Determination of the Mortar Strength Using Double Punch Testing

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 193 (2017) 104 – 111

International Conference on Analytical Models and New Concepts in Concrete and Masonry Structures AMCM’2017

Determination of the mortar strength using double punch testing Piotr Matyseka*, Szymon SerĊgaa, Stanisáaw KaĔkaa a

Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland

Abstract The paper presents results of the Authors’ own studies on mortar strength using the DPT method. The results of experimental tests and numerical analyses are compared. Numerical analyses were performed for the 3D model, which consist of mortar, capping gypsum and steel punch. In the numerical simulation mortar was modelled using the Drucker-Prager plasticity model with strain hardening in the compression regime. For tension, a multidirectional smeared crack model was applied. The interface elements were used between mortar and gypsum and between the gypsum and steel punch in order to model the behavior of these joints. A good agreement between the results of numerical calculations and experimental research was obtained. On the basis of calibrated numerical model the effect of lining gypsum and the influence of sample thickness was analyzed. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2017 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility the scientific committee of the International Conference onModels Analytical Models and New Peer-review under responsibility of theofscientific committee of the International Conference on Analytical and New Concepts in Concrete and Masonry Structures. Concepts Concrete andinMasonry Structures Keywords: Mortar strength; double punch test; historical mortars; 3D numerical modelling

1. Introduction Determination of mortar strength in masonry is an important issue in the analyses of many existing structures. Due to the small thickness of the joints in masonry it is impossible to carry out tests on mortar prismatic samples (40 x 40 x 160 mm) proposed in standards for new masonry structures (EN-1015-1011 [1]). Currently, several nondestructive tests (NDT) and minor-destructive tests (MDT) are developed to estimate the strength of the mortar in the masonry joints [2,3,4]. One of them is double punch test (DPT). In the DPT method determination of mortar

* Corresponding author. Tel.: +48-12-628-21-60; fax: +48-12-632-09-66. E-mail address: [email protected]

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Analytical Models and New Concepts in Concrete and Masonry Structures

doi:10.1016/j.proeng.2017.06.192

Piotr Matysek et al. / Procedia Engineering 193 (2017) 104 – 111

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strength is performed on samples cut from the joints. The DPT method is introduced to DIN 18555-9 [5] and UIC 778-3R [6] codes. However, interpretation of the test results conducted by DPT is not straightforward. Many factors related to the geometry of the mortar samples and the method of their preparation for tests influences the results of experiments. A typical sample for testing the compressive strength of the mortar using DPT method has a height equal to the thickness of the mortar joint and cross section of 50 mm x 50 mm. Samples with cross sections of a circle with a diameter of 50 mm may also be used. A compressive load is applied to the samples in their center through the steel punchs with a diameter of 20 mm. The samples are then compressed locally on a small area. The loading of the samples in the DPT method is quite different than one used in the tests of mortars according to EN-1015-1011 [1]. The numerical calculations presented in [4] showed that in mortar samples tested using the DPT method transverse compressive stresses are created. Values of transverse stresses in mortar are a small percent of the vertical compressive stress. As a result the mortar strength tested using the DPT method is generally greater than the mortar compressive strength determined according to EN-1015-1011. However, the results of numerical calculations presented in [4] were conducted for the linear elastic material behavior. This fact strongly limited the scope of conclusions. In this paper a more advanced numerical approach is presented. Numerical analyses were performed for the 3D model. Mortar was modelled using the Drucker-Prager plasticity with strain hardening in the compression regime. For tension the multidirectional smeared crack model was used. The results of experiments and numerical calculations are compared and commented. Moreover, a supplementary parametric study concerning the influence of the thickness of mortar and lining gypsum strength on failure load and behavior of DPT sample is presented at the end of the paper. 2. Experimental research Tests were carried out on cement-lime mortar. The composition of the mortar is given in Table 1. The cylindrical samples (50 mm x 120 mm) and prismatic samples (40 mm x 40 mm x 160 mm) of the mortar were prepared. Table 1. Composition of tested mortar Component

Weight [kg]

Sand (0 ÷ 2 mm)

1309

Hydrated lime

164

Cement

184

Water

254

The samples were seasoned for 28 days in accordance with the recommendations of EN-1015-1011 [1]. Cylindrical samples before testing were cut to the proper size. The mortar compressive strength and the stress-strain curves was determined using cylindrical samples with a height of 100 mm (samples CC). The tensile strength of the mortar was tested on mortar cylinders with a length of 50 mm (samples CT). The samples to double punch testing (sample CD) were cut from cylindrical samples with a diameter of 50 mm. The CD samples before testing were aligned with gypsum (according to the recommendations of DIN 18555-9 [5]). A steel punch with a diameter of 20 mm was used. Fig.1 shows above mentioned mortar samples prepared for testing. The tests were carried out under displacement-control, at rates of 0.1mm/min (samples CC) and 0.01mm/min (samples CD). In addition to the destructive forces displacements were also recorded – see Fig. 1 (sample CC and CD). Prismatic samples 40 mm x 40 mm x 160 mm were tested in bending (samples CE/2) and under compression (samples CE/1) according to EN-1015- 1011 [1]. The test results are presented in Table 2. In the case of the DPT method, strength of mortar was determined as the ratio of the maximum load to the punch cross-section area.

