ce travail a pour objectif de modéliser l'ensemble mortier/bloc et d'analyser la résistance mécanique à l'interface. l'étude prend comme support d'étude une batisse historique au Maroc. Nous choisissons un mur de la construction et nous procédons à une simulation numérique. Nous étudierons la répartition des contraintes dans le mur. Deux cas seront considérés : un mur sollicité non restauré et un mur sollicité non restauré. Le but de ces simulations étant de comparer les répartitions des contraintes dans chacun des deux cas afin de justifier ou non l’intérêt de l’utilisation d’un mortier de restauration de faible résistance. Les caractéristiques mécaniques obtenues lors des essais non-conventionnels, en l’occurrence le module d’élasticité statique et le coefficient de Poisson seront utilisés dans cette analyse. le comportement du système est considéré comme élastoplastique

BIDEQ, Mustapha

DESCAMPS, Thierry

FIHRI FASSI, Hichame

HAMMOU, Youness

LAMANT, T.

TIRONI, Simone

VANPARYS, Laurent

I-Revues

21ème Congrès Français de Mécanique                                                                  Bordeaux, 26 au 30 août 2013 
  
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Study of mechanical compatibility at the mortar-block 
interface in a heritage building 
Y. HAMMOUa, H. FIHRI FASSIa, L. VAN PARYSb,M. BIDEQc. DESCAMPSb, S. TIRONIb , , N. LAMANTb 
a. Faculté Des Sciences et Techniques (FST), Route de Casablanca, SETTAT (Maroc)  
b. Université de Mons(UMONS) - Faculté Polytechnique, 20 Place du Parc, MONS (Belgique) 
c. ENSA de Safi, Maroc 
 
Résumé :  
Ce travail a pour objectif de modéliser l'ensemble mortier/bloc et d'analyser la potentielle occurrence de 
problèmes mécaniques aux interfaces en présence d'une éventuelle incompatibilité. L’étude prend comme 
support un bâtiment historique au Maroc. Les auteurs choisissent  une cellule représentative de la 
construction et procèdent à une simulation numérique, étudiant la répartition des contraintes dans la 
maçonnerie. Pour mener à bien ces analyses, les caractéristiques mécaniques (Module de Résistance et 
Module d'Elasticité) sont obtenues au moyen de techniques non-conventionnelles adaptées au domaine de la 
Conservation du Patrimoine qui sont brièvement décrites. Le scenario retenu pour l’étude concerne un mur 
porteur restauré au moyen d’un mortier non adéquat. Le but des simulations est de comparer la répartition 
des sollicitations internes entre la situation d’origine et la situation restaurée afin de quantifier les risques, 
pour les matériaux devant être conservés, liés au phénomène de « déviation de contraintes » et justifier ou 
non l’attention particulière à porter sur le choix d’un mortier spécifique à la restauration de ce bâtiment. 
 
 
Abstract : 
This research work aims at modeling the mortar-block assembly for analyzing the potential occurrence of 
mechanical problems at interfaces as the consequence of an eventual incompatibility. The study considers a 
heritage building located in Morocco. The authors focus their attention on a representative part of the 
building and perform numerical simulations, studying the stress repartition inside the masonry. For carrying 
out efficient analysis, the mechanical characteristics (Modulus of Resistance, Modulus of Elasticity) are 
collected through non conventional testing techniques dedicated to the field of Heritage Conservation that 
are briefly described. The scenario considered in the proposed study concerns a bearing wall restored with a 
non adequate mortar. The goal of the modeling works is to compare the repartition of internal solicitations 
between the original situation and the restored one in order to quantify the risk, for materials that should be 
conserved, associated with the “stress shielding” phenomenon and to justify the particular attention to be 
paid for the choice of a specific mortar for interventions to be carried out on the concerned building. 
 
Mots clefs: masonry, numerical simulation, compatibility, stress shielding 
1 Introduction 
Masonry has been used for centuries in many places around the world. Most of the master pieces of our 
heritage are then erected with this material. For several reasons, these heritage structures should be preserved 
in order to be transmitted to following generations. Although they may appear trivial, restoration works are 
easily impacted by parasite problems associated with (essentially mechanical) incompatibilities between 
conserved and brought materials. These problems affect, economically and technically, the durability of the 
operations and constitute a point of interest for people engaged in structural mechanics. 
 
21ème Congrès Français de Mécanique                                                                  Bordeaux, 26 au 30 août 2013 
  
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2 Heritage masonry: specificities, weaknesses and challenge 
Erectable with many types of bricks or stones with mortar joints according to varied patterns, the masonry 
concept concerns a wide range of building materials that are characterized by heterogeneous mechanical 
behavior [1]. Based on old constituents and ancient techniques (even if the know-how could be of advanced 
level at their construction period), heritage masonry may suffer of low mechanical properties still restricted 
by degradations induced by aggressive environments or exceptional conditions to which they are exposed 
[2,3]. In order to preserve ancient structures, restoration campaigns will generally opt for the replacement of 
altered parts by more reliable ones. Such kind of works carried out on masonries may sometimes concern 
bricks or stone but, in almost any case, will lead to partial mortar replacement (at least pointing operations). 
A specific attention should then be paid in the prescription of the works: contemporary elements should 
achieve a sufficient compatibility (mechanical, aesthetical, …) with the ones that are kept. 
3 Non conventional data acquisition on materials in heritage buildings  
In order to better document the problems of incompatibility between contemporary mortars and old 
masonries, the characterization of mechanical properties is of crucial interest in the approach of the subject. 
Nevertheless, extracting great quantities of materials within a structure whose value justifies the conservation 
in order to perform conventional characterization tests is a delicate and discussed spot. For the needs of the 
present research, the authors rely on experimental devices which make it possible to collect mechanical data 
on materials (compressive strength through the Modulus of Resistance and rigidity through the Modulus of 
Elasticity) through very few destructive approaches, namely: 
1- “Translational Cutting Test” [3], to obtain the properties of resistance of materials. Not usual in classical 
material mechanics, it is widely used in the petroleum industry. It consists in tracing at the surface of a 
sample by removing successively thin layers of material with a rectangular Polymer Diamond Coated cutter 
of width w, a groove at constant shallow depth d. The cutter is inclined by an angle θ  and is displaced at 
constant horizontal velocity v. The magnitude and inclination of the force F acting on the cutter are 
accurately measured and recorded during the test. Thanks to a dedicated phenomenological model, the 
Modulus of Resistance of the tested material may be computed from the relationship between the recorded 
force and the destroyed section. This technique is characterized by its simplicity, its time efficiency, the 
measuring accuracy and the main characters of the test which is relatively not very destructive due to the 
limited quantity of the necessary sample for the realization of the test as well as not dependent on the 
experimental procedures and analysis compared to the type of studied materials. 
FIG. 1 - Schematic action of the PDC cutter (left) and experimental device at UMONS (right) 
2- “Pulse Sonic Test” [4], to obtain the properties of rigidity of materials. Usually encountered in classical 
material mechanics where it is used in many fields, it relies on the well-known relationship linking the sound 
velocity inside a material with the dynamic version of the Modulus of Elasticity. Many experimental devices 
are commercially available: an emitter sends a sonic pulse on a given location at the surface of the material, a 
receiver detects it at another place and embedded computer-aided facilities allow determining the sound 
velocity based on the distance between emitter and receiver. 
 
 
 
21ème Congrès Français de Mécanique                                                                  Bordeaux, 26 au 30 août 2013 
  
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4 Masonry typology for present study  
Typical of systems that may be encountered in Morocco, the masonry pattern constituting the minaret walls 
of AL MASJID AL AADAM Mosque in the old medina of Safi town (Figure 2) is chosen as starting point 
for the present study, focusing on potential restorations that would affect the front wall. In its preliminary 
shape, the proposed parametric study will rely on numerical simulations carried out on an elementary cell 
that is representative of the masonry encountered in the minaret wall (Figure 3). 
 
 
 
FIG. 2 - Al Masjid Al Aadam rebuilt in 1807 FIG. 3 –  elementary cell: front view (left), section (right) 
The proposed method is general: once developed, it is directly transposable to any other masonry pattern 
concerned by restoration operations where contemporary mortar is brought. The elementary cell is composed 
of the conserved elements (block and mortar) and of the new mortar that is used for pointing both faces of 
the considered wall after weathered mortar material has been removed on a 2 cm depth. The preserved 
blocks are parallelepiped elements of 9 x 6 x 19 cm3 and all the joints (head joints and bed joints) present a 
thickness of 1 cm. Due to its position inside the minaret wall, the cell is assumed to be impacted by a static 
load pressure of 10 daN/cm2, taking the weight of above elements (wall and flagstone) into account. For 
replicating the natural confinement acting on the cell while circumventing edge effects, rigid plates are 
placed on the superior and under the inferior face of the elementary cell with hard contact and friction 
without sliding conditions and continuity conditions are imposed on lateral facets of the cell. Numerical 
simulations are performed with SIMULIA ABAQUS software [4], coupled with Matlab which manages the 
parametric study (see below) and controls the ABAQUS calculation files. A tridimensional model is 
considered. In this preliminary approach, homogeneous and isotropic linear materials are considered for the 
simulations although more complicated studies (even with damage for blocks and/or mortar) are in progress.  
5 Simulated scenario 
In classical conservation approaches, repointing is a restoration operation that will concern joints (usual 
weak point of the structure) once they will have reach a given degree of alteration. The intervention consists 
of the digging of the joints manually or with a mechanical tool. According to their cohesion, the adherence 
and the state of degradation, the joints are dismantled on 1 to 3 cm of depth (in our scenario 2 cm) in order to 
guaranty a satisfying embedding for the new mortar that will be brought. Before repointing, masonry will be 
washed by brushing and often vacuum-cleaned with compressed air or high-pressure water flows depending 
on the friability of materials.  Once the surface of the joint humidified, the filling must be made following 
distinct steps to maximize adherence and avoid any possible shrinking of the new mortar.  
Mechanical incompatibility problems associated with repointing operations intervenes in relationship with 
the recourse to great resistance and/or great stiffness contemporary mortars compared to those of old block 
and mortar. The usage of inappropriate binders (nervous cement, industrial limes, …) in mortar mixes is the 
crucial problem of the 20th and 21st centuries. It may give birth to mortars that are not adapted to the “work” 
of the old buildings. In the short-term, the stress shielding phenomena has to be feared as it creates zones 
with stress increase and can potentially promote damages in sensitive blocks (Figure 4). In the long-term, a 
mortar that is too rigid will not be able to follow the displacement of the structures over the years; tensions 
will appear between the blocks and the mortar, mechanically affecting the structural behavior of masonry.  
21ème Congrès Français de Mécanique                                                                  Bordeaux, 26 au 30 août 2013 
  
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For helping practitioners to orientate their day-to-day practice, the authors undertook to determine range of 
parameters associated with limit state configurations. Based on such boundary knowledge, it becomes 
possible to quantify practical risks associated with situations that are faced. In the proposed parametric study, 
the fixed morphology of the masonry cell will be considered under fixed loading but the Modulus of 
Elasticity of the new mortar will be modified (between 1 and 30 times the MOE of conserved mortar) for 
several values of MOE for the conserved block (between 40 and 120 times the MOE of conserved mortar). 
Such an approach is likely to highlight the occurrence of the stress shielding phenomenon.  
 
Designation of Material Modulus of Elasticity  [daN/cm2]  Poisson's ratio[-] Density [kg/cm3] 
Conserved mortar 3 000 0.25 0.0020 
Conserved block 40 x 3000  120 x 3000 0.25 0.0020 
New mortar 1 x 3000  30 x 3000 0.25 0.0020 
 
Tab. 1 – Mechanical properties of various materials used in the parametric modeling 
 
 
FIG. 4 – Stress shielding scheme: masonry repointed with identical mortar (left) or too rigid mortar (right) 
6 Preliminary Results 
With regard to field observations, the present study presents evolution of results around edges of blocks 
concerned by the restoration process. The treatment of the results of the simulation are involved for a local 
interest volume on the corner of the block, see (figure 5) 
 
 
FIG. 5 – schematic view of the elementary cell and local interest volume for results visualization 
21ème Congrès Français de Mécanique                                                                  Bordeaux, 26 au 30 août 2013 
  
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For each pertinent face of the local interest volume, the evolution of stresses associated with specific damage 
patterns are plotted in Figure 6, Figure 7 and Figure 8. The maximal tensile stress on the Stretcher face may 
be responsible for crack initiations while compressive stresses for Head and Bed faces could eventually lead 
to crushing if blocks are composed with weak or weathered material. The presented results of these 
preliminary investigations outline the stress shielding phenomenon may take place under specific range of 
properties and, further than some boundaries, no critical evolution should be feared any more. Such 
considerations may now be used as guidelines for the setup of advanced simulations that are now in progress, 
namely taking damage into account with the Barcelona Model implemented in ABAQUS SIMULIA. 
 
FIG. 6 - Evolution of ratio “max tensile stress / max tensile stress (ref before restoration)” for Stretcher face 
(S) of local volume, with the ratio ENM / ECM for several ECU/ECM values and under fixed loading 
 
 
FIG. 7 - Evolution of the ratio “compress stress max / compress stress max (ref before restoration)” for 
Header face (H) of local volume, with the ratio ENM/ ECM for several ECU/ECM values and under fixed loading  
21ème Congrès Français de Mécanique                                                                  Bordeaux, 26 au 30 août 2013 
  
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FIG. 8 - Evolution of the ratio “compress stress max / compress stress max (ref before restoration)” for Bed 
face (B) of local volume, with the ratio ENM/ ECM for several ECU/ECM values and under fixed loading  
7 Conclusions and further works 
Although mechanical incompatibility plays a great role in the durability associated to restoration operations 
carried out on heritage masonry, the current recourse to trial & error approaches is not a fatality. The present 
work proposes preliminary results showing that numerical simulation may be used for documenting the 
situation faced by practitioners. Since these results are still partial, no strong conclusion may be edited. 
Nevertheless, encouraged by the presented observations, further investigations are now in progress. They 
rely on damageable material models for the blocks and will help establishing practical tools, usable on the 
building sites for risk estimation. 
8 Acknowledgement 
The authors would like to thank the Agence Universitaire de la Francophonie as well as Wallonie Bruxellles 
International for their financial support that allowed both the authors from Morocco to join the Civil 
Engineering Department of UMONS for initiating this research work. 
References 
 [1] R.PEALES, Modélisation du comportement mécanique par éléments discrets des ouvrages maçonnés 
tridimensionnels : contribution à la définition d'éléments de contacts surfaciques, Thèse de doctorat de 
l'université de Montpellier II, 23-36, 2007. 
[2] A.THOIKONOMOPOULOU, Approches numériques pour l’étude du comportement des structures 
maçonnées anciennes : un outil base sur le calcul a la rupture et la visualisation graphique, Thèse de 
doctorat  de Ecole Nationale Supérieure D’architecture De Paris La Villette Ecole Doctorale «Ville, 
Transports Et Territoire», Université Paris-Est, 6-9, 2009. 
[3] F.FOUCHAL, Contribution à la modélisation numérique des interfaces dans les structures maçonnées, 
Thèse de doctorat  de l’université de Reims Champagne-Ardenne , 43-51, 2006. 
[4] L. VAN PARYS, F. DAGRAIN, L. LEOSKOOL , The recourse to cutting-based tomography for 
quantifying the surface strengthening of altered stones, ICDS12-International conference durable 
structures: from construction to rehabilitation  Lisbon, Portugal. 
[6] ABAQUS ,ABAQUS Version 6-10-1, User documentation. Dassault systèmes Simulia. 


Study of mechanical compatibility at the mortar-block interface in a heritage building

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