12TH INTERNATIONAL

BRICK/BLOCK Masonry c O N F E R E N C E

SHEAR BEHAVIOUR OF BED JOINTS

Rob Van der Pluijm', Harry Rutten 2, Martien Ceelen

'TNO Building and Construction Research, formerly also Eindhoven

University of Technology, r.vanderpluijm@bouw.tno.nl

' Eindhoven University of Technology

ABSTRACT

This paper discusses some aspects of the behaviour of bed joints under combined she­ar and tension or compression (perpendicular to the bed joint) . A unique test arran­gement has been developed, making possible the establishment of a shear failure en­velope for the joints + bond interface. Nearly ali properties needed to describe the shear behaviour of joint + bond interfa­ce, depend on the stress perpendicular to the bed joint. These properties inc/ude she­ar strength, mode /I fracture energy, cohesion softening and dilatancy. This paper fo­cusses on the failure envelope, mode /I fracture energy, cohesion softening and dilatancy. A more complete description of shear behaviour of bed joints can be found in Van der Pluijm '999

.(7). To describe cohesion softening, formulae originally developed for tension softening could be used. A formula describing dilatancy as a function of the shear displacement is proposed.

Key words: Shear, bond interface, mortar-joints, (post peak) behaviour, failure en­velope, mode /I fracture energy, dilatancy behaviour.

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INTRODUCTION

In 1993, Van der Pluijm(5) presented an experimental study concerning the beha­viour of bed joints under combined shear and compression . However, the test arrangement used in 1993 could not be used to carry out tests under shear and tension . In a newly developed arrangement in the Pieter van Musschenbroek la­boratory of the Eindhoven University of Technology, tests were carried out under programmable combinations of tension or compression (perpendicular to the bed joint) and shear, making possible the establishment of the failure envelope for the joint + bond interface loaded in shear.

From a shear test, carried out wi th pre-compression, schematic diagrams as pre­sented in Figure 1 may be obtained. This behaviour shows a great similarity with the behaviour under tension except for the tail that does not fali back to zero, but becomes stable at a certa in shear stress leveI. This levei corresponds with the dry friction of two non-bonded surfaces.

The shear strength can be described on the basis of Coulomb's friction failure cri­terion (already used by Mann and Müller'977,(4»). This 2-parameter criterion reads as follows:

1:u = Co - otan ep (1 )

1:u shear strength of a test; Co cohesion or shear bond strength, i.e. the shear strength at o = O; ep: angle of internai friction (not necessarily equal to the coefficient of dry friction

fl) ·

The descending branch between 1:u and 1:" can be seen as softening of the cohe­sion . The mode 11 fracture energy C,,, was used by Lourenço'996,(3) to define the des­cending branch beyond the peak via softening of the cohesion in eq . (1), by re­placing Co with the following expression :

C, residual cohesion; Co initial cohesion; C", mode 11 fracture energy; vp': plastic shear displacement (occurring beyond the peak).

(2)

Describing the residual cohesion with eq. (2) in eq . (1) while the shear stresses re­duce to 1:,,, implies that a gap will arise when tanep is not equal tot the friction co­efficient fl . This can be observed in Figure 1 .

To overcome this problem, Lourenço'996,(3) also implemented a linear softening of tanep coupled to the cohesion.

Figure 1. Schematic diagram af defarmatian (v) controlled shear tests (3 different s-/eve/s)

cr

Van Zijl '996.(9) explored the usability of an equation developed for the tensile beha­viour of plain concrete by Hordijk et al. '990.(1) by changing the mode I parameters in corresponding mode li parameters, resulting in the following formula:

(3)

V nonlin : shear displacement over which the cohesion reduces to zero;

c"

c2 : dimensionless constants, c, = 3.0, c2 = 6.93

Both equations will be discussed in section 5.

An important phenomenon in a shear test, is the occurrence of a displacement perpendicular to the imposed shear displacement, both occurring at and beyond the peak. Thishenomenon is generally denoted as dilatancy and is usually descri­bed in terms of a dilatancy angle 'JI of which the tangent is equal to the ratio bet­ween the normal and shear displacements, incrementally written as:

ta n'JI = dUpl

dV P1

(4)

In Figure 2, the 'plastic' displacement upl perpendicular to the shear displacement that occurs beyond the peak in a 'r-v diagram, is plotted against the plastic shear displacement vpl for a test with pre-compression . With the definition of the dila­tancy in mind, it can be seen that the dilatancy decreases (softens) with increa­sing shear displacement.

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Figure 2. Example of the normal displacement upl as a function of the shear displacement vpl beyond the peak of a test carried out with pre-compression

~ ;f

t

0.1

o.os

0.06

0.04

0.02

o o 0.25 0.5 0.75

---. vpl [rrvn]

Physically, it is the result of a crack surface that is not perfectly smooth, so shea­ring goes hand in hand with an uplift. Of course, the maximum uplift is limited and related to the roughness of the crack surfaces. In case of bond failure the roughness of surface of the unit will be an important factor.

In the next section the test arrangement is presented. In the sections thereafter results are presented and discussed. No specific data of specimens, mortar or unit compressive strength are presented. It is the intention to discuss the behaviour in general and not related to specific test series. Details can be found in (7).

2. JOINT SHEAR TESTING ARRANGEMENT

To be able to carry out tests under combined shear and tension, the bi-axial arrangement, schematically drawn in Figure 3, was developed in the Pieter van Muschenbroek laboratory of the Eindhoven University of Technology. A couplet

Figure 3. Schematic view of bi-axial arrangement in the Pieter van Musschenbroek laboratory

LVDT's

LVDT's . . ~shear dlrecllon

normal dlrecllon '

F,_

/\M

I ~~I\ D MU M F, =2 M / d __ F.

loading of specimen wilhoul normal force

specimen is glued between the upper and bottom platens, which are both con­nected to their own parallelogram-mechanism. The arrangement makes it possi­ble to move both platens independently of each other: the bottom platen in the shear direction and the upper platen in the direction perpendicular to the bed joint. As the platens are kept parallel, they form restraints at both sides of the spe­cimens. As a result, shear movement of the bottom platen leads to apure shear force in the centre of the specimen.

The displacements were measured on the front- and on the backside of a speci­men. 50 four normal and two shear displacements were measured.

In the tests, the two actuators were controlled independently of each other. Each jack was controlled via a Schenck S59 Servo-controller by a para meter that followed a sta­tic or dynamic command value. The para meter itself could be fed by two signals that could be mixed in any proportion using dedicated electronics. Most of the tests we­re carried out under a cOnstant compression force and increasing shear displace­ment. The LVDT's on the specimen were used to control the shear displacement.

3. GENERAL OBSERVATIONS

In a lot of shear tests carried out with compression, bond failure in the interface occurred. Bond failure combined with tensile failure of the units (near the heads of the units) was also an important mechanism. However, also other failure mo­des may occur. The different failure modes are presented in Figure 4.

A combined normal and shear stress state may result in principal tensile stresses greater than the tensile strength of the unit. Apart from the principal tensile stress occurring resulting from the applied average stresses cr and 't, tensile stresses al­so occur due to:

• the bending moments that increase from the middle to its maximum value ne­ar the platens cause extra tensile stresses (see Figure 3);

• the linear elastic stress distribution in the test arrangement that does not lead to a constant stress field within the specimen.

Figure 4. Failure mechanisms that may occur in a shear specimen

bond failure failure in mortar and bond faílure and diagonal tensile bond failure tensile failure af units failure of units

near their heads

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As expected, the strength and friction levei were dependent on the compression stress leveI.

The scatter of strength values obtained at the same levei of pre-compression was small. If the results of ali test series are considered, the average CV of the shear strength per pre-compression levei was 12% and 25% per pre-tension leveI. The CV for the test with pre-compression is significantly less than with the tests with pre-tension. The CV of 25% is in line with CV's normally found for the tensile or flexural bond strength.

The descending branch after the peak becomes less steep with increasing pre­compression. Consequently the fracture energy also increases with the levei of pre-compression.

4. SHEAR FAILURE ENVELOPE OF jOINTS + BOND INTERFACE

Tests in the bi-axial test arrangement were carried out with masonry consisting of wired cut clay bricks (wc-J096) with a general purpose mortar (GPM) 1:1 :6, de­signed in the laboratory and masonry consisting of calcium silicate blocks (C5-block96) with a prefabricated thin layer mortar (TLM). For each of those masonry types, series of tests were carried out with constant normal stress leveis of -0.6, -0.3, O, +0.05, +0.1, +0.15, +0.2 N/mm2 and increasing shear deformation. Also a series with constant shear stress and a monotonic increase of the normal defor­mation was carried out with the clay brick specimens. The problem was to obtain a point on the failure envelope with a relatively high mean tensile stress. This test series proved to be very successful. Also tests were carried out to measure the ten­sile bond strength {,b and mode I fracture energy in a tensile test arrangement with fully restrained platens (see (6)).

Figure 5 . Failure stress points of the wc-j096 + 1: 1:6 series (Ieft) and the CS-block96 + TLM series (right)

2.5

o ~,

~ 1.5

!

i 0.5

O -1.5

, , , ,

-1

---

o corrbined tests o tensile tests

• n-ean

- -- Frt(lín. regr.)

, o ., o

.... ,~ .... ,

r/lO

. ~ O O

0 .0

-DS O 0.5

-+ normal stress a [ N'mm2 ]

1 O rorTbined tests O tensile tests

~ 1.6 • rrean

'! Frt(lin. regr.) --_._-- ------

~ 'O, 8_ 1.2

11: o ' ~ m -5i 0.8

00

0.4

i O -1 -D.S O 0.5

-+ normal stress a [N'mm2]

In the following two figures, ali points that can be obtained from the tensile and bi-axial tests of the two masonry types, are plotted in the (J-1: stress plane. Also mean values for groups of data tested with the same constant normal or shear stress are drawn.

The already indicated, usually large scatter for tests with tension is obvious.

In Figure 6 the mean values of series with equal normal stress leveis are presen­ted dimensionless by dividing the normal stress by the tensile strength and the shear stress by the cohesion. They are plotted together with failure envelopes used by Rots et aI. 1993.(B) and Lourenço'99 •. (2).

Observing Figure 6, it may be concluded that the combination of Coulomb's fric­tion with the parabolic fit through de cohesion c and the tensile bond strength f.b is more suitable than Coulomb friction with a tension cut-off at f.b' However, the present amount of test data is far too small to perform a reliable statistical analy­sis and reject one of the two failure envelopes.

A remark about the parabolic tension cut-off used in combination with Coulomb's friction has to be made: a smooth transition between both criteria is only obtai­ned when:

(5)

With tan<p = 0.75, which is a reasonable lower bound, eq . (5) becomes:

(6)

This is somewhat conservative compared with the mean value of 2.0 for the ratio CO/f.b generally found in (7), but taking the standard deviation of the ratio Coff.b (=0.55) into account, completely plausible.

"';'" ~

S' -~

i

2.5 I

2~ ~lomJ;

I (!l v..o-J096 + GPM 1: 1 :61

~ I t> CS-bl0ck96 + Tl.M

~ 1.5

t>~ Lourenco et a1. 1994

1

~ I 7 0.5

Rol! el al. 1V \ I (!l

o -4 -3 -2 -1 O 1

----+- cr I fttJ [-]

Figure 6 Groups of mean test data together with failure envelopes according to Rots et 01. /993,(8), and Lourenço et 01. /994.(2)

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5. MODE 11 FRACTURE ENERGY AND COHESION SOFTENING

The mode 11 fracture energy G", becomes larger with increasing compressive stress. This trend was already observed in Van der Pluijm'993,(5), The correlation co­efficient of the regression lines of the series presented in 1993 for clay brick ma­sonry were low (r' < 0.74), and consequently, they could only be considered as an indication of the general tendency. In the series where only one failure me­chanism occurred, namely:

• bond failure in the wc-j096 + 1 :1 :6 series and CS-brick90 + 1 :2:9 and + 1: '/2: 4 '/2 series and

• combined bond + mortar failure in the CS-block96 + TLM series,

high correlation coefficients were obtained when a linear relation between the fracture energy and the normal stress was assumed. These series are pictured to­gether in Figure 7, including the linear regression lines.

In the other series this was not the case. In those series often bond failure com­bined with tensile failure of the units near their head si de occurred. Clearly, crac­king of the units influenced the amount of absorbed energy and made the results more diffuse leading to too high values that should not be included in any mo­dei only used to describe shear failure of joints,

It was concluded that mode 11 fracture energy G", of the joint + bond interface is linear dependent of the normal stress leveI.

The wc-j096+ 1:1:6 and CS-block96 + TLM series that embraced tests with pre­tension as well as tests with pre-compression (see Figure 7), indicates that the li-

Figure 7, Mode /I fracture energy of series in which one type of failure prevailed as a function of the normal stress

0.15 ,---- --,----,------,-------,

cjl ~ 0.1 I-----j--'<'''l--+---j------j

~

j = 0.05 1-~6.l~lL.

~ t oL=~~--~--~~~~

-1.2 -0.8 -0.4 o 0.4

normal stress (J [l\IImm2)

near dependency can be used up to the tensile (bond) strength. The increase of the fracture energy with decreasing normal stress can vary considerably, depen­ding on the test-series.

When joints + bond interfaces or the interfaces themselves are considered sepa­rately in a masonry model the following recommendation is made about the magnitude of the mode 11 fracture energy.

Looking to the test data obtained in relation to the type of crack surface, the line obtained for CS-brick90 + 1 :2:9 series can be considered as a lower bound, be­cause the crack surface was very smooth and the out of plane tolerance of the bed face of the unit was very small ($ 0.1 mm). Furthermore the shear bond strength was also low in this series (0.14 N/mm2). An upper bound is harder to provide. In the absence of more test data, especially with high strength thin layer mortars, the line through the CS-block96 + TLM series can be considered as an upper bound for bond and/or mortar failure.

The equations of those two regression lines are (CfII in N/mm, 0 in N/mm2):

lower bound: C", = - 0.020 + 0.005 (7)

upper bound: Cf" = - 0.140 + 0.02 (8)

In analogy with the findings of Hordijk et al. 1990,(1), it was explored whether a rela­

tion could be found between the mode 11 fracture energy, the initial cohesion and the distance V nenf;n (over which the cohesion reduces to zero). In Figure 8 V nenf;n is plotted against CII/Ce for ali tests with pre-compression.

E E

~ .,.g

t

1.2

0.8

o (§l

~ o o co

o

o

0.4 1-----=@Il:F----I------I

o~------~------~~----~ o 0.1 0.2 0.3

Gm I Co [mm]

Figure 8. Distance vnanlin (aver which the cohesian reduces to zero) as a function of the ratio between mode /I fracture energy and cohesion

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Taking into account that data from ali tests are plotted, it is remarkable that a cle­ar linear trend can be observed. The correlation coefficient of the linear trend equalled 0.96. The formula for the linear regression line reads:

(9)

In Figure 9, the applicability of both eq. (2) and (3) is demonstrated for test se­ries carried out in the bi-axial arrangement. Softening according to eq. (2) is de­noted by exponential softening and according to eq. (3) by Hordijk softening. The distance Vnonl;n for eq. (3) was derived using eq. (9).

In Figure 9, it can be observed that eq. (3) results in initially steeper descending branches. Eq. (3) is more appropriate especially for the first part of the descen­ding branches.

Using eq. (2), the absorbed energy always equals the 'input' value GIII• Knowing this, it can be observed in Figure 9 that this is not true for the energy dissipated ac­cording the Hordijk softening. This is caused by the use of eq. (9) instead of the equation used in tension by Hordijk ( w, = 5.14 ~fI ). The parameters (, and ( 2

should be changed to 'release' ali the fracture energy when eq. (9) is used. Howe­ver, it is doubtful if such a modification of eq. (3) would still result in the reasonably adequate descriptions as obtained. This possibility was not explored further.

In general, it can be stated that eq. (3) in combination with eq. (9) gives a bet­ter approximation of the first (and most important part) of the descending branch than exponential softening, even though the dissipated energy in the mo­dei is less than the 'input' value. However, Van Zijl '996.(9) showed that the applica­tion of eq. (2) in a numerical simulation of the shear tests carried out in the 1993 arrangement (5), gives a reasonable approximation of the experimental results and Lourenço'996.(l) also showed that behaviour of shear walls could be approxi­mated reasonably well using eq. (2).

Figure 9. Application of eq. (2) (exponential softening) and eq. (3). (Hordijk softening) for the cohesion softening of shear tests.

1.6 1.6 ---

'E - experitT'l8l'lls 1 - experi~s

~ - - - Hordijk SClfteniflg - - - Hordijk sdtening - exponet1ia1 softening ~ - exponertial sdtering

12

~ ~ ! t 0.8

~~~ 0=-0.6 Nhnm

0=-0.3 Nh'rlm t 0= -0.3 Nhnm t 0.0 0.0 o 0.2 O .• 0.6 o 0.2 0.4 0.6

_ a) clay brick series wc·j096 + 1 :1:6 - bj cálcium si lícaie series CS·block96 + TLM

6. DILATANCY

Before dilatancy itself will be discussed, first the plastic displacements upl and vpl

of one of the series carried out in the bi-axial arrangement of the Pieter van Muss­chenbroek laboratory are analyzed . With those series it was possible to gain in­sight in the difference between tests carried out with pre-compression and tests with pre-tension. In Figure 10 the plastic normal displacements are plotted against the plastic shear displacements for the series with calcium silicate blocks (CS-block96 + TLM)

It can be observed that the initial slopes of the diagrams increase with increasing normal stress. Comparing different series with different modes of failure it was ob­vious that the type of failure influenced the magnitude of the normal displacement considerably. In Figure 4, it could already be observed that failure in the mortar would go hand in hand with larger normal displacements than with bond failure.

The correspondence between the initial slopes of the diagrams of tests with pre­tension and the initial slope of the tests with zero pre-compression, indicates that the normal displacements in the tests with zero pre-compression were already in­fluenced by tensile micro cracking . As a consequence, dilatancy should be mo­delled on the basis of tests with pre-compression.

For the dilatancy angle \jI the following tendencies could be observed during analysis.

• The initial value of the dilatancy angle decreases with increasing compressive stresses.

• Often, the dilatancy angle gradually reduces to zero with increasing shear dis­placement. However, also curves could be observed where the dilatancy angle remains more or less constant at a certain levei before dropping back to zero,

Figure 7 O. Normal displacement upi as a function of the shear displacement vpl

of the calcium silicate series CS-block96 + TLM

~ ;p.

0.2 hlH--+~~--+-~

i __ ,'.[nm]

a) general overview

0.03

0.02

0.01 IIAlr-lF.f-h-.4--f -- o> O.ONlrrm' ~O"=O.ONlrmf

-e-a"' .().3Nf~ - .. - a=.Q.6NJrmf

O~--~--~=c====~ o 0.025 0.00 0.075 -- ,'. [ mm ]

b) detailed view

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especially for normal stress leveis of -0.5 N/mm2 and -1 .0 N/mm2. This kind of behaviour could be associated with other types of failure than pure bond failu­re, e.g. combined bond and mortar failure. A failure mechanism according to Figure 4c may go hand in hand with rotation of broken pieces of units, resul­ting in irregular dilatancy behaviour.

• Of course the roughness of the crack surface determines the dilatancy beha­viour. In case of bond failure, the units themselves influence the roughness of the crack surfaces, and consequently the dilatancy.

• The limited amount of data did not show an influence of the tensile bond strength levei on the dilatancy.

To find a general formula describing dilatancy, it was assumed that the roughness of the crack surface is independent of the strength. Furthermore, it could be ob­served that the point where tamjf reduces to zero, is not much influenced by the pre-compression levei, especially when pure bond failure occurs. Therefore, a two-parameter expression is proposed with the initial value of the dilatancy and a roughness distance r after which the dilatancy is reduced to zero:

vpl :;; r: tamjf = tan\jfo { 2 (~ )'5 - 3 vpl + I} r r

(10)

V pl :;; r : tan\jf = O

tan\jfo: initial (maximum) value of the tangent of the dilatancy angle

r: roughness distance over which Man\jf reduces to zero.

The parameter tan\jfo can be estimated on the basis of Figure 11. In Figure 11 tan\jfo is presented per brick type as a function of the normal stress.

Figure 11. Influence of normal stress on tanyo per masonry type

..:.. #-c: ~

t

1.2

o day brick + GPM

'" C&brick90 + GPM t> C&block96 + TLM o da brick+ PM

o 0.8 o C&block96 + TLM

O~----~----~----~----~ -1.2 -0.9 -0.6 -0.3 o

normal stress (J (Nlmm2]

Table 7. Suggested values of the parameters of eq. (7 O) to describe dilatancy softening; r on the basis of fitting, tanyo according to linear regression lines of Figure 7 7

day brick + GPM CS-brick + GPM CS-block + TlM (bond failure) (bond failure) (bond+mortar failure)

cr [N/mm' ] -0.1 ·1.0 -0. 1 -0.9 -0.3 -0.6

r [ .] 0.75 0.3 0.75

tanyo [-] 0.91 0.33 0.38 0.10 0.65 0.45

It can be observed that the initial value tamjfo decreases with increasing compres­sive stress. The correlation coefficients of the linear regression lines were low, var­ying between 0.55 up to 0.76. The low correlation coefficients indicate that the use of the linear trend lines for values of tan\jfo, may result in large deviations com­pared with single test results .

Recommendations for the parameters of eq. (10) to describe the dilatancy of tes­ted masonry series, are presented in Table 1.

The recommendations are not intended to get an 'as good as' possible match with the obtained test data. The suggested values for r were not determined on the basis of some statistical method. The variation in the data is too large and too much influenced by various phenomena to make a robust approach possible. The most important consideration was that modelling of the dilatancy should be ba­sed on bond and/or mortar failure. It can be seen that for the rougher bond sur­faces of the clay brick + GPM, r was taken equal to 0.75 and for the smoother crack surfaces of the CS-bricks +GPM specimens equal to 0.3. The roughness of the partially bond / mortar failure in the CS-block96 + TLM series made a higher value for r compared with CS-brick90 + GPM series necessary.

In Figure 12, an overview is given of the suggested theoretical behaviour on the basis of the data measured in the test series.

Figure 72. Suggested theoretical approach for dilatancy behaviour and test data

t 0.25 0.5 0.75

~ vpI [rrrn]

(Iay briCks + GPW ' .

Eperirnentaldata(.rcf.a~ms)

-a" ..()1p.u~

- -o - o- -o,3 N1rm12

_. _. o- .{).5Wmml

O·-O6~

t ~2~--~--~--~ o 0.2 0.4 06

.-. vpI (rnTl]

't5-orickS + Gpf0- ' .

t o '---::-':::---::':=-c'::--' o 0.75 1 -+ vpI [mnJ

'(3-brocks96';: n f;l - .

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Especially for the CS-block96 + TLM, it is clear that the irregular behaviour of the test results is ignored with the theoretical approach.

7. CONClUDING REMARKS

From the experiments, important conclusions with regard to the failure envelope and post peak behaviour could be drawn. Continued research, especially with more brick-mortar combinations, is necessary in this field. Special attention has to be paid to obtain data sets with one type of failure, beca use combined failure mo­des often lead to diffuse post-peak data. Notches in specimens might be a possi­bility to avoid cracks in units. It is also recommended to carry out test series with a relatively low pre-compression levei e.g. 0.05 N/mm2, to gain more insight in the dilatancy phenomenon.

ACKNOWlEDGEMENTS

The described research was supported by the Dutch masonry industries and the Dutch Technology Foundation under grant EBW 3367.

REFERENCES

1. Hordijk, DA; Reinhardt, H.W. (1990), Testing and modelling of plain concrete under mode 110· ading, Micro Mechanics of fai lure of quasi brittle materiais, Elsevier Applied Science, pp.559-568, ISBN 1-85166-511-0

2. Lourenço, P.B; Rots, j.G.; Blauwendraad, j. (1994) Implementation of an interface cap model for the analyses of masonry structures, Proceedings of the EURO-C conference on Computational Modelling of Concrete Structures, Innsbruck, Austria

3. Lourenço, P.B. (1996), Computational Strategies for Masonry Structures, PhD-Thesis, Delft Uni­versity of Technology, Delft, The Netherlands, ISBN 90-407-1221-2

4. Mann, W., H. Müller (1977), 8ruchkriterien für querbeanspruchtes Mauerwerk und ihre Anwen­dung auf gemauerte Windscheiben, Bericht der Technische Hochschule Darmstadt

5. Pluijm, R. van der (1993), Shear behaviour of bed joints, Proceedings of the 6th North American Masonry Conference, Philadelphia, USA, 6-9 june, pp.125-136.

6. Pluijm, R. van der, (1996), Measuring of bond, a comparative experimental research, Procee­dings of the 7th North American Masonry Conference, South Bend, Indiana, 2-5 june, pp 267-281

7. Pluijm, R. van der (1999), Out-of-Plane Bending of Masonry, Behaviour and Strength, PhD­thesis, Eindhoven University of Technology, ISBN 90-6814-099-x

8. Rots, j.G.; Lourenço, P.B.(1993), Fracture simulations of masonry using non-linear interface ele­ments, proceedings of the 6'" NAMC. Vol. 2, pp 983-993, Drexel University, Phi ladelphia, USA

9. Zijl, G.P.A.G. van (1996), Shear transfer across bed joints in masonry: A numerical study, Tech­nical report 03.21.0.22.28, Delft University of Technology.