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a)

b)

c)

Fig. 1. Mortar samples prepared to tests: (a) sample CC, (b) sample CT, (c) sample CD. Table 2.The results of the compressive strength tests of mortar. Strength parameters of the mortar

Sample numbers

Range value [MPa]

Mean value [MPa]

Compressive strength fcyl – test on cylindrical samples 50 mm x 100 mm – samples CC

3

4.29 – 4.34

4.3

Tensile strength f t,cyl – tests on cylindrical samples 50 mm x 50 mm – samples CT

3

0.83 – 0.99

0.9

Compressive strength fprism – tests according to EN-10151011– samples CE/1

6

3.51 – 4.39

4.0

Tensile strength ft,prim – test according to EN-1015-1011 – samples CE/2

3

0.99 – 1.04

1.0

Stress under compression fDPT – DPT testing – samples 50 mm x 16 mm samples CD

6

5.21 – 6.83

5.9

The results in Table 2 show that the typical lime-cement mortar was selected for the experimental study. This kind of mortar was often used for the construction of masonry structures at the end of the nineteenth century and in the first decades of the twentieth century. 3. Numerical analysis 3.1. Finite element model Numerical analysis of the DPT test was performed using DIANA finite element code [7]. Mortar, capping gypsum and steel punchs were modelled in 3D. The following types of finite elements were used: twenty-node isoparametric solid brick and fifteen-node isoparametric wedge. All types of used elements are based on quadratic interpolation of shape functions. The topology of FE mesh adopted in calculations is presented in Fig. 2. Due to the symmetry of sample’s geometry and loads one quarter of the sample with proper boundary conditions was considered. XZ, YZ, and XY are the planes of symmetry.

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Fig. 2. Finite element model for DPT sample.

In order to model a proper behavior of contact zones between the steel punch and gypsum or mortar and gypsum sixteen- and twelve-node interface elements with zero thickness was used at the contact surfaces. 3.2. Constitutive models for materials The complex behavior of quasi brittle materials like mortar and gypsum in multidirectional stress state was described by combining two constitutive models: Drucker-Prager plasticity and a multidirectional smeared crack approach. The fundamental assumption for these approaches is decomposition of total strain tensor into the elastic, plastic and crack strain part. Among other things this assumption allows combining different material behavior in a straightforward manner – see [8] for more details. In Drucker-Prager model the plastic strain is initiated when the following yield condition is satisfied: F ( σ, κ ) = 3J 2 + α F I1 − (1 − α F ) f c (κ ) = 0

(1)

where σ is the stress tensor, J2 is the second deviatoric stress tensor invariant, I1 is the first invariant of stress tensor, f c (κ ) is the compression strength as the function of the internal state variable κ , κ =

2 3

pl εijpl εijpl , ε ij is a

plastic strain tensor, α F is a material constant. The plastic strain rate is defined by the flow rule and governed by plastic potential in the form: G ( σ, κ ) = 3J 2 + αG I1

(2)

where αG is a material constant. In the present study the associated flow rule is considered, i.e. αG = α F . The function f c (κ ) is calculated from the uniaxial stress-strain relationship shown in Fig. 3a,b. In the uniaxial case

the relation between κ and ε pl is given by:

κ =−

1 + 2αG2 1 − αG

ε pl

(3)

The values of material constants describing plastic behavior of mortar and gypsum are shown in Table 3. If the principal stress σ 1 reaches the tensile strength ft another mechanism governs the material behavior. In the presented approach a multidirectional fixed crack model was used [9]. The first crack appeared after fulfilling Rankine maximum principal stress criterion. Consecutive cracks in the same integration point may appear only if maximum tensile stress exceeds ft and inclination angle between the primary crack and new σ 1 direction exceeds threshold angle θt . The constitutive relationship for Mode-I cracking is based on fracture energy Gf. The tension

