in o wider context.

ln the survey different opprooches to the design of shotcrete liningswill

be distinguished:

o) One woy is to moke uso of others experiences. ln the literoture one

finds cose histories, which report doto from shotcrete works. The dif-

ferent syslems for rock clossificotion ore olso ossigned to this group

since lhey olso contqin collected experiences through thol support meos-

ures ore correloted to the rock closses.

b) Another woy is triql ond error qpprooch where meosurements qre used

to check the behoviour of the rock moss ond the lining.

c) A third woy is rough colculotions for bosic foilure mechonisms, either

pure theoreticol block models or lorge scole tests combined with theo-

reticol considerolions. ln this connection the expression lorge scole tests

meons test where the looding block is of o reolistic size ond the sur-

rounding rock-shotcrete structure ìs sufficîently lorge for on exominolion

of o locol foilure.

2. DESIGN BASED ON EXPERIENCE

2.1 CASE HISTORIES

A typìcol cose hisrory contoins o descriplion of the geology, the selected

support system ond the execution of the construction work.

Exomples of cose histories ore /l/, /2/, /3/, /a/ ond /5/.

These histories of course give voluoble informoiion to experienced engi-

neers, lf lhe results qre generolized ond referred to ìn other popers there

is o greot risk, however, thot we suddenly hove got quonlitotive rules

of thumb for which ihe prerequisites hove been forgolten, ln /6/ ønd

/7/ "" exomple of this process con be found.

ln /6/ i+ îs stoled thot certoin design rules for the use of shotcrete in

the blocky rock of Woshington were found volid during construction,

These rules were reloted to the diometer of lhe opening, the height

of verticol sidewolls, the block size ond ioint chorocteristics. ln fi/then the height of the sidewol ls is soid to be generolly importont in

very blocky ground with reference to /6/.

The ofher three porometers ore soid to be limiting the use of shotcrete

in loosening ground in generol without ony reference to /6/,

The oulhors "î /7/ ore of course owore of the conneciion wilh /6/ but

the reqders of fr/ moy not be ond thus o new rule of lhumb hos been

creoted.

This is unfortunote becouse il is nol told whot influence differeni odhesion

condiÌions, o different rotio of oh / ov or even o different direction of

the lunnel would hove hod.

It is the Author's opinion thoi cose histories os Ìhe bosis for design rules

should be used with the utmost core in discussions ond wriiten popers.

Of course, lhe experiences of others sholl be compored with ones own

but they hove to be onolyzed corefully before they ore generolized.

2.2 DESIGN BASED ON ROCK CLASSIFICATION

There ore vorious systems for rock clossificotion which serve os o bosis

for The design of tunnel supporl systems. The most common systems ore

the RQD - index by Deere, the Rock Moss Quolity by Borton et ol

ond Rock Closses by Louffer. They ore described in severol popers/ see

for instonce /8/, /9/, /lO/ ond /ll/.

These systems qre not scrutinized here bul some remqrks concerning the

use of shotcrete will be mode.

ln /9/ o correlotion is found between the degree of support ond the rock

closs for Scondinovion tunnels. According to the Author's opinion, this

result is rrot ostonishing, The rock-closses, índependent of system, describe

in some woy or other how stoble ihe rock is, ond the selected degree of

support ìhen is o mirror for the expectotions of this degree of stobility'

There is nothing to be soid obout this - the sysiems of rock clossificqtion

occount for collected experiences from o lol of tunneling works.

There ore, however, some shorlcomings which hqve to be pointed out. At

leost two of these remorks ore eorlier known, others hove becomeevident

os o consequence of the Swedish shotcrete investigotion presenled in chop-

ler 4.2.

c) The rock closs does not tell whot influence on the stobility o voriotion

of the tunnel direction moy hove.

b) The stote of stress in the rock moss is not considered, excepl for BortonS

system,

c) The minerol composïtion of the rock moss, which is of the utmost impor-

tonce for lhe odhesion ond thus the corrying copocity of o shotcrele lin-

ing in severol looding coses, is not told by lhe rock closs'

d) Normolly o thìcker lining ondþr decreosed boli dislonces ore recommended

when the rock closs indicqte worse condiìíons. ln mony coses, however, os

shown by the investigotion presenled in chopler 4.2, a thin lining moy hove

the some corrying copocity os o thick one'

FORT IFI KAT IONSFöRVALTN INGENForskn ingsbyrôn

Ropport nr l2l:4torttft dnr ó9óó F

l%5-07-01

speciol edition

1979-02-01

PLANE SHOTCRETE LAYERS SUBJECTED TO PUNCH LOADS

by

Jonos Holmgren

CONTENTS

NOTATIONS

r. lNiBAPUql.aN

2. EARLIER INVESTIGA

3. LoaÞlNc-cas!

4, TEST RIG AND TEST SP

.I MAIN TESTS

.2 CONTROL TESTS

,21 Tesl cubes

.22 Test beoms

,23 Testing of the odhesion strength

5. MIXING OF CONCREIE, SHOTCRETING AND CURING

6, DEFORMATION MEASU

7. TEST DESCRTPTTONS

.I A BASIC DESCRIPTION OF THE TESTS. TERMINOLOGY

,2 TESTS WITH UNREINFORCED SHOTCRETE

,21 Tests under normol odhesion conditions

.3 REINFORCED SHOTCRETE COMBINED WITH ROCK BOLTS

.3'l Description of reinforced test specimens

,32 Observed foilure modes

.33 Deformotions

8. lnf tWO-Ott"t¡NSIOX

.I GENERAL REMARKS

.2 THE UNCRACKED SHOTCRETE LAYER ACTING AS AN ISOTROPIC

CIRCULAR PLATE

8.3 THE CRACKED REINFORCED SHOTCRETE LAYER STUDIED WITH

THE YIELD LINE THEORY

.4 THE CRACKED REINFORCED SHOTCREIE LAYER ACTING AS A

CIRCULAR MEMBRANE

e. !U1"1^44ßY

'r0. Nrro or runtHm nes

REF ERENCES

NOTATIOI{S

fod

f¡,

fc

p

P¡

P

Pr

ô

(MPo)

(MPo)

(MPo)

(kN/m)

(kN/m)

(kN)

(kN)

(rr)

odhesion strength

flexurol strength

compressive sfrength

line lood olong lhe crqck fhotseporofes two rock blocks

line lood ot foilure

totol lood ot eoch section ofthe test equipment

foilure lood

nominol wid*r where qdhesion

stresses oct

with different indices represents

sÌreseso (MPo)

l. |NTRODUCTIOI.¡

The investigotion presented in this report is the first sfep in o ioinl proiecÌ befween

the Royol Swedish Fortificqtions Administrotion (FortF) ond the Swedish Rock Mechonics

Reseqrch Foundolion (BeFo).

Its oim is betfer knowledge of shofcrefe os q meons of rock strengthening' lf this

oim is reoched consideroble economic sovings could be mode since the thicknesses

of shotcrete used in proctice probobly ore overestimoted becou.se of this lock of

knowleCge ond the psycho!ogy of sofely.

The problem corn¡rlex is o lorge one ond it hos to be exomined step-wise. To stort

with q rother simple cose is studïed which is defined in chopter 3.

The experimentol ond fheoreticol work described in rhis report hos been corried out

by the Author under the guidonce of o reference group. Members of the reference

group were initiolly Eddy Abrohomsson, Torbförn Hohn, Håkon Sundquisf, oll ForfFi

Sten G. A. Bergmon, Consultont, Sfen Biurström, BeFo; Cloes Alberts, Sïob¡lqtor ABi

ond loler Bengf Broms, Swedish Geotechnicol lnstitute, Stig Siìllstrtim, Swedish Sfote

Power Boord.

The tests were modê ot the Reseorch Sfotion of the Reseorch Deporfment of FortF.

The test rig hos been designed by the Design Deporfment of FortF.

2. EARLIER INVESTIGATIONS

The interoction befween shotcrete ond hord rocks hos nof been invesfigoted previously

in Scondinovio to the knowle,Jge of the outhor. östlund (/3/), Sallslram (/4/) ond

Poìiörvi (/5/) invesligoted the properÌies of the shotcrete itself' Barbo (/6/) hos

published results from some odhesion fests on shotcrele o1>plied to different minerols.

The number of tests is rother limited ond of course the structurol behqviour of the

shotcrete hos not been defermined in his investigotion.

ln Austrio severol invesligotors hove studie,J the use of shotcrete os tunnei lining.

The investigoted rock moteriols were weok, ho\/r'ever, so the problem studied is prin-

cipolly the one of o concrete pipe surrounded by soil. (Ref. /7/, /B/' /9/, /10/).See olso chopter 3.

This investigotion is concerned with high strength iointed rocks'

3. LOADING CASE

A rother simple looding cose, the punching of o lorge rock frogment through o ¡:lone

shotcrete loyer, wos chosen for lhis investigotion.

This cose wos studied by Rotter (/1/) who osumed o sheor foilure in the shotcrete

loyer. This led fo fhe conclusion ihof o 3 cm shotcrete loyer could corry 13 fimes

the weight of o rock pyromide hoving o bose oreo of on" t2. The consequence of

this model wqs fhqt the corrying copocity of the shotcrete loyer wos proporfionol to

the loyer thickness ond the sheor streirgth of the shotcrete'

Fig 3 o Looding cose in this investigotion

4. TEST RIG AND TEST SPECIMENS

4.1 MAIN TESTS

The moin tests were mode in the 3.7 m x 1.2 m test rig shown in Fig 4 o, Rock

slobs of fine-groine<J grey gronite were tested. The middle slob wos presse'J uppwords

during o fest for procTico! reosons. The rig wos fixed to the ground with o hinge

porollell to the test specimen ond wos filted to moke fhe rock surfoce verticol during

the opplicotion ond curing of the shotcrele.

The different porfs of fhe rig were bolonced ogoinsf eoch other with respecï to the

deformqfions in order to ovoid bending of the shotcrete loyer. The fulfilment of this

wos checked with o slroìn gouge during one of fhe tests. The lood wos o¡rplied with

two porollell*connected hondpumped hydroulic iocks.

ROCK SLABS at----\\\\

STEEL RIG c HINGE

Fig 4o Test rig

4,2 CONTROL TESTS

A flot box 45 x 45 cm wifh the heighi equol to the ihickness of the shotcrete in

the moin test wos Shotcreted ond stored together with the moin fest specimerr.

Orr the lesting doy cubes ond beoms were sowed out of this shotcrete plote

4.21 Test cubes

The side length of the cubes wos the some os the thickness of the shotcrete ioyer in

the moin specimen except for the 2 cm loyer. ln thqt cose 4 cm cubes were used.

The I cm cubes were investigofed in o 1.0 MN tesfing mochine. A mechonicol

force gouge wos puf inlo the lesting mochine when fhe 4 cm cubes were Ìested.

The compressive strengThs presented in this report ore the meon volues of four cubes.

No correction for rhe size of the cube hos been mode.

4.22 Test beoms

The spon length wos 40 cm for the investigoted beoms. A Two point looding system

wos used. The loqd wos opplied of the third points. The cross section wos sqrrore

ond the side length wos equol fo the thickness of the shotcrete loyer in the moín

specimen, except for the specimens with o 2 cm shotcrele cover where 4 cm beoms

were used.

The 8 x I cm beoms were looded by o hydroulic iock. The opplied lood wos meosured

with o mechonicol force gouge. The 4 x 4 cm beoms were looded with leod weìghfs.

The flexurql strengths giverr r'n this reporf represent the meon volues for two tests

No correction for beorn size hos bee¡r mqde.

4.23 Testing of the odhesion strength

Cores with 50 ¡nm diometer were drilled in the shofcrete down to the rock surfoce.

A sfeel plote with o centric pin wos glued to the top of eoch core with epoxy resin

The cores were loqded in tension. The corresponding force wos meosured qf foilure.

The odhesion strength, fo., the force divided by the coreorec¡' wos colculqted.

Three cores were tested for eoch test in the moin test series.

5. M¡XING OF COI{CRET SHOTCRETING AND CURING

Stondord cement ond grovel (0-8 mm) were used for the concrete. The weighr rotio

wqs l:4.5. The qmount of woter odded to the shofcrete wos reguloted by fhe nozzle-

mon ond wos normolly kepf os smoll os possible.

The specimers with2 cm loyer were shotcreted in one operotion. The specimens wilh

4 or B cm cover were normolly shotcreted in fwo loyers. The second loyer wos opplied

obout lhree hours offer the firsf loyer.

A few hours ofter the shotcreting the concrele wos covered with plostic sheefs qnd it

wos then kepÌ domp until the testing'

6. DEFORIVIATION MEASUREMENTS

The deformotions were meosured wifh diol gouges. The occurocy of the reodings wo,i

obout 0.01 mm. The fest orrongement is described lofer in connection wifh the

descriptions of the different TesTs.

7. TEST DESCRIPTIONS AND TEST RESULTS

7.1 A BASIC DESCRIPTIOI.¡ OF THE TESTS. TERMINOLOGY

P/2

APPLIEDLOAD

PP/2

SLABS

tig 7 o Principol view of moin test specimen.

OUTER

ROCK SLABMIDDLEROCK SLAB

OUTERROCK SLAB

7.3 REINFORCED SHOICRETE COMI]INED WITH ROCK BOLTS

7.31 Description of reinforced lest specimens

Five tests were mode with I cm reinforced shotcrete combined wittr rock bolts, The

test specímens ore shown in Fig 7 f.

Test Al wos mqde moïnly to demonstrote thot o plone reinforcement is nof effecfive

under fhe looding condifions chosen if if is not fixed properly to the rock due to the

chorocter of the odhesion foilure.

Test A 2 corresponded lo the common cose when the reinforcemenf nets qre ottoched

to rock bolts only with thin steel wires.

* C6c200, 22OMPo

A'1.

42.

A3.

Ai..

Shottow

#"M¡ddl.e rock sl.ob

+16 c200, 220

*á8c : t00MPoo

A5.

outer rock stob

Fig 7 f Test specimens in series A

The odhesion crock spreod olong Ìhe rock-shofcrete inlerfoce ot o lood of obouT one

third the foilure lood until the concrefe cover foÎled by bending. see Fig 7 c.

The foilure lood wos not offected by the loyer thíckness except in the 2-cm tests

probobly becouse of the rother lorge slit (^"5 mm) between the Iock slobs'

The dependence of the odhesion strenglh wos obvious:

P¡ô = =-:_ (see Fig Z d)

tod

wos neorly o constont with o volue of obout 30 mm. This indicoted thoï only o

norrow bond of shotcrete ot o crock corried the lood.

Þ

OUTERROCK SLAB

Fig 7 d Norninol qdhesion stress block

SHOTCRETE

dod

ô

- Scm

T1-- Ê.o

C\¡

-1 8cm

.., 6 5 Cfn

E(J\1

Ê(Jo

Fig 7 c Sholcrete loyers ofter foilure

Test rig in festing position.

Unreinforced shotcrete loyer ofter foilure

7.21 -lests under normol odhesion conditions

The mqin results ore shown in Toble I . The couse of foilure wos olwoys too high

odhesion stresses between the shotcrete qnd the rock surfoce.

26

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mm

P¡

kN/m

Pf

kN/section

fod

MPq

f'bt

MPo

fc

MPo

Loyerthick-ness

cm

Nozzle -mon

Ag"doys

TestNo

X

xx

XXXX

Dry test cores.

Molfuncfion of test rig.

Adhesion porfly eliminoted p = PÆ.4 insteod of P/.15

Rock surfoce dirty by diesel smoke.

Toble I Moin test results.

For the reinforced test specimens it wos possible io increose fhe o¡rplied lood ofter

ihe odhesion crock propogofion in some coses. For fhese fests o finol foilure lood

or secondory foilure loqd existed.

7.2 TESTS WITH UNREINFORCED SHOTCRETE

Ten tests under normol odhesion condilions ond fhree tests under specio! conditions

were mode. The loyer thickness ond concrefe oge were voried. Also reinforced

fesfspecimens ore discussed in fhis chopter since fhe reinforcemenf did not function

until ofter the primory foilure.

Diol gouges were used to sheck ihe movement of the rock slobs in tests l-13. The

gouges were ottoched to o sleel frome, which wos free frorn fhe fest rig, ond pointed

to smqll gloss plotes glued to the concrele surfoce.

The ongulor displocement wos obout 0.0001 rodions for fhe two ouler rock slobs neor

moximum lood in mosf coses. This deformotion did not seem to offect the test results

since the stroins in fhe concrete surfoce obove fhe slit between fhe slobs were neglible

The middle rock slob wos pressed upwords by the lood P during o lest. The o,rter

rock slobs were restroined by the loods P/2. The opplied lood wos disfribuÌed from

the middle slob fo fhe oufer slobs by the shotcrefe loyer.

The o¡rplied lood, P, ond the verlicol displocement, w, of the middle slob were

meosured during the test.

Af o cerfoin lood level, the foilure lood on oChesion crock formed belween

the shoicrete ond the surfoce of the oufer rock slobs neor fhe slit between the rock

slobs. Thïs ho1>pened in oll tests. The lood suddenly Cro¡rped to one third or less

when fhe odhesion crock formed. This lood wos colled fhe odhesion crock propogo-

fion lood ond it remoined neorly consfont during the crock prol)ogotion until q flex-

urol foilure fook ploce in the sholcrete loyer.

PRIMARY FAILURE LOADP

tW:lMIDDLESLAB OUTER

SLAB

ADHESION CRACKPROPAGATION LOAD

w

p P/2

UNCRACKEDSTATE

p P/2

"ADHESION CRACKING" "FLEXURALCRACKING"

Irp P/2

,lI

Fig 7 b Principol lood-displocement diogrom for unreinforced test specimens

:I'

i

i

I

Test rig in shotcreting position.

I

Operotor in shotcreting position.

2P'l 1.2 MPo

nom,,.,n2 Ç + r¡

using o modified formulo by Nylonder ond Kinnunen Vll/).

B is o nominol width of the closp ond h is fhe effective depfh of the shotcrete

loyer. In this cose P in the originol formulo is reploced by 2 P becouse the rock

bolt is subiecfed to lood on one side only.

The theoreticol foilure stress occording to Nylonder ond Kinnunen (/11/) is 1.4 MPo.

Thus the meosured foilure lood wos 80 % of the theoreticolly colculoted lood. This

result indicotes thot the closps did nof tronsfer the lood quite properly frorn the con-

crete Ío the bolfs since the punching Ìheory mentioned.:bove normolly underestimotes

the foilure lood.

A consideroble drop of fhe lood occurred ofter the odhesion foilure in Test A 4. lt

wos, however, possible to increose the lood up to 3ó % of the primory fqilure looC

The crock potTern wos the some os for Test A 3.

The foilure wos cqused by punching. The nominol sheor siress ol fqilure wos

r = 1.3 MPo, which is equol to the theoreticol volue. This indicotes thotnom

the FortF closps tronsferred the lood more prot)erly from the concrete to the bolfs

ond thoT the foilure lood corresponded to the omount of reinforcement in ogreemenT

with the punching Ìheory menfioned obove.

ln Test A 5 the decreose of the lood wos smoller fhon for the other tests. lt wqs

possible to increose the lood up fo 94 % of the primory foilure lood (only 75 "/" of

the primory foilure looC for Test A 3, though). During the relooding severol fine

flexurol crocks developed ond o consideroble curvoture wos noticed. The foilure wos

by punching ot one side of lhe test specimen ond more like q beom sheor foilure ot

the other side. The nominol sheor stress ot foilure wqs 3,0 MPo, which corresponds

ll0 % of fhe theoreticol volue.

i\.T,

î

pl First lover_t

þ 6 to keep fhereinforcement closeto the first loyer

A

_Jt_

T_

I

--+I

-+I

FisTs Closp used together wilh rock bolts in Tests A4 ond A5'

7,33 Deformotions

ln Fig 7 h the relotive displocement of the middle slob is plotted ogoinsf the opplied

looC. Test specimen A 5 is of speciol interest. A properly designed reinforcement

in conbinoTion with on effecfive closp gove <l very slrong ond ductile shotcrete cover.

The plostic energy in TesT A 5 ot foilure wqs six times Ìhe energy in Test A 3. The

energy rotios for Tesls 45, A 4, A3 were ó:l .ó:l .0.

P-

Lruz"üP

tkNl

180

160

1/.0

80

70

60

50

ú0

30

20

10

<- A3<-- A4

--- A5<- A2

PPrimory foi[ure [oods

A

12

10

I60

40

00

20

010n30ô0 50 60 w Fnrrü

tig 7 h Lood-deformotion curves for Tesfs A 2- A 5.I M¡: = l0 kN, I kp/cm = I kN/m. Arrows show fheprimory foilure loods for fhe differenf tesfs.

8.4 THE CRACKED REINFORCED SHOTCRETE LAYER ACTING AS A CIRCULAR

MEMBRANË

The effect of the fwo-woy reinforcement is token into occount by osuming fhot it

octs os rodiol reinforcement with çocing equol fo c when r = r-. lt hos olso been

osumed thot it reoches some chorocterislic tension

o foilure sfress f-.b

The line lood [ ,-- which meons I ot membrone foilure cqn fhen be colculoted from' mþr

2,,; , " 2¡r = -o A, f^ sinv'mþr o c þ Þ

where A, is the oreq of one reinforcing bor ond Y is the slope of the membrone.b

AçThe line lood 5 , =

'O ,

't sin Yis thus independent of r-.¡-mbr c ' o

The ongle $ is defermined bY

try

tB over the distonce r to R ofo

sin g

Then

A¡'fg "n-=T;

lf, for exomple, AO = 0.5 lO-4 ^2 çg A¡,

fB = ó50 MPo, c = 0,2 m, es= 0.Q2 (2 "/")

; , = 32 kN/m < 40 kN/m' mbr

If insieod eU is 0.08 then

ñ.b. = ó0 kN/m > 40 kN/m

It is therefore of greot imporlonce fo hove on occurote volue of

embedded in concrete.

tB'+

P.br = c

€B

for bors

Pz

tlro I

P1

--Jz-.-.P2

without rein forcementwith reinforcement

200

tk Nl

150

P

100

50

0

ø9-'Sq{= 8cm

P2

P1

-o gc

99-q100

-

P¡PL

Ytsq--

0 0.5 1.0 1 5 20 iif'Theoreticolly colculoled primory (P,) ond secondory (Pr) foilure

loods for plone circulor sholcrete loyers. P, is colculoted both

for unreinforced shotcrete loyers ond reinforced ones.

f,. = ó.0 MPo, f , ô = 20 kN/m.bt od

Fig 8e

Yield strength of reinforcemenì = 500 MPo

Pz

+ tlro I

t.----.-}IP1

izP2

ry1Ð-

Ð

-¿

---

,g Ð --'¿'¿-

w it hout reínforcement

with reinf orcementP

[t N]

200

150

100

50

0

Pz

Pt$P2

P2

P2

L/a

to

\"

+¿¿ L-9þ -

200 0.5 1.0 1.5

^a*îf 'Theoreticolly colculoted primory (P,) ond secondory (Pr) foilure

loods for plone circulor shotcrete loyers. P, is colculoted both

for unreinforced shotcrete loyers ond reinforced ones.

fO, = ó.0 MPo, fo. . ô = 40 kN/m.

Yield strenglh of reinforcement = 500 MPq,

Fis Bd

il480

56

46

40

3ó

64

44

3t

26

22

20

0r5

t.0

2.0

3.0

4.0

5.0

gt0mm

ø8mm

ø6mm

Requiredreinforcementoreo

To

Areo ofmovingblock

2m

Cenfer distoncefor bor

0.ó

0.9

t.3l.ót.82.0

178

125

88

72

ó3

56

Toble 2 Required two-woy reinforcemerrt to mointoin plote effect for on 8 cm

plone shotcrete loyer. lt is ossumed lhof the shofcrete - rock interfoce

con corry o line lood which is 13.3 kN/m qffer the primory odhesion

foilure.

The foble shows thot it is possible to reinforce ogoinst downfoll of smoll blocks ond

thoÌ normolly used reinforcement is insufficient under the ossumed circumstonces.

ln Fig 8d - e curves for reinforced shotcrete ore plotted os o comporison wilh equi-

volenl curves for unreinforced shoTcrete. The curves show lhot commonly used omounts

of reinforcement ore normolly insufficient if plote oction is to be mointoined ofler

the odhesion foilure. The figures show, however, thot the qction of reinforcement

bors becomes more efficient ol bqd odhesion conditions.

Consider one sector element qs indicoted in Fig I c.

fot 2O

m'Rd9

rD¿=0

R.

Fig g c Sector element in the yield line onolys¡s

The reinforcement net is normolly ploced close to the rock surfqce. The lever orms

for the forces in the reinforcement ore therefore smoll where the bending co'rses

compression neoresf to the rock surfoce. The momenls of these forces become smoll,

too, ond ore ossumed to be zero in this simplified onolyeis. The equilibrium equo-

fion for the seclor elemenf becomes:

rdq+-J-

p ro

d9 (R - ro) m'Rd 9

which givesr

tn'= þ ro(r-fr)

It is interesting to investigqte if it is possible to puT in lhe omount of reinforcemenf

required by this eg'¡otion.

At, for exomple rO/R= 1/3, p = ¿O kN/m, h = 8 cm, l, = +OO MPo the

following reinforcement will be required for o circulor block.

o þ r6d9

P2

ln the following P. = 2 n ro LA. ô represenls the lood when lhe odhesion crock

forms. During fhe developmenf of the odhesion crock fhe lood ist

P =2 n r.+'f-.-,. ô ond especiollywhen theplore foils the lood isrJod

fo* ' h'

ln Fig 8d - e P' ond P, os functions of the block oreo A = t ,o2 ore given for lwo

commonly used thicknesses of the shotcrete layer, 4 ond 8 cm. Fig 8d represents very

good odhesion conditions ond Fig 8e represents foir odhesion conditions. lÌ con bee

eosily seen in these figures thot P, olwoys is much smoller Thon P' which meons thot

fhere is no redundonce in on unreinforced plone shotcrete lining.

8.3 THE CRACKED REINFORCED SHOTCRETE LAYER STUDIED WITH

THE YIELD LINE THEORY

The looding cose is the sqme os in Fig 8 o. The qssumed yield line pottern is

shown in Fig 8 b below.

f6

R

Fig 8 b Yield line pottern

8.2 THE UNCRACKED SHOTCRETE LAYER ACTING AS AN ISO|ROPIC

CIRCUI.AR PLATE

The looding cose is indicoted in Fig I o below

P

LOOSE

BLOCK

å*r16

FIRM ROCK

! uuIT wHERE ADHESION

i cnacr srABrlrzEsI

ln

Fig I o Looding cose for circulor plote.

ln Timoshenko's "Theory of Plotes on'C Shells" solutions ore given for fhis cose

The moximum .bending stress, a ¡ con be colculoled from the relotionship

KP

mqx hz

ln fhis equotion P is the opplied lood ot the cenfer of the rock piece ond k is o

conslont which hos been colculofed for differerrf rotios Ry'o. R is the rodius of

the circulor plote ond ro is the rqdius of the moving rock piece. Timoshenko gives

k for Poisson's rotio = 0.3, which is not olwoys quile correct for concrete. His

volues qre used here without ony corrections, however.

8. THE TWO-DIMENSlOl.lAL PLANE CASE - A THEORETICAL STUDY

8. I GENERAL REfuTARKS

The performed fests were one-dimensionol, since slrips of constont width were tested.

ln reolity fhe plone cose neorly olwoys is Ìwo-dimensionol , An odhesion crock oround

o single rock piece spreods more or less like o ring on o woter surfqce. Since the

periphery of the foilure zone grows lorger ond lorger the beoring copocity hoe to

increose since the foilure lood hos been found to be proportionol to the length of

the foilure zone. The odhesion crock hos to stobilize somewhere. It is of interesf

Io study o circulor concrele plote ond exomine which lood it con corry.

ln the following on otternpt will be mode to get on ideo of whot might hoppen ofter

fhe primory odhesion foilure.

Four coses cqn be distinguished:

o) An uncrocked circulor concrete plote corries the lood ofter the odhesion

crock hos srobilized.

b) A crocked reinforced circulor concrete ploïe corries the iood'

c) A circulor membrone corries the lood.

d) The reinforcement bors ore torn off ond the slob collopses.

ln the follorving onolysis fwo fundomentol ossumptions ore mode:

I) An odhesion crock forms when the distributed sheor force, þ, is +O kN/m '

The crock stobilizes when þ = 13.3 kNr/t. This osumption hos been empiricolly

confirmed by the tests, but is probobly not volid for oll rock moteriols.

2) The lood follows the movemenfs of the concrefe plote. This ossum¡:tion is

probobly not reotistic for oll rock loods, especiol ly ot lorge deformcrtions.

Closp used in Tests A 4 ond 45. (The FortF closp )

Reinforcemenf used in TesÌ A 5.

Test specimen A 5 ofter foilure.

Cloç used in Tesf A 3

Test specimen A 3 ofter foilure.

3 PROVN I NG

Dragprovnìngarna utfördes i en MTS provningsmaskin vid FOA, Ursvik.

Armerìngsstängerna fästes i provningsmaskinen med hydrauliska kläm-

backar, som eliminerar glidnìng i infästnìngen. Härigenom kunde

provningsmaskinens inbyggda ìägesgivare användas för töiningsmät-

ni ngen.

Styrprogrammet, som var utarbetat av ./ Et"iksson, FoA, medgav atttöjningshastigheten kunde hållas 1åg under provets första skede,

för att sedan successivt ökas inom ett övergångsområde upp till en

högre nivå inom det senare skedet.

Vìd prov l-12 och lT-20 och tillhörande kontrollprov var töjnìngs-hastigheten L = q.ll'lO-5 l/s upp tiìl bedömd sträckgräns varefterden långsamt ökades till 3.13'lO-4 |/s. Vid prov .l32-162

med kontroll-prov som utfördes vid ett senare tiIIfälIe var motsvarande töjnings-hastìgheter 2.50'10-5 l/s respektive 1.67'lo-4 l/s.

Detta innebar att sträckgränsen uppnåddes på 45 s vid prov l-8, på

65 s vid prov 9-12, på 95 s vìd prov 13?-162 och på 35 s vìd prov

17 -20.

Under provningens gång registrerades kraft och ìängdändrìng konti-

nuerìigt på en x-y-skrivare.

4 PROVN I NGSRE SU LTAT

4. I Betongens hål I fasthetsvärden

Kubhållfastheten för betongen vid prov l-12 och 17-20 var 31.2 MPa

Draghållfastheten var l.B MPa. Det skall dock erinras om att den

använda provningsmetoden för draghållfasthet rymmer stora felmõi-'l iqheter. Kubhållfastheten för sprutbetongen vid prov 132-162 var

40.9 MPa och dess böidraghållfasthet var B'5 l4Pa.

Ð+

'I .0

1.0

0 .44

0.44'l .0'I .0

0.3'l

0. 31

1.0't .0

0.31

0.31

0. 93

0. 93

0.28

0.28

1.0'I .0

0. 3l

0,31

deoø80ø 120

ú 120

ü 120

ø 120

ø 216

ø ?16

ú 120

d 120

ø 216

ø ?16

tl 30x 1 00

n 30x100

Ü 00x'100

Dl00x l00

ø 120

ø 120

ø 216

ø 216

1

2

2

4

5

6

7

o

9

10

tl12

132

142

152

162

17

l8'19

20

ú8ú8dgø8ø12ø12ø12ø12ø12ø12ø12ú12ø6óaø6ø6ø12ø12ø12ø12

Ss 26

Nps 50

Ks 60

Ks 40

il

s prutbetongålder l0 d.

utgår p.g.a.skada

nr

ProvArmerì ngs -procent

lo

Betong-

tvärsni ttlrr]

Armerì ngs -kval i tet

Armeri ngs-

stång

lttlAnm

Tabell I Sammanställnìng av armeringskvalitet, stångdìameter,provkroppstvärsnitt och armeringsprocent.

Kind of reinforcement, bar diøneter" cross section ofthe test specimen, percenta.ge of z'einforcemenl;.Tests 732-162 uev,e made uíth shotcrel;e al; an ageof 10 dags.

SPl9!Þ9!ons

H3LI,

Provkropp 132 och 142

t'",il

100

Provkropp 152 och 162

Fig 2a Provkroppar

Teet speeimens

Sprutbetongens tryckhållfasthet provades med tre utsågade I cm

kuber.

Sprutbetongens böjdraghållfasthet provades ned två oarmerade böj-balkar 40 x 8 x 8 cm belastade med punktlaster i tredjedelspunkterna

ã---1

I

PROBLEMSTALLN ING

För att kunna bedöma en armerad betongkonstruktions verkningssätt

vid överpåverkan (vapenlast, ras' påkörning etc.) är det av stor

betydelse att känna til'l den energìupptagande förmågan i konstruk-

ti onen.

Vad beträffar armeringen föreligger veterlìgt endast ett mindre

försöksmaterial avseende brottfö11ängningen hos icke betongingjutna

armerìngsstänger av större 1ängd än mätområdet vid standarddragprov.

För ingjutna armerìngsstänger saknas j stort grund1äggande data

beträffande brottförlängning. Föreliggande begränsade, experimen*

telIa undersökning syftar ti'l I att visa hur o-e-dìagrammet för en

'lång (längd >> l0'da) armeringsstång påverkas av krìnggjutning av

betong i ett renodlat dragförsök.

? P ROV KROPPAR

20 st provkroppar enligt fig 2a och tabell I tì'llverkades' Vid

prov l-ì2 och l7-20 bestod provkroppen av en rak armeringsstång

centrìskt ingjuten i en 800 mm lång, cirkulär betongcylinder' Vid

prov l32-.l62 bestod provkroppen av en stång kììppt ur ett nät med

20 cm maskvidd. Härvid kvarlämnades l0 cm långa tvärpìnnar' Nät-

strimlan sprutades in med sprutbetong så att en provkropp med rek-

tangulärt tvärsnjtt erhöl ls. Tvärsnittsdimension och ingående arme-

ring i de olika provkropparna framgår av tabe'lI ì'

Till varie huvudprov uttogs ett armeringsprov ur samma stång utom

vìd nätproven. Kontrollproverna vid nätproven bestod av två nät-

strimlor klippta ur samma nät som stängerna till huvudproven'

Betongens tryckhållfasthet provades med fyra normenliga kuber

Betongens draghåìlfasthet uppskattades med hiälp av tre lossdrag-

nìngsprov av 42 mm kärnor som borrades ur kuber'

Beteckn i nqar

Au area hos armeringsstång

Ab area hos betongtvärsnitt

du stångd i ameter

db diameter hos betongcYl inder

e rel at'iv för'l ängnì ng hos provkropp

.B re1. förlängning vìd brott

å = deldt rel. förlängnìng per tidsenhet

o dragkraft/nomineìl stångarea

oB o vid brott

u armeringsarea/betongarea

Notati ons

Au area of reinforcement bar

Ab area of concrete cross section

da bar diameter

db diameter of concrete cyl inder

e relative eìongation of test specimen

.B e at failure

é = deldt Ê per time unit

o tension force/nominal bar area

oB o at fai lure

u reinforcement area/concrete area

['2]

['2]

[**l

Irr]

l%)

l%)

Ir lsl

Iuna]

Iuna]I

"t1lh)

['2]

I'Il*rl

lnr]

l%l

l%l

[ru']

lueal

lMPal

l%l

INNTHALLSFCIRTICKN ING

Beteckni ngar

Notati ons

I PROBLEþISTALLNING

2 PROVKROPPAR

3 PROVNING

4 PROVNINGSRESULTAT

4.1 Betongens hållfasthetsvärden

4.2 Spnickbi Idning

4.3 Spännings- töjningsdiagram

5 LINVTRKAN VID BALK AVIRKAD AV PUNKTLAST PA

MITTTN. EXEMPIL

6 SAMMANFATTNING

7 SUMMARY

Referens

2

¿

5

5

5

7

7

12

l5

l6

17

Förord

Föreliggande undersökning har utförts vid Institutionen förByggnadsstatik, KTH, med anslag från Civìlförsvarsstyrelsen,Fortifìkationsförvaltningen och Stiftelsen Bergteknisk Forsk-

ning. Behjälp1ìga vìd utförande och redovisnìng har varitB AhLgren, E Ask, B y\arLstvön och r waLL vid institutionensamt ./ Ev"iksson och E Wermqoíst uid Försvarets Forsknings-

ansta l t.

Stockholm 1975-06-.l3

Jonas Holmgren

DIFORMATIONER HOS INGJUTNA ARMERINGSSTANGER

AV

Jonas Holmgren

MTDDELANDT NR I]4INSTITUTIONTN FUR BYGGNADSSTATIK

KUNGL TEKNISKA HUGSKOLAN

STOCKHOLM I975

/2/

/3/

/4/

/s/

/6/

n/

/8/

/e/

/10/

/11 /

BIEËBINçTI

Rotter, E. ,'spritzbeton und seine proktische Anwendung im Unlerlogebou".

Berg- und Hüttenmönnische Monotshefte, Jg. l0ó (19ól)25/6, pp. 152-165'

Al berTs, C. "Bergförstörkning genom betongsprutnìng och in[ektering. " IVA-

meddelonde 142, Stockholm 1965, pp. 23ì-238.

Ösïlund, L, "Undersökningor röronde sprutbetong" (lnvestigotìons of gunite),

English summory. Nordisk Betong (1961):4, pp. 401'420.

Söllström, S.',Hôllfosthetstillvöxten hos spruTbeiong med occelereronde

tillsotsmedel". IVA-ropport 4, Stockholm l9ó8, pp' 143-'l58.

Poiiörvi, H. ,'Kvolitetskontroll ov sprutbetong iFinlond". Nordisk Betong

(1973):5, pp. 3-9.

Borbo, F. Kontor for fiellsprengningsteknikk och den Norske lngeni/rforening

Förelösning, Oslo l9ó4.

v. Robcewicz, L, "Die hol bsteÌfe schole ols Mittel zur empirisch -wissen-

schqftlichen Bemessung von Hohlroumboulen"' Rock Mechonics, Suppl' l,

l%0, pp.58-ó8.

Detzlhofer, H. ,'Erfohrungen bei der sicherung von stollenousbrÜchen in

gebröchen und druckhoften Gebirgsstrecken". Rock Mechonics, Suppl' l,

1970, pp.69-86.

v. Robcewicz, L. & Golser, J. "Princìples of dimensioning the supporting

system for the New Austriqn tunnelling method ". Woter Power, Morch

1973, pp.83-93.

Linder, R. "spritzbeton im Felshohlroumbou". Die Boutechnik, Jg. 40

(19ó3):10, pp. 32ó-331; Jg. 40 (19ó3):ll, pp. 383-388'

Kinnunen, s, & Nylonder, H. ',Punching of concrete slobs without sheor

reinforcement". Tronsqctions of the Royol lnstitute of Technology, Stockholm,

No. l58, l9ó0.

") Conventionol reinforcement nets close fo fhe íirst loyer of shofcrefe ore of

little or no volue even if they ore combined with o reinforcemenl coge oround

the rock bolt. The tests showed fhot the reinforcement must be'designed os

for ordinory reinforced concrete members ond be combined with o proper rein-

forcement coge oround the rock bolt.

d) Some fheoreficol considerofions indicote thot the reserve strengfh (residuol

strength) is lower thon the strength of the primory odhesion foilure for conven-

tionolly reinforced shotcrete.

e) Some tests with occeleroting odmixtures for shotcrefe show certoin undesiroble

effects which hove to be exomined more closely.

IO. NEED OF FURTHER RESEARCH

o) lt is quite noturol to invesfigote olso curved shofcrefe loyers since only plone

shotcrete loyers were studied in this investigotion. The odhesíon strength will

probobly be importonf for the primory foilure olso for lhese tests but Ìhe

progressive development of the foilure hos to be studied.

b) lt is qlso desiroble to moke o systemotic study of the odhesion slrength for

different minerols since this foctor hos o decisive influence on the sfructurol

behoviour of shotcrete.

c) The effects of the occelerofing odmixtures hove lo be closer exornined.

Fiber reinforced shotcrete in combinotion with rock bolts might olso be worfh

while to study. A lot of money con be soved if the bor reinforcemenf con

be obolished.

Some preporotory tests by the Author hove shown, lhot eu for bors surrounded by

concrete moy be 1/3 to l/2 e, for free bors. The investigoted bors were 8 mm

,jeformed bors ond 5 mm bors from reinforcement nets. The bors from the reinforce-

ment nefs hod 100 mm pieces of the tronsverse bors left. The bors were surrounded

by 145 mm concrele cylinders. The length of the test specimens wos 800 mm. lt

wos olso found out thot e, tor reinforcement nets could be so smol I os 0.5 %'

For o reinforcement nef:

-LtA¡ = o.zg lo-- m', f, = óoo MPo, c = o'l m

e ^ = 0.005b

; , = 16.7 kN/m <40 kN/m'mþr

This indicotes thot reinforcement nets ore more unrelioble thon loose bors

9. SUMMTARY

ln this poper there ore described l8 lorge scole tests on plone shotcrete loyers in

combinotion with rock blocks. The oge of the concrete ond fhe loyer Ìhickness

were voried.

For five of Ìhe test specimens the influence of the reinforcement orrongement ond

fhe rock bolts wos investigoted.

The following mqin conclusions were drown

o) For fhe unreinforced plone shofcrete loyer foilure wos olwoys due to odhesion

foilure olong the shotcrete - rock interfoce. The foilure lood wqs indepen-

dent of the loyer thickness within the intervol 2-8 cm. For good rock moteriols,

however, the foilure lood is rolher high. A plone shotcrete loyer corries o

rock cylinder with one squore meter bose oreo ond five melers height.

b) After lhe primory odhesion foilure the lood dropped fo one third the primory

foilure lood or less. The odhesion crock propogoted olong the rock surfoce

until bending foilure tock ploce in the shotcrete'

Vid armerìngsstänger ur nät Nps 50 d 6 och u = 0.93 % var er2/3tìll l/3 av e, för frìa stänger. Vìd p = 0.28 % var eU omkring ì/6av eU för fria stänger. eU för fria stänger Nps 50 Ø 6 uar 6 %.

Vid släta stänger (Ss 26, I ì2) skiljde sìg et vid ingjutna stänger

inte från e, vìd fria stänger p.g.a. att tvärkontraktionen hos

stängerna var så stor att all samverkan mellan stål och betong upp-

hörde. Efter brott hade stångdiametern minskat till ll mm. eU förSs 26 d l2 var 20-25 %.

Vid samtlìga prov med ingiutna stänger, men särskilt vid större

betongarea, erhölls större last v'id fördelad töining lika med

sträckgränstöjning för fri stång än vad som svarar mot sträckgräns

multìpìicerad med stångarea. Förklaringen torde vara att armerìngs-

stången vìd uppsprìckningen lokalt kommer upp ì konsoliderìngs-

området ìntill sprickorna, medan lasten mellan sprickorna tas av

armering och betong i samverkan. Detta har säkerìigen stor betydelse

vi d böjnì ng av betongbal k med I i ten armeri ngsmängd.

Vid snabba förlopp, såsont vid vapenlaster, påkörning o.d., torde

ovannämnda effekt kunna påräknas. I'lan kan då sannolikt utgå ìfrånatt momentupptagande förnlågan blir större än vad som anges av

sträckgränskraft i armerìng multiplicerad med inre hävarm' Huru-

vida fenomenet uppträder vìd långvarig beìastning är inte utretti och med denna undersöknìng. Det förefaller emellertid inteosannolikt att viss krypning och uppspricknìng i den betong sont

omger armerìngsstångens kammar närmast int'ill en spricka skulle

kunna ge större töjningsvärden vid långtidsprovning än vid denna

undersökni ng.

6MPd

dMPo Ao '0,28'10-¿

A¡'30'10¿4o.0,28'1da

-LAr" 30'10

@

Ao'0,28 t04

A¡'100 10a

@

@

dMPo Ao - 0,28 10

4

A¡= 100 '10-a

oMPo

500

@

dMPo Ao'0,28 '10-a

A¡"0

gMPo

Ao . 0,28 t0 a

At- o

Fiq 4e o-e-diaqram för stänger ur nät Nps 50 I 6 omgìvna av sprut-s betong ðamt tillhörañde kontroìlstänger. Aa = stångarea'Ab = tptutbttongarea'Stress-strain reLationshíp for bars from reinfot'eement netsNps 50 ó 6 sut:rounded by Áhotcrete artd the corz'espondíngiontroL bat's, Aa z aret of the bat', Ab = aYea of thesurroundíng shotcrete.

120

@

gMPo

qMPo

d¡ '1200

o

@ @

î,%

o-e-diagram för ìngjutna stänger Ks 60 d l2 och tillhörandekontrollstänger. d5 = betongcylinderns djameter.

Stt ess-sty,ain relatíonship for deformed z'eínforcenent barsKs 60 ó 72 su.t'rotmde.d by concrete artd the coz'r'espondíngcontroL bars, d6 = díønetet: of the conct'ete eylínder,

Ø

dMPod¡

0a

MPo216

Fig 4c

ûMPo

0

o

db

" 216

@0

Fia 4d o-c-diaqram för ingjutna stänger Ss 26 d l2 och tillhörande--:-¿i kontrolístänger' du = betongcyl inderns diameter'

Stress-strain reLationshíp for smooth baz's Ss 26 ø 12 and

the co:nrespon&ing conl;roL bars' db = d'íameten of l;he conerel:e

cylinder.

d ØdMPoo

d¡ d¡'80

d¡- 160

.0

d¡"0

ód

d¡'160

o

o

d¡-0

d¡'0

d¡'0

d¡' o

e

@

@daMPd

¿%

dt" 120 d 0 d¡''120

@g

MPoodMPo

d¡ =216 d¡ '216

Fig 4b o-e-diagram för ingiutna stänger Ks 40 och til lhörande kontrol l-stänger. Vid försök l-4 var d" = B, vid försök 5-8 var d¿.= 12'

da = armeringsstångens diametðr, d5 = betongscylinderns dìa-meter i mm.

Stress-slx:aín relationship for defoz:ned reínforcenenl: bans Ks 40

suz'v'ounded by concrete or¿d the coz'r'espondíng controL bars' Attests 7-4 da = B' at tests 5-8 da = ,12. .do = &ícrnel;et' of the bat',db = dianetèz' of the concrete cyLinder in ntm.

4.2 Spri ckbi1dn'i ng

Några sprìckbilder redovisas i fig 4a. Den för ögat synliga uppsprick-

ningen började oftast vid last motsvarande armeringens sträckgräns.

vid stornrängd omgìvande betong erhöìls ett fåtal sprickor, vìd liten

mängd var antalet sprìckor större. vìd provnìng av betongìnsprutade

nätstr.imlor uppstod de första sprickorna vid armeringens tvärpinnar.

Vjd brott var sprìckbredderna av storleksordningen cm.

4.3 Spännìngs-töiningsdiagram

I fig 4b-e redovisas o-e-dìagram för de ìngjutna provkropparna

med til lhörande kontrollstänger. o är beräknat såsom registrerad'last divìderad med nominelì stångarea och e är total förìängning

hos provkr"oppen dìviderad med provkroppens ursprunglìga längd

(800 mm).

Trots kraftig uppsprìckning ì många fall inverkade betongìngjut-

ningen avsevärt på brottför1ängningen (eg). Vìd armerìngsstänger

Ks 40 d I minskade eU ti1ì 0.6 à 0.35 av e, för fria stänger' Den

större minsknìngen hänför sìg tììl större mängd (u = 0'44%) omgi-

vande betong.

Vid Ks 40 ø 12 var minsknìngen av eU vìd 1ìten mängd (u = I %) om-

gìvande betong mindre än vid ó B, förmodligen beroende på sämre

effektivìtet hos kammarna vid denna stångdìameter. vid den större

mängden omgivande betong var eB ungefär densamma vid 6 12 (u = 0'31)

som vid d e (u = 0.44 %)' ES för frìa stänger Ks 40 var vid d I17-19% och vid ó 12 14-16%.

Vid armeringsstänger Ks 60 d l2 reducerades et tì1ì omkring 3/4 av

eu för fria stänger vìd v = l%' Vid u = 0'3ì% var et för ingjutna

stänger omkrìng 0.6 av e, för fnia stänger. et för fria stänger

Ks 60 d 12 var 13-14%.

q

6

4

3

-{

4

3

I7

Fi9 4a Sprìckbi'lder. Provkroppar 2, 3, 6, 7, 9, 1 1, 17, 132och 142. Siffror vid sprickor anger ordnìngsfijlid.Cz,ack patterns, Test specinens 2, 3, 6, 7, 9, 77, 17,732 artd 142, Fígures at; the cracks indícate order ofqppeatance.

I

CONTENTS

NOTATIONS

r. tNi3op-uçuaN_

2. LOADING CASE AND SU

3, TEST RIG AND TEST SP

3.I MAIN TESTS

3.2 CONTROL TESTS

3.21 Testing of the compressíve slrength

3.22 Tesring of the flexurol strength

3.23 Testing of the tensile odhesion strenglh

4. MTXTNG OF CONCRETL S

5. ^4EASUSEMENIå

6.

ó.I ARCHES WITHOUT END SUPPORTS

6.2 ARCHES WITH END SUPPORTS

7, STRESS SITUATION AT SHOTCREIED ROCK JOINTS STUDIED BY

7.1

7.2

7.3

7.31

7.32

7.33

7.4

7.41

IHE-aSLALru.ryINTRODUCTION

FE-MESH AND METHOD OF EVALUATION

FORCE INCLINED TO THE ROCK SURFACE

lnfluence of different moduli of elosticity

lnfluence of different FE-meshs

lnfluence of the force inclinotion

FORCE PARALLELL TO THE ROCK SURFACE

Generol remorks

FORT IF IKAI I()N5F()KVAL I N INþENForskn ingsbyrån

CURVED SHOTCRE'TE LAYERS SUBJECTED TO PUNCH LOADS

by

Jonos Holmgren

Kopporl nr rrr:fFortt/F dnr 901 F

1C79-01-24

A simple example shows that suspens'ion action and membrane action

can take a lot more energy than beams and pìates in bending. The

exampìe ìs strongly simplified but shows all the same that these

actions should be regarded when desìgnìng a structure which might

be subjected to extreme loads of disastrous character.

REFERENS

Bír,ke, H: "Kupoleffekt vid betongpìattor". Meddeiande nr 'l0B frånInstitutionen för Byggnadsstatik' Kungl Teknìska Högskolan,Stockholm

.l975.

7 SUI,IMARY

l9 tension tests on reinforcement bars surrounded by concrete were

made. The stress-strain relationship for bars of 800 mm length was

registered for the cast-in bars as weìl as for the correspondìng

control bars.

The loading veìocity was very low compared with the velocities used

ìn rapid tests with steel. 0n the other hand the velocity lvas not

low if the time-dependent characteristics of concrete are taken into

considerati on.

At deformed bars and bars from reinforcement nets the failure straindecreased when the bar was surrounded by concrete. The failure strajnwas dependent on the bar diameter and the amount of surrounding con-

crete. When the bar diameter increased the fa.ilure strain increased

if the reinforcement percentage was kept constant. [^lhen the rein-forcement percentage decreased the failure strain decreased.

At smooth bars the bond between steel and concrete dìsappeared

totally at ìarge strains even at small reinforcement percentages

At strains corresponding to the yield ìnterval for free bars the

load was higher for cast-in bars than for free bars. The explanatìon

is probably that the steel localìy at the cracks reaches the strainhardenìng stress. Between the cracks the load is carried by the

steel and the concrete together at lower stress and strain levels.Thìs phenomena did not appear at smooth bars.

tlhen desìgning concrete members for disaster loads the failurestrain can be put equaì to B % for deformed bars. If smooth bars

are used the failure strain can be put equaì to lB to 20 %.

Reinforcement nets are unreliabìe in th'is respect. At pre-tests forthis investigation a net was found that had a failure strajn of only

ì.5 % for a free bar and 0.4 1l for a cast-in bar. Since nets according

to code requìrements shall have a failure straìn of at least 3 % the

failure strain for cast-in nets mjght be put equaì to I %.

6 SAMMANFATTN I NG

l9 dragprovnìngar av armerìngsstänger omgivna av betong utfördes.o-e-diagram för 800 mm mätlängd registrerades för de betongingjutnastängerna l iksom även för motsvarande oìngjutna kontrolìstänger.

Beìastningshastigheten var mycket 1åg jämfört med vad som brukar anses

vara snabba försök med stålmaterial. Däremot kan den inte anses vara

låg vid beaktande av betongs tìdsberoende egenskaper.

Vid kamfõrsedd armering samt nät minskade brottöjnìngen när stången varìngjuten i betong. Brottöjnìngen var beroende av stångdiameter och

mängden ongìvande betong. Vid ökande stångdìameter blev brottöjningenstörre än vid mindre stångdìameter och samma armerìngsprocent. Vid

ökande mängd omgìvande betong minskade brottöjnìngen.

Vid släta stänger upphörde samverkan mellan stål och betong fuì1ständìgtvid stora töjnìngar oberoende av mängden omgivande betong. Vìd töjnìnomotsvarande sträckgränsområde för icke ìngjuten armering var lasten vidìngjuten armering högre än vid icke ìngjuten armering, vilket förklarasav att stålet lokalt vìd sprickorna kommer upp i konsoììderìngsspänning

medan lasten tas av stål och betong i samverkan meìlan sprìckorna. Dettafenomen uppträdde ìnte vid släta stänger.

V.id dimensjonering med avseende på överpåverkan kan brottöjningen förìngjutna kamstål sättas till B %. Vid sìäta stänger kan brottöjningarupp tiìI lB à 20 % utnyttjas.

Nät bör användas med försjktìghet såsom energìupptagande element i be-

tongkonstrukti oner. Brottöjnì ngen kan varj era starkt, exempeì vj s erhöl'l s

för en ìngjuten nätstång en brottöjnìng på endast 0.4 % vid förprovningartill denna undersökning. Detta värde gä1lde ett nät med fri brottöjningpå endast 1.5 % vilket är'lägre än normerat värde 3 %. 0m nät används som

energiupptagande armering bör brottöjningen ej sättas högre än ì %.

I ett enkelt exempeì visas att lin- och membranverkan hos ba1kar och

piattor är väsentlig att söka utnyttja vid konstruktioner sonl kan ut-sättas för överpåverkan. Dessa effekter kan ge större bidraq tillenergì upptagni ngen än ba'l k- och pì attverkan.

I fìg 5b redovisas last-nedböjningskurva dels för en lina bestående

av en ìngjuten armeringsstång med o-e-diagram enligt prov B, deìs

för en ljna bestående av en icke ingjuten stång med samma o-e-dia-gram som kontrolìprovet tìII prov 8. (Se fig 4b).

Av fìguren framgår att den procentuella skjllnaden i lastupptagande

förmåga vid viss nedböjning är stor (ända upp till 25 %) melìan en

ingjuten och en ìcke ìngjuten lina i töjnìngsomrâdel 1/2 - 2 %.

PKN

80

Bro

du=

20

0

lt

s

ql 0,2 0,3

Fig 5b Last-nedböjnìngskurvor för lina av ìngjuten (d5 = 2.l6)resp icke ìngjuten (d¡ = 0) armeringsstång þ 12 Ks 40 medo-r-diagram enligt fig 4b, prov B med kontrollprov,Load-defLection cuv.ues at suspensíon act¡,on of etbedded(d6 = 2161 and non-ernbedded (d6 . 0) bat's d 12 Ks 40 ?n¿thstv.ess-stz,aín z:elationships according to fíg 4b, tests B,

P

Fig 5a

/.0

30 =10

20

P

t

15

05

10

Ao = 1,0 cm2

10

15

Ao = 0,5 cm2

t

.16,710

0,01

01

0,'l

Exempel. Till vänster i diagrammet last-nedböjningskurvorerhållna från försök av Birke ll I ned armerade modellbalkar.I diagrammet har inlagts beräknade last-nedböjnìngskurvorvid l inverkan hos armerinçn lgIãã'erade med för'l ängnìng e) .

Antaget, förenklat o-e-dìagram för det ingjutna stålet visasì fì9.Eæample. To the Left Load-deflection curues fz,om tests byBirke lll on reínfov,ced modeL beans. The fígure aTso shouscaLcuLated Load-defLection cuyües assuming suspension actionof the t'einforcement, The stt'ain e is shoun, The assumed,'ídealized stz'ess-strain relatíonship for the embedded baris also shoun.

7

00 v

5 LINVERKAN VID BALK AVERKAD AV PUNKTLAST PA MITTEN. EXEMPEL

Vid sådan förankring av underkantsarmeringen att horisonteìl drag-

kraft vid balkunpìag kan upptas, torde förutsättningar för lin-verkan hos armeringen i ett sent brottskede föreligga. Balk med

punktìast på mitten studeras under förutsättning enligt ovan.

Vid Iinverkan är sambandet melIan Iast P och förlängning av arme-

rì ngen :

,t z'o _ - .n 2 /2e + e-. _ ,B ^a fi_llu *]

där o, är brottspännìng för armerìngen, för enkelhets skull förut-satt konstant över hela töjnìngsområdet. Au är armerìngens area

och e är förde]ad töjning över armeringens he'la längd. Härledning-

arna är gjorda under antagande av rätlinjìgt ökande nedböjning

från upplag till balkmitt. Det förutsätts även att töjningen, e,

är jämnt fördelad från upplag tiì l balkmjtt.

Mittnedböjningen y erhål ls ur

Sambanden enligt ovan har tillämpats på ett exempeì i fig 5a. Där

visas last-nedböiningskurvor för fyra armerade model lbalkar provade

av Birke ftl. t samma diagram är inrjtade beräknade ìast-nedböjnìngs-

kurvor för armeringen under förutsättning av linverkan. Exemplet vì-sar tydligt att stora vinster beträffande energiupptagande förmåga

hos balkar och plattor är att göra om konstruktionerna utformas med

målsättningen att i möjììgaste mån nyttìggöra lin- eller membranverkan.

Det skall dock påpekas att exempìet är 'idealiserat såtillvida attdet förutsatts att förhållandena vid dragprov med centriskt ingiuten

armeringsstång är dìrekt överförbara t.ill det studerade fallet.

y_lT-Z

2Ê/2¿ +

0,30

0,45

0,46

0,47

0,55

0,37

0,34

8r8'l0,8

I ó,3

17 ,6

14,3

15,2

t 3,0

350

485

6s2

705

571

1212

r 039

305

418

579

621

496

1046

877

vlx2450

300 0

335 x

2g3 x

ó]3 0

5570

29,6

23,9

35,4

37,2

26,1

40,9

38, I

4,5

4

4

4

IB

4t0

ilt2

l3

14

l5

tó

anom

c

onom

MPoir

tf

kN/m

6f

kN/m

pf

kN/m

fc

MPo

tcm

Testno

Toble 3

Uncrock -ed stote

Prirmry foiture[ood

Foilure loqds ot Tests I0-lóRemorks

x Buckling of middle port.

o Sh"ol- foilure.

P

Secondory foítureIood

Middl.eslob

w

Outer stob

:Hw,lPAdhesion crocking

wwSheor crocking

Principol lood-displocement curve ond foilure modes for shot-

crete orch with end supports.

Fig ó c

ln Tests 10, 13, t4 ond 15 the odhesion crock spreod to the horizontol

port of the shotcrele loyer ond the whole orch turned free from the rock

blocks, At the 4 cm-tesls lhis leod ro buckling of the horizontol port.

ln Tests ll,12, 15 qnd ló the foílure wos o sheqr foilure becouse of

high compressive stresses in the "leg" of the shotcrete orch. See fig óc.

The most imporlont test results ore shown in Tobles 2 ond 3.

Toble 2 Adhesion foilure loods for differenl porÌs of the test specimen

Tests l0-ló.

0,58

0,59

0,43

0,22

0,27

0,20

0,24

t7l24s

300

335

283

ó13

557

r00

145

130

75

75

125

r35

t00

t20

210

315

r00

tó5

r40

75

75

125

135

4

4,

4

4

4

8

8

5

l0

ilt2

t3

t4

l5

ló

Pf od, min

Þ¡

Pf

kN/mRìghtside

Middleblock

Leftside

Verticol lood ot odhesionfoilure

Þf,od kN/mtcm

Testno

Þ

[t ruzn!

error in the verticql force is +5% ond in the horizontol force -5% the

error ín the eccentricity will be obout 2 cm.

The tesl resulls show, however, lhot the corried verticol line lood, þ,

is highly influenced by the horizontol line lood, ñ, ol the ioint (Fig ób).

25

o t= 4cmx t=8cm

9

t

200

100

7 --'X\)/'t'xg

v6r

p= +h/3

o1,2

4po

0100 200 300 4oo ñ [rruzm]

Fig ób Applied verticol line lood, pç, ot foilure, os o function of the

correspondîng horizontol line lood, hr. Tests 'l-9. When plotting

the volues for Test specimens no I ond I their low odhesion

strengths hos been occounled for by proportioning the foilure volues

6.2 ARCHES WITH END SUPPORTS

The ìests were corrîed out in the some woy os the tests wiTh orches wilh-

out end supports.

,At the some lood levels os in Tests I -9 on odhesion foilure took ploce ol

one of the ioints. The odhesion crock propogoted oll the woy to the end

supporl. After lhol the lood could be increosed ogoin. At o somewhot high-

er lood level on odhesion crock developed qt the other ioint.

0

2.3

0.4

4.1

1.7

- t.8

-0.2

20

20

5

ló

0

I

9

-l

28

40

102

62

142

176

107

187

24

35

89

54

124

t54

94

164

r.3

2.0

LI2.0

t.92.0

1.9

t.3l.ó

8.2

12.8

8.8

9.7

8.ó

4.6

7.1

8.4

8.0

33. r

59.2

28.l

30. 3

u.l30. 0

44.s

45. I

46.9

4

4

4

4

4

4

III

Ì

2

3

4

5

6

7

I9

e

cm

B

o

pf

kN/m

Pr

kNfeclion

fõd

MPo

fu,

MPo

fc

MPo

Loyerthickness

cm

Test

Toble l Moin tesl results for shotcrete orches without end supports

þ ond e ore defined in chopter ó,1.

The ongle g in Toble I is colculoted os orcton (V/H)-25o where V qnd

H ore the verticol ond horizontol forces ot foilure. p thus represents

lhe ongle between the resultont support force ond the inclined, lined

rock surfoce. See olso Fîg 7g, p 23. The eccentricity, e, is then col-

culoted from the volue of p ond geometricql dolo for the test rig.

ln Tests I qnd 2 the rock blocks portly rested on their supports by mis-

toke during the whole lest. The meosurement of the reoction forces then

become erroneous ond the ongle B could only be iudged to be less thon

2oo.

The test resulls show thot some voriotion of the ongle B hos been ob-

loined, The colculoled volues of the eccentricily, e, however, ore in

some coses lorger thon the moximum eccentricities obtoined from colcu-

lotions ossuming o lineor stress distribution over the shotcrete section ond

moteriol strengths equol lo those obtoined from control tesfs' One explono-

tion is thot the colculoted volue of the eccentricity is very sensilive to

smoll errors in the meosured forces in the steel bors. For instonce if the

P

From thot on lhe lood wos increosed obout 8 kN in eoch siep. V/hile

the lood wos kept constont in eoch step gouge reodings were token.

The foilure wos olwoys sudden, ll wos olwoys o spolling foilure of the

shotcrete loyer from one of the fixed blocks. See Fig óo.

There wos no cleor indicotion thot the thickness of the loyer influenced

lhe corrying copocity.

ln Toble I the most importont test results ore shown.

Foiture lood

Míddl.estob Outer slob

tP :

iUncrock-, Adhes¡on crocking'ed stote '

Fíg óo Principol lood-displocemenl curve qnd foilure mode for

shotcrete qrch without end supports,

wffi

5

4. MIXING OF CONCRFTE,

Stondord cement ond grovel (0-8 mm) were used for the concrete. The

weight rotio wos t:4.5. The omount of woter odded to the shotcrete

wos reguloled by the nozzlemon ond wos normolly kepl ot o procticol

minimum.

The specimens were normolly shotcreted in two loyers. The second

loyer wos opplied obour three hours ofter the first one.

MIASUßIMINII

The lood wos opplied through hydroulic [ocks ond meqsured by o mono-

meter which wos connected to the hydroulic system. The iocks ond

the some monometer were colibroted in o loborotory testing mochine,

The reoction forces in the steel bqrs were meosured with stroin gouges

coupled os o full brîdge. The evolution of lhe stroins wos done by reod-

îng the unbolonce of the gouge bridge on o digitol voltmeter with o

sensitivity of 0.01 mV. The steel bors were colibroted in o loborotory

tesring mochine togelher with the some voltmeter ond conslont-voltoge

source.

ln Tests l3-ló the verticol displocemenl belween the fixed rock blocks

ond the looded one wqs meosured with diol gouges with o sensiTivity

of 0.01 mm.

6. TEST DESCRIPTIONS AND TEST RESULTS

6.1 ARCHES WITHOUT END SUPPORTS

At the beginning of eoch test zero reodings were token, Then the horizon-

tol sleel bors were tensioned lo oboul 3 kN while the rock blocks were

still resting on their supports. Then the lood wos increosed to obout 40 kN

- q level corresponding to four times the weight of the rock blocks ond

the shotcrete.

3.2 CONTROL TESTS

A flot box 45 x 45 cm with the height equol to the thickness of the

shotcrete in the moÌn tesl wos shotcreted ond stored together with

the moin test specimen. On the testing doy cubes ond beoms were

sowed out of this shotcrete plote.

3.21 Testing of the compressive strenglh

The 8 cm cubes were investigoted in o L0 MN testing mochine, A

mechonicol force gouge wos put înto the testing mochine when the 4

cm cubes were tesled. The compressive strengths presented in this re-

port ore the meon volues of three cubes, No correcTion for the size

of the cube wos mode.

3.22 Testing of the flexurol strength

The spon length of the investigoted beoms wos 40 cm. A two point

looding system wos used. The loods were opplied ot fhe third points,

The cross section wos squore ond the side length wos equol to lhe

thickness of the shotcrete loyer in the moin specimen.

The flexurol slrengths given in this report represent the meon volues

of two lests. No correction for beom size wos mode.

3,23 Tesling of the odhesion slrength

Cores with 42 mm diometer were sepõroted from the shotcrete by drill-ing down to the rock surfoce. A steel plore with o centric pin wos

glued to the lop of eoch core with epoxy resin. The cores were looded

in tension, ond the force wos meosured ot foilure. The odhesìon strength,

fo* the force divided by the core qreo/ wos colculoted, Three cores

were tested for eoch test in the moin test series.

As eqrlier the test rig wos fixed to the ground with o hinge porollel

to the long side. This orrongement mode shotcreling ond curing possible

with the rock surfoce in o verticol position while the test were per-

formed wiTh the free block in o horizontol position looded upwords.

ln Tests l-14 the width of the 4 cm shotcrete loyer wos 87 cm ond

in Tests l5-ló with B cm thickness 48 cm. The 48 cm loyer wos di-

vided into two strips of 24 cm eqch. The reoson for hoving o smoller

width of the thicker loyers tested with end supports wos the limiled

lood copocity of the hydroulic iocks.

ln Tests l-10 the odhesion between the sholcrete ond the middle rock

slob wos prevented ot two 12 cm wide strips ocross the slob ot eoch

ioint. The purpose wos to get on even distribulion of lhe compressive

stresses in lhe shotcrete oì the [oints'

f l-\---l I I..tt T1

'i,llii\ rril"ii,!liirll-

Steel r

Fig 3o Test rig. Fig. shows the test rig when testing shotcrele orches

wilhout end supports,

e

tol plone, Horizontol ond verticol sleel bors Q5Q ond Q26 mm res-

pectively were inÌroduced to tqke the horizontol ond verlicol reoc-

tions during looding. The steel bors were equipped with stroin gouges

for the evoluotion of the respective forces. The horizontol bors could

be ploced on three different levels - by this orrongement the direction

of the resultonl support reoction could be voried, though within o

limited ronge.

Fig 2o Looding cose studied in Tests l-9

Fig 2b Looding cose studied in Tests l0-ló

lNlßaDuçI_toN

This report deqls with the second step of o lorge Swedish sholcrete investigo-

tion, The first step of it wqs presented ond reported in /l/.

ln /1/ o description is given of lorge scole tests mode with plone shot-

crete loyers, both unreinforced ond reinforced. The report olso con-

toins results of cqlculotions on some theoreticol models.

The purpose of the first slep wos lo study the foilure mechonism of plone

shotcrete loyers subiected to punch loqds from penetroting blocks. By

the combinotion of tests ond theoreticol colculotions used in /l/ it was

possible to disTinguish belween o good design ond o less good design of

o sholcrete lining in different situqtions. The resulls presented in,/l/ore qssumed to be volid even for linings with o slightly curved shope'

The purpose of the present port of the investigotion wos to study the

foílure mechonism of curved shotcrete loyers subiected to punch loods.

LOADING CASE AND SU

ln this step of the investigolion the tested shotcrete structures were sub-

iecled to o punch lood from o single block,

Two different supporÌ orrongements were used:

ln the firsÌ 9 tesrs the shotcrete lining wos fixed to the rock blocks by

its qdhesion only (Fig 2o).

ln tests l0-ló the sholcrete lining olso hod iixed end supports (Fig 2b).

J TEST RIG AND TEST SP

3.1 MAIN TESTS

The moin tests were mode in the 3,7 m x 1,2 m test rig used in the

first step. lt wqs now modified to be suited to the new geometricol

condilions. The outer rock slobs were ploced in 25o ongle to o horizon-

2

NOTATIONS

E" modulus of elosticity for concrete

E, modulus of elosticity for rock

e eccentricity

LA odhesion strength

f¡* flexurol strength

f" compressive strength

F horizontol line lood olong o [oint

H horizontol force

p verticol line lood olong o ioint

P verticol loqd

r resultqnt line lood olong o ioint

R resultont force

t thickness of shotcrete loyer

V verticol reoction force

P ongle

o normol slress

r sheor slress

indices: f for foilure, h for horizontol, v for verticol

(MPo)

(MPo)

(".)

(MPo)

(MPo)

(MPo)

(kN/m)

(kN)

(kN/m)

(kN)

(kN/m)

(kN)

("r)

(kN)

(-)

(MPo)

(MPo)

7.42 lnfluence of the eccentricily

7.5 SOME CONCLUDING REMARKS ON THE FE-CALCULATIONS

8. SUI'^MABY

RETERENCES

(F1u+ F2u) cosd, + (F1* + F2r) sincr

r-L

,,, = (F1x + Fzx) cosc -(F1, + F2r) sina

-t/t

Rock

Shotcrete x

a

Fty

L F

Tronsformotion of nodol forces to stresses olong the element

bou ndory .

F^Jy

Fi77c

FigTo "Old" FE-mesh.

5

FisTb "New" FE-mesh

of the elements ot the ioint olong the contoct surfoce between tho

lining ond the fixed slob.

The resultont of the restroint forces on the free block ond the opplied

lood wos colculoted. The resultqnt line lood, F, is presented in the

figures for eoch looding cqse togelher with the corresponding verticol

ond horizonlol line loods, þ ond ñ. The nodol forces on the elements

situoted in the interesting oreo were tronsformed monuol ly to distribut-

ed forces (stresses) olong the element boundory perpendiculor ond por-

ollel to the rock surfoce (Fig 7c).

7 stness srtu¡ttoN ll.lOlNtS StUotro gV lHEORYoFELAST|CI

7.1 INTRODUCTION

The test described in /1/ were performed with the tronsferred lood

from shotcrete fo rock perpendiculor to the rock surfoce. The tests

described in this report were performed with the resullont force ot

the ioint octing neorly porollel to the rock surfoce.

ln the first cose it ìs obvious thot the tensile odhesion strength is

decisive for the foÌlure. ln ìhe second cose it could be lhe tensile

or the sheor odhesion strength or o combinotion of ihem which governs

the foilure,

ln order to illustrote this sub[ect some finile element colculotìons

were mode of the stress slote neor the ioint between lwo elostic

slobs lined wiïh o loyer of elostic moteriol .

7.2 FE-MESH AND METHOD OF EVALUTION

The first FE-colculotions were mqde with o monuolly constructed mesh

(Fig 7o). Loter on lhis mesh wos reploced with onother one which

wos outomoticolly constructed by o seT of progroms for the construc-

tion of FE-meshes, which wos developed ot the Reseorch Dept. of

the Royol Swedish Fortificotions Administrotion /2/ (tig 7b).

The colculotions were mode by o commerciolly ovoiloble Progrqm

(STARDYNE). The ossumption for the colculotions were plone stoie

of stress ond homogenous, isotropic, elostic moleriol . The defoult

volue 0,3 for Poisson's rqtìo wos used.

The computer progrom gove element stresses, nodol displocements ond

nodol forces for the whole structure. ln this treolment ottention wos

poid only to the restroint forces ot the supports ond the nodol forces

ç

A

Þ

kN/m

6Ct)

l.æ

æ0

13R 131

14R L

0

0

Fis ód

10 A [mm]

Verticol displocement, 6 , of the middle block qs o function

of the opplied verticol line load, þ. Numbers ot curves in-

dicole test number. R stonds for right side ond L for left side.

5

The test specimens I l-ló, which were nol provided with odhesion Preven-

tive tope on the middle rock neorest to the ioínt, showed lhe some be-

hoviour ot odhesion foilure os test specimens I-10. The odhesion foilure

lood level wos olso the some for these two groups.

The deformotion meqsurements ore shown in Fig ód. The curves show thot

no speciol indicotion of on imminent foilure is to be expected in coses

similor to the ones tested here. The gop between the shotcrete ond the

rock wos severol millimeters ot loods considerobly lower thon the foilure

lood. These results suggest thot shotcrete linings moy stond free from the

rock without ony noliceoble signs of being heovily looded. The pressure

of woter or ice in such o gop moy become fotol în the long run.

Foilure of Test specimen no ó.

Foilure of Test specimen no I l.

7.3 FORCE INCLINED TO THE ROCK SURFACE

7.31 lnfluence of different moduli of elosricily

One looding cose (Fig 7d) wos treoled with the volues 5 ond I

of the ralio modulus of elosticity for rock to modulus of elosticity

for concrete (E/Ec), The results ore shown in Figs 7e-f. The

moximum tensile odhesíon stress is only slightly influenced by the

voriotion of E/8., while the mqximum sheor odhesìon slress is

obviously influenced.

The sheor slress level, however, is lower thon the odhesion stress

level in both coses. The sheor strength of o normol, rough rock-

shotcrete interfoce con be [udged to be much hïgher fhon lhe

tensile strengih. Becouse of thot iT con be ossumed thot the tensile

odhesion slrength olone is decisive for the foilure. The influence

of the rotio En/Ê.wos iudged to be of less importonce thon other

porometers ond thus this rotio wos kept constont ond equol to 1

in the continued porl of the investìgotion.

7.32 lnfluence of different FE-meshes,

As the mesh hoppen to be oltered during the investigotion qn oPpor-

tunity wos given to study lhe effect of this chonge ond thus get on

ideo of the reliobility of the FE-colculotions in this respecr'

ln the old mesh the number of nodes ond elements were 174 ond 15ó

respectively. ln the new one the corresponding numbers werc 202

ond 2ól.

A comporìson of Figs 7f ond 7i shows thot the moximum tensile od-

hesion slress ot the contoct surfoce obtoined wìth the old grid is

93/o of the srress obtoined with the new one. The corresponding

percenloge for the sheor odhesion stresses is 64/"'

400

40:

A comporison of the principol stresses in elements equol ly situoted

in the two meshes neor fhe ioint show thot the difference between

the results of the two meshes is relotively smoll os for os The rodii

ond ongulor position of the Mohr circles ore concerned. Where the

obsolute volue of one principol stress, however, is much smoller

thqn the other one, lorge relotive differences in those smollerprinci-

pol slresses ore of course obtoined when the two grids ore compored.

500

R

tigTd Looding cose A ond resultont force in this cose forE/E = 5,

ùoo

I2

-4¡-Q2

0

0

O1

uoo'4s I

-0.1

ta

l1

- o.l 16

cr¡

0 T//

Stress distribut¡ons ot the ioint, Looding cose A' Er/E"

Þ = 50 kN/m, ñ = ß.7 kN/m, -= 51.9 kN/m.

Notice different scoles for o ond r .

6

Ilg

7A

l1

16

cD)

tisTe =5

J

¿

7

0

-4t

4ro

¡1Þo

aI

2

tg

/2

-Q¿

- o.t

oc¡,

0 T//2

6'

IlO

t2

74

76

ch

Fig 7f Slress distributions qt the ioint. Looding cose A. E/Ec= 1.

Þ = 50 kN/m, ñ = 16.7 kN/m, r= 52.7 kN/m.

Notíce different scoles for o ond t .

A comporison of this kind con of course only give on indicorion

if the FE-solution is sensilive for for The subdivision of the slruc-

ture into elements, The results show thot the choice of mesh does

not seriously influence the results in oreos where the stresses ore

of on inleresTing mognitude.

7.33 lnfluence of lhe force inclinotion

When the middle slob of the FE-structure is looded, the curvoture

ond the prevented horizontol movemenls ot the supports ond qt

corner neqrest lo the shotcrete ioint couse o horizontol force. This

horizonlol force together with the opplied verticol loqd defÌnes

the looding cose qt the ioinr. By chonging the lood position ond

thus the momenl curve some voriotion of the incl inotion of lhe

resultqnt force wqs obÌoined, The ongle ts (see Fig 7g) wos 57.0o,

46.6o ond 39,óo in lhe three coses sludied' The voriotion of the

moximum tensile odhesion stress becouse of the chonged ongle of

inclinotion is rother smoll (Figs 7h to i). The voriqtion of the

moximum sheor stress is lorger but the slress level is low in oll

three coses.

ItPl P2 P3

P

FigTg Looding coses B, C ond D ond the corresponding resultont

forces for E/8.= l. P = P' + PZ+ P3,

p

o

J

?

o

-o.e

t

-o¿

Uro

ttqa

gr

2I

6

t0

t2

l1

-Qt

0

î6

cr¡

o Tx

Stress distributions ol the ioint. Looding cose B. Ê/Ec= l.

Þ = 5o kN/m, ñ = 5.5 kN/m, i = 50.3 kN,/m.

Notice different scoles for o ond r .

2

ô

0

lO

t¿

t4

16

cr¡

Fis 7h

I

üoo

J

2

ùro

0

'o.r

0

o

'Qa

2

O1

T//

6

t0

t¿-o.J

l1

16

e¡¡

0

¿

1

6

I/0

t2

/1

t6

Stress distributions ot the ioint, Looding cose C. E,,/E"

Þ = 5o kN/m, ñ = 15.9 kN/m, F= 52.5 kN/m.

Notice different scoles for o ond r .

ct¡

= t.Fis 7i

J

tr4

4ro

¿

Io

oJ-

-43

-Q2

-Qt

o

16

c¡,

o T//

tig 7i Stress distributions ot the ioint. Looding cose D. ErlE"

Þ = 50 kN/m, Ë = 22.9 kN/m, i = 55.0 kN/m.

Nolice different scoles for o ond t .

?

6

Il0

t2

l1

16

C¡,

= t.

7.4 FORCE PARALLEL TO THE ROCK SURFACE

7.41 Generol remorks.

7.42

For the colculotions in thís cose one boundory condition wos chonged

compored with ihe eorl ier coses. To obtoin o resultont force porollel

to the rock surfoce it wos not possible to keep the condition of the

left verticol boundory being o seclion of symmetry. The restroints

olong this boundory were releosed ond two of the nodes were looded

with horizonlol forces which produced the desired resultont force to-

gether with the verticol lood. By voriotion of the rotio belween the

two horizontol forces the eccentricity of the resultont force wos vori-

ed relotive lo the cross section of the shotcrete loyer.

The colculotions were performed for the "old" mesh with equol moduli

of elosticity for the lwo moteriols ond wîth three volues of the eccen-

triciTy: +2.Q, t 0.0 qnd - 1,2 cm. Here lhe minus sign implies thot

the resultont force octs obove the midpoint of the cross-section of

the shotcrete loyer, see tig 7k.

These eccentricities ore chosen smoller thon the eccentricily ot tensile

crocking, At tensile crocking of o 4 cm section the eccentricity of

on qxiol force equol to the one used in the FE-colculotions is 2.4 cm

when the flexurol tensile strength is 8 MPo.

lnfluence of the eccentricity.

The results of the FE-colculotions ore shown in Figs Tlto n. The

stresses ore only slightly offected by the voriotion of the eccentric-

ity'

From the slress mognitudes ond distribuTions in this coses it con be

concluded lhot the tensile odhesion strength olone is decisive for the

foilure, There ore two reosons for such o stotement:

o) The tensile odhesion stress obtoined by this onolysis is lorger lhon

the moximum sheqr stress.

b) The tensile odhesion strength is probobly olwoys lower thon the

sheor strength becouse of the roughness of the contoçt surfoce'

Fis 7k Looding cose E' F = 50 kN/m, ñ = 107 kN/m, F= ll8 kN/m

hoo

4

3

¿

0

-4s

o

hoo

-?s

ûr

T//

?

t2-?o

-zs

to

cr¡

2

lo

c¡,

Stress distribuTions ot the ioint. Looding cose E. E/8"

e = *2.0 cm.

Notice different scoles for o ond r .

=ltis 7l

hoo

J

I

2

I

t.0

'o.s

0

0

ùoo

'?.5

'2.9

-15

g I

cr¡

1,//

cr¡

Stress distributions ot fhe ioint. Looding cose E. E/Ec= l.e = to.Notice different scoles for o ond t .

¿

Fig 7m

!0¡

hoo

?

0

'tg-4s

0

J

'1s'/5

-4s

6¡

T//

c¡,

Looding cose E. Ea/E.

?

4oo

ta

c¡,

Stress distributions ot the ioint

e=-1.2cm.= l.Fis 7n

Nolice different scqles for o ond r .

7.5 SOME CONCLUDING REMARKS ON THE FE-CALCULATIONS

It must be cleorly stoted thot the tensile odhesion peok slress is

highly influenced by the locol geometry ot the ioint. The exoct

solution for o shorp corner in on elostic med¡um is on înfînite

tensile odhesíon stress. The FE-colculotions, however, give over-

oge stresses which ore considered vol id for eoch elemenl os o

whole. These elements ore not smoll compored to the oreq where

the stress peok is situqted. Of course this meqns thqt the obsolute

volues of the moximum odhesion stress connot be used for o com-

poríson with volues of the odhesion strength obtoined from core

tests. The FE-results represent some unknown stress concentrotion

foclor ond the core tests on other unknown one. At the lorge scole

tests the locol geomelry probobly wos fovouroble for the stress

distribution. The ioint between the rock blocks wos filled with

fobric before shotcreting but this could not prevenl the shofcrele

from penetroting some millimeters inlo the ioint ond thus forming

o smooth lronsilion from sholcrefe to rock.

It ís uncertoin ìf the different FE-results con be compored with

eoch other when regording the "overoge peok stress" becouse of

the bíg difference in stress grodient. The stress grodient seems to

be much lorger ol o force porollel to the rock surfoce ihon ot o

force inclined to the surfoce.

Whot con be concluded from the FE-colculotions, however, is thot

tensile odhesion slresses probobly olwoys governs the foilure ot shot*

creted rock ioints subiected to punch loods.

The sheor slress obtoined by this onolysis ìs of o smoller mognitude

thon the tensile stress. lt is qlso distributed over o lorger length

thon the tensile odhesion stress.

8. 5U^ MA8Y

ló curved shotcrete loyers interocting with rock blocks were tested

in o lorge scole.

The tests showed thot the primory foilure of the shotcrete-rock

structure olwoys is qn qdhesion foilure. The primory foilure lood is

in proctice independent of the loyer thickness. For the lested coses

the primory foilure is olso the finol foilure unless end supports for

the shotcrete orch qre provided.

A shotcrete orch with end supports subiected to lorge compressive

forces moy stond free from the rock over lorge oreos.

Finite - element colculotions of the stress stote ot the rock-shot-

crete interfoce neor o ioint indicote thot the governing porometer

determining the foilure is the tensíle odhesion strengfh roìher thon

the interfoce sheor strength, This stotemenl seems to be volid for

oll looding coses when shofcrete interocts with hord, iointed rock

REFERENC ES

/l/ Holmgren J. "Plone shotcrele loyers subiected to punch

loods". Royol Swdeish Fortificotions Adm., Reseorch Dept.,

Reporr l2l:4. Stockholm 175.

/2/ Keiier U. "Hiõlpmedel för generering ov indoto for finito

elementprogrom" (lnput doto generotors for finiÌe element

progroms). FoU bygg I (1928): l, pp 4-7. StockhohlfTE