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A METHOD FOR PREDICTING PRISM STRENGTH AND YOUNG'S MODULUS OF GROUTED MASONRY

Akio Ba~y*1 a nd Osamu SS2bU*2 Head and Rsearcher

Construction Tequniques Division, Production Department Building Research Institute, Ministry of Construction

Tatehara 1 , Tsukuba-shi, Ibaraki-ken, #305 Japan

ABSTRACT

This paper dea l s with a predictive method of the basic compressive strength of grouted masonry i n order to estimate the prism strength on the basis of t he properties of components , that is, strength , e l astic modul us and vol umetric r atio of grouting parto To predict the prism strength, the two types of masonry assemblages are discussed in relation to the contribution of grout to prism strength. A fundamental predictive procedure is proposed on the both classified cases considering the effects of construction factors, water absorption, bleeding and so forth .

INTRODUCTION

Compressive strength and Young's modul us of masonry assemblages are the fundamental properties for the structural de sign of masonry bu i ldin gs. Many studies concerning prism strength have been performed in the restric tion of tr a di tional ungrouted masonry. On the other hand , Fully grouted reinforced masonry has been clarified as a structural ty pe with an excellent aseismic performance. Grouted masonry is also an indispensable materia l form for reinforced masonry. The predictive method of prism strength of grouted masonry is not so c lear in the codes and the specifications except i n some countries.

Therefore, the composite mechanis m of masonry units, joint and grout in grouted prisms shall be fundamently focused in o rder to effectuate alI co mponents and to predict the prism strengt h. In this paper, uniaxial compressive strength and secant modulus of grouted masonry prisms are exa mined on the composite law . So me types of practical equations and concepts are proposed for i dentifying the fundamental mechanical properties of the composite and the components.

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In the pred i ctive procedure of the prism strength, masonry assemblages are classified into the two types in relation to the effect of grout strength . High Young ' s modulus of masonry units or discontinuity of grout reduces the effect of grout strength. Usual rigidity of units and continuity of grout effectuate the strength of the three components . The discontinuity is some times improved by pro per construction procedures especially in grouti ng processes on si te . This item is discussed on the basis of the experimental resulls . The classificatio n is the first fundamental in the predic t ive procedure .

On the second fundamental, the process of prediction is proposed in the both classification. The concept of "Efficiency" and "Strength or Stress Contribution Factor of Grout " is defined in the case of the gro ut ed masonry . The two predictive equations are practieally presented in the both cases a nd examined on t he basis of the past data .

NOTATIONS

fe Uniaxial Compressive Strength

E Young ' s Modulus

li Poisson ' s Ra t io

Suffix u , j , g an d f mea n unit, joint , grout an d face shell part respeetively.

Fcm : Prism Strength of Grouted Masonry

P Ratio of Joint Thickness to Unit Height

p' Volumetrie Ratio of Hollow Part t o Overall Volume of Masonry

~ = Ej/Eu ' ~"= Eg/Eu' a' = Eg/Ef

r = fc/feu ' r" = feg/fcu ' r' = fcg/fcf

e = Fcm/fcu( l-P' ) , es = fef/feu

Ktu : Ratio of Tensile Strength to Comressive One of Un i ts

PREDI CTI VE PROCEDURE OF PRISM STRENGTH

Prism Strength is ge nerally determined as follows,

(1) Ex peri mental method based on the sta ndard test metho d of pr ism strength

(2) Predie t ive met hod base d on a se t of ex perimenta l val ues of unia xial compressive strength of units , joint a nd gr out

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(3) Simplified predictive method based on a set of values of standardized component marterials

A predictive procedure examined herein is to establish the latter two methods. The former one is though to be the most fundamental method for dertermining the prism strength. This method shall be adoped as often as possible.

In order to predict the prism strength of grouted masonry, the two following items shall be considered,

(1) Kinds of component materials and their combinations

(2) Construction procedures for preparation for grouting and grouting

On the first item, various aspects of materials could be listed. The most important aspects to be considered are thought to be as follows,

(1) On units: Kinds of materials, Shape and size of grouting cores

(2) On grout materials: Kinds of grout mate rials, Kinds of admixtures

(3) On joint materials: Strength of joint materials related to that of units

(4) On combinations : Units and grouting materials related to construction procedures and their elastic modulus

On the second item, the two following aspects shall be considerd,

(1) Prelvetting : Necessit y of prewet ting uni ts before lay ing and grouting and required degree of wetness

(2) Grouting procedures: High lift or low lift

The various aspects mentioned above are supposed to have a great influence on the value and its fluctuation of the actual prism stength. Therefore, a fundame ntal predictive procedure stated afterwards can be applied to some appropriate choices and combinations of materials and const ructi on procedures witho ut any defect in grouting parts of grouted prisms. Especially, the predictive procedure ca nnot be appilicable to the typica l following cases,

(1) Highly absor ptive units or un its with small hollow

(2) Absorptive units without appropriate prewetting or admixture

In these cases , grouting part might contain defects so that continuity of grouted masonry cannot be assured and no contribution to prism strength can be done by grout. Furthermore, low lift grouting methods are doubtfull in forming the continuity without any proper procedure in details.

The predictive equations for grouted masonry prisms can be proposed which are corresponded to the two cases in relation to the degree of contribution of grout to the prism strength.

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PREDICTIVE EQUATIONS DF PRISM STRENGTH

In the general case of prediction , the uniaxial compressive strength of grouted masonry, prism strength can be deter mined as the following equation (Eq.l),

Fc:n iJ' 2s (1-

(1-iJ ') feu 1- J' - - - - Eq. 1

Where, Fcm/(l-fi')fcu : Efficiency of grouted masonry

P'fcg/(l- ~')fcu: Strength contribution factor of grout

: Efficiency before grouting

This equation is reformed from an original parallel equation (Eq.2) in order to present the lowest value of the possible range of prism strength.

Fcm

O-P ') tu

o' ,,' - :3'

- - - - Eq. 2 < 1 cu

f , f g , and es usually can be determined experimentally. The mlnlmun value o~ e s can be dertemined on the basis of the following eq uation (Eqs.3 and 4).

T = , , T = ç

1 ,

T o

i LJ < T e s = T = o

/ c > T e s = , u = o

( 1 - ~ , ( 1 - " ) p ) ,- J

1 - J - ,!.: j -;; ( ~- ~:J " . r- J

- - - - Eq . 3

- - - - Eq . 4

When the experimenta l value of Ktu ' li u and ).l j is not available , the value of ro ca n be 0.5.

In the special cases when the grouting part cannot contribute to the prism strength, the predictive equation ca n be presented as Eq uation 5.

Fc:n - - - - Eq . 5

Eve n in these cases, the prism strength can be determined experimentally. In Equation 5, e s can be determ ine d in the same manner to the gene ral cases mentioned previously.

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EXPERIMENTAL EXAMINATIONS ON PREDICTIVE PROCEDURES

Ex perim e ntal Da ta used in this exa mi na110f of the pred ic t ive eq ua tions a r e mainl y r e por ted in t he a ut hor s pa per prese n te d at th e fi r s t J TCCMAR i nclud i ng othe r experiment al s tud ies . Masonr y un i ts, j oint ma teriaI s and grout mate r iaIs used i n t his e xa mi nation are s hown in the pa per.

Ex per imental r elat ionshi ps from t he a uther(AB) ' s pa per[ 6 j are presented in Fig ur e 1. Mos t e x pe r ime nt a l data fa lI a bove th e l i ne s hown by Eq. 1 when 0 . 3 ,0. 5 a nd 0 .7 a r e ass um ed as e s • Accor d ing t o th is autho r paper , va r ious exper i ments are pl otted as s how n i n Figure 2 a nd the t heor etical lower lim it also can be s ho wn in t he sa me f igure based on Eqs 3 a nd 4

Fi gure 1

:J u --

'-,

M

~ o

o o I o 8

I 8 o ~

, : Clay C· CCnc.re i ~

i o Co o / I I CO c/ I o ,,0//(; o 0Yl

u I o 'Co' / ! LL o !

6 00

~b /~o_v o / I·

~ --E

, o o , OU C" ~ ~ ~ ~ I ~ . . ~ I

l o 1 2 3

fl'.fe 9 I( l-f)} feu

Pr e di c ti ve Relat i ons h i p (lower lim i t) be t wee n Efficiency and Stre n g t h Co n t r i but ion Factor of Grout i n Co mpar i son with Expe r i mental Fl uc tua t ion Range

o o

()

o

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oU o

o

00 tl o ü

Figure 2 Predictive Relationship (lower limit) between Efficiency of Ungrout Masonry (es ) and Ratio of Joint Strength to Uni~ Strength ({) in comparison with Experimental Fluctuation Range[6J

EFFECTS OF YOUNG' S MODULUS OF COMPONENTS

When a uniaxial compressive load is applied to grouted masonry, the uniaxial strain is assumed to be equal in both the face shell part and the grouting part on the basis of a simple paraI leI modelo The theoretical value of the prism strength can be calculated as follows,

7= CX / T ~

~c :n (l - - - - - Eq. 6

(1-{3' ) t c ; (l -;3') Ef

rem - - - - Eq. 7

(1 - .3' ) ' c f (1 -':' ) tf

Equation 6 conducts Figure 3. In the case of lJ ~ 1, grout fracture mainly occurs. On the other hand, face shell fracture occurs in the case of '1 ~ 1. In the above discussion, non l i near behaviour and Poisson's effect are not considered.

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Lnr· --------------------------~

~

~

~r)r - I ~cJ

u Li.

1= Q..'/ r'~ 1 Fac:? 5heil F,;;.c;ure

\

'1 ~ 1 Graut F,acture

_ _ .I

'1/'1

E I V 7 / -1

s: o 2 3 L.

«'1]/'(1-13')

Figure 3 Simple Prediction of, Prism Strength and Failure Mode Based on Stress Contribution Facter of Grout

~

C: ,

" c u

L!...

l---:,

•

o

o o

o o

'0

o

o

o

.. ...

()

.. :lI o

...

2

~'(J' / (1 - (J')

/

..

Face She! \ Fr ac ture • ctay J C'Jn<.. re te

Grcu t Frdc;:ure ... C!2 y :g Concret e

/ .

-l

I

:!

Figure 4 Experimental Examination of Failure Mode Based on Predictive Method Using Stress Contrbution Factor of Grout

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Figure 4 sho\"s the experimental relationship betwe en F cm/(l - /i')f u and E '13' /(l - /J')Ef , where the latter can be called "Stress Contribution 'Factor oI Grout". When'l is smaller than 1, the experimintal values falI in a theoretical line. A little defference from the line is thought to be due to a water absorbing effect by units.

E u LL_

o

o o

o o

o

o

7-,1 /

o

o

• C:ay

o Cone; e te

2 L.

,,'n' / (1 - n')

Figure 5 Ex perimental Examination on Relationship Prism Streng th and Stress Contribution Factor of Grout

Figure 5 shows the similar plots to the case of Figure 4 . In this fig ure , in the case of grout fracrure is plotted by modifying the vertical values to devided by 1 . Except with grout defects due to water absoptio n by absorptive units , alI values falI along the t heoretical line.

Units with small grouting cores and highly absoptive units cannot offer t he common trend mentioned above . These cases are thought to have no complete contribution to prism strength by grout .

Furthermore, units ar gro u t which show a great difference in '7 from 1.0 , can not be applicable to the general predictive method. Especially in the case of 1 ~ 1, the contr ibution of units seems to be great. Many units with thin web may have a gr eat possibility of exfoliation of face shells under an earthquake loading and a long term ve r t i cal loading. These cases correspond to strong concrete units and very strong clay units with usual grout materiaIs .

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PREDICTIVE PROCEDURE OF YOUNG' S MODULUS OF GROUTED PRISM

Determining methods of Young's modulus of grouted prisms are generally listed as follows,

(1) Experimental methods

(2) Predictive methods

Predict ive methods for determining Youngs modulus can be conducted on the basis of a composite law which was proposed in the authers' paper[2l. This com posite law is founded on a simple parallel model composed of the face shell part and the grout part in grouted masonry.

A fundamental predictive equation is shown in the following,

j3' l- • C(' - - - - Eq. 8

0-)') Ef l-) ,

lf Young's modulus of the face shell part and the grout part is clarified at the same uniax ia l strain to the strain of grouted masomry, Young's molulus of masonry can be calculated precisely as shown in Figure 6.

~,.-------------------------------------.

<D

~r -::-'" c::: ,

w -'" LU

-0' I o

o. f-:::-BM (1/3 Secant , 500u) 6 Ao. OF8T (1/3 Secant, 500",) o. OHBN (1/3 Secani,SOO",) ..

/i

o •

i _ _ E __ I+~'" Ef(I-fl'J - I-fl'

2 3 L.

,,'fl' I (I-il') 5

Figure 6 Experimental Examination of Predictive Equation for Young's Modulus of Grouted Masonry Experimental Examination of Theoreí~lal Predictive Equation for Young's Modulus of Grouted Masonry

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Eq. 8 is not so practical that the following equation can be conducted on the basis of this equation and an assumption of neglecting joint parts.

Em {3' 1+ • C( I , - - - - Eq • .9

(l - (3 ' ) Eu - {3'

The comparison of Eq. 9 with th e experimental data used in Figure 6 is presented in Figure 7.

Figure 7

w

~Ir------------------------------'

o

o Hollow Concrete • Hoilow Cloy ,:, Bona Eeom Concreie ~ Bona 8eom Cic y

2 ,;:rl'1 (1·· (3' )

I,

Experimental Examination of Pract:i-,cal Predictive Equation for Young's Modulus of Grouted Masonry[2J

CONCLUSIONS

The fol1owing conc1us i ons ca n be c onducted on the basis of the discussions mentioned above.

(1) A predictive procedure for determining the prism strength of grouted masonry especia11y focusing on the contribution of grout .

(2) A concept on efficiency is proposed to be app1icable to every type of masonry , ungrout and grout ed masonry.

(3) A factor on the contribution of grout to prism strength is proposed which is ca11ed "Streng th Contri bu tion Factor of Grout".

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(4) A predictive relationship between efficiency and "Strength Contribution Factor of Grout" is proposed for grouted masonry and examined experimintally.

(5) Appropriate combinations of units and grout are discussed especially focusing on Young's modulus of components and construction procedures for preventing d2fect from occurring on site.

(6) A compos ite law concerning Youn g ' s modulus of grouted masonry is propose d for its predictive purpose.

REFERENCES

[1) O.Senbu and A.Baba, "Mechan ica l Properties of Ma so nry Units," First Joint Technical Coordinating Committee on Masonry Resea r c h, To k yo, Japan, August, 1985

[2) A.Baba and O.Senbu, "In flu e ncing Factors on Prism Strength of Grouted Masonry and Fracture Mechanism under Uniaxial Loading," ditto

[3) G.R.Kingsley a nd R.H.Atk inson , "A Study and Compressive Stress-Stra i n Behavior of Concrete and Clay Masonry," ditto

[4) N.J.N.Priestley, "Predicti o n of Masonry Compression Strength," New Zealand Concrete Construction, March and April, 1984

[5) R.H.Atkinson, J.L.No land and D.P.Abrams, "A Deforma tion Failure Theory for Stack-Bond Brick Masonry Prisms in Compression," 7th International Brick Masonry Conference, Melbourne, Australia, Feb, 1985

[6) A.Baba, "A Suggested Concept for Predicting Pr ism St rength," ditto