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softening behavior adopted in the simulations is given in [10]. For Mode-II fracture the constant shear retention approach applies ( β s ). Table 3 summarizes the elastic (E – Young’s modulus, ν - Poisson’s ratio), plastic and fracture material constants adopted for mortar and gypsum. Table 3 Mechanical properties for mortar and gypsum

ν

E [GPa]

fc [MPa]

ft [MPa]

Gf [N/mm]

βs

αF

αG

[-]

[-]

[-]

[-]

[º]

Mortar

2.7

0.1

4.3

0.9

0.04

0.05

0.12

0.12

40

Gypsum

3.0

0.3

5.0

1.0

0.04

0.05

0.12

0.12

40

a)

θt

b)

Fig. 3. (a) mortar uniaxial stress-strain relationships, (b) mortar fc (κ ) function.

The steel punch - gypsum and gypsum - mortar contact was described by nonlinear elastic interface. Due to the lack of experimental data the simple uncoupled constitutive model was adopted in the analysis. In the case of the mortar/gypsum interface the stiffness in normal direction K nMG for compression and tension equaled 2.0·102MPa/mm and 0.1MPa/mm, respectively. The first value models the compression compliance of mortar weakened layer near the gypsum lining (the result of cutting and mechanical preparing of a sample). This stiffness was adopted by the trial-and-error method in order to obtain the best agreement between the measured and calculated loading-displacement path. The second one simulates brittle cracking. In the tangential direction stiffness of the interface was K tMG = 103MPa/mm. The tangential stiffness models the effect of friction that introduces the confinement in mortar near the gypsum lining. This stiffness was estimated to achieve the least difference between the simulated and experimental ultimate load. Mechanical parameters of steel punch - gypsum interface were the same as for mortar - gypsum interface except for compressive stiffness in normal direction K nSPG , which was equal to 104MPa/mm.

3.3. Solution strategy An incremental iterative procedure was employed for analyzed samples. The displacement controlled loading was applied in the analysis. The master control node was located at the center of steel punch top surface. The others nodes at this surface have the same displacement along the vertical axis as the master control node. The size of displacement increment was manually chosen and equaled 2·10-3mm. The increments were reduced to 2·10-4mm for calculation steps close to the failure load. For each displacement increment the equilibrium between internal and external forces was calculated using the Newton-Raphson procedure. The out-of-balance force and displacement norms were used as convergence criteria. In order to increase the convergence rate the line search algorithm was employed during the iteration process. 4. Discussion of results The results of experimental research and numerical calculations are presented in Table 4. The values of experimental and calculated failure forces (Fult) differ less than 2%. Consequently, there are small differences in the fDPT values determined in experiments and on the basis of numerical calculations.

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Piotr Matysek et al. / Procedia Engineering 193 (2017) 104 – 111 Table 4 Results of experimental research and numerical calculations Parameter

Experiments

Numerical calculations

Fult

[N]

1855.6

1894.1

fDPT=Pult / Apunch

[MPa]

5.9

6.0

fDPT / fcyl

[-]

1.37

1.40

fDPT / fprism

[-]

1.48

1.51

The values of fDPT are greater than the mortar strength determined on cylindrical sample (CC) – fcyl and the prismatic samples (CE/1) – fprism, respectively by 37% and 48%. A similar effect was described in [3]. In DPT tests mortar is in the complex state of stresses generated by load (local compression), the effects of friction between gypsum and mortar as well as confinement induced by not loaded area of mortar – Fig.4. The largest transverse compressive stresses in radial ( σ rr ) and circumferential ( σ θθ ) directions are located directly under loading transferred from gypsum to mortar. These stresses gradually decrease in a vertical direction towards the center plane of the sample. The maximum confining to vertical stresses near the sample center are 17%, both for radial and circumferential direction. The stress state in the sample explains the effect of higher fDPT strength compared with the strength obtained on cylinders. The higher vertical compressive stresses are associated with the higher confining pressure near the top surface of mortar sample. In the deeper layers of mortar the confining pressure is less (or even tensile stresses may appear). However, due to the sample geometry the vertical stress redistribution is possible over a greater area and the stresses σ zz in lower confinement zones are less. The failure of sample is associated with loss of confinement due to severe radial cracking that occurs in the free of load mortar area. σ zz [MPa]

σ rr [MPa]

σ θθ [MPa]

Fig. 4. Stress distributions for load equals 1.8kN.

Fig. 5. Calculation vs experiment - load-displacement diagram.

In Fig. 5 the force - vertical displacement diagrams obtained experimentally and numerically are compared. The numerical simulations correctly reproduce the experimental load-displacement path. The differences can be noted only for the post critical region where in experiments mortar behaves in a more ductile manner. In the numerical simulation a few steps after reaching the peak-load a severe jump in force is observed. For this calculation step the convergence criteria were not satisfied.

110


a)

b)

c)

Fig. 6. Mortar after test: a) top view, b) separated double cone, c) numerical prediction of failure mode – equivalent plastic strain ( κ ).

The numerical model also correctly reproduces the failure mode – see Fig. 6. In Fig. 6 the views of mortar sample after test are presented (Fig. 6a,b). Usually a few radial cracks appeared associated with the crushing of mortar between steel punches. The classical double cone failure mode was observed in the core of the mortar sample. Similar failure mode was obtained in calculations. For post-peak loads the material damage localizes in inclined narrow bands which connect in the center of the sample – see Fig. 6c where the equivalent plastic strain κ is presented. The inclination angle and range of damages band are quite similar in the test and simulations – compare Fig. 6b and Fig. 6c. 5. Parametric study In present studies the influence of two parameters on displacement-load behavior of DPT samples were investigated. Firstly, the effect of mortar thickness was considered. In Fig. 7a the load-displacement diagrams for three thickness of mortar: 10mm, 16mm (experimentally tested), 25mm are presented. All types of mortar samples behave in a similar manner. Moreover, the failure loads are almost equal. This observation is in contrast to experimental findings published in [3]. The experimental studies in [3] show that the thinner the mortar the higher the failure force is obtained. Fig. 8 shows the distribution of diagonal stresses. One can observe from this figure that for thinner mortars the vertical compressive stress is distributed over a smaller area than in the thicker one. On the other hand the thinner mortars have higher levels of confinement. The resultant of these two mechanisms provides similar failure loads for each thickness. In the authors’ opinion the mechanism that cause the effect of mortar thickness on fDPD has not been properly recognized yet and more experimental as well as numerical studies are needed in this area. a)

b)

Fig. 7. Parametric study: a) effect of mortar thickness, b) effect of gypsum compressive strength.

The gypsum strength has a noticeable influence on numerical failure load and on load-displacement behavior – Fig. 7b. The lower gypsum strength the lower failure loads is obtained and also the higher decrease in sample’s stiffness is observed. This effect can be explained by the smaller effective load area for samples with weak gypsum lining. The gypsum crushes near the steel punch edge that reduces the force transfer area. It should also be pointed out that the mechanical properties of gypsum are strongly dependent on time and humidity. Due to this fact in

111


experimental campaigns great care has to be taken on time of gypsum hardening and environmental conditions during performing tests. σ rr [MPa]

σ θθ [MPa]

t=25mm

t=10mm

σ zz [MPa]

Fig. 8. Stress distributions for load equals 1.8kN.

6. Summary and conclusions The mortar in samples tested using the DPT method is in a complex stress state determined by the geometry of samples and the method of application of a compressive load. The transverse compressive stresses cause the strength fDPT (conventionally called the mortar strength by DPT testing) is considerably greater than the mortar compressive strength determined on samples according to code EN-1015-1011. For the tested cement-lime mortar 48% difference was obtained. A good agreement between experimental results and numerical calculations in the area of failure load and the failure mode of the samples tested by DPT method was found. It has been shown that the numerical simulation can be a useful tool for the analysis of the DPT tests. The numerical study of the effect of sample thickness on fDPT was in contrast to experimental results reported in [3]. Due to this fact more research is needed to explain the mechanism that governs fDPT – sample thickness effect. Currently, the authors’ experimental and numerical investigations in this issue are in progress. In the presented studies samples CD (tested using the DPT method) were cut from cylindrical samples CC. The point was the analysis of DPT test in terms of the geometry of samples and method of compressive load transferring. The mortar in masonry is laid between the bricks. So, hardening of the mortar is carried out under specific conditions. For this reason, the difference between fDPT strength and mortar compression strength determined on cylindrical or prismatic samples can be larger than shown in Table 4 - see [2] [11]. References [1] EN EN-1015-1011: 2007, Methods of test for mortar for masonry - Determination of flexural and compressive strength. CEN. Brussels,2006. [2] L. Pelà, P. Roca & A. Aprile, Comparison of MDT techniques for mechanical characterization of historical masonry, in: Structural Analysis of Historical Constructions 2016, Van Balen & Verstrynge (Eds), Taylor & Francis Group, London, pp. 769-775. [3] E. Sassoni, E. Franzoni, C. Mazzotti, Influence of sample thickness on characterization of bedding mortars from historic masonries by double punch test (DPT),in: Key Engineering Materials. 624 (2015) 322-329. [4] L. Pelà, A. Benedetti, D. Marastoni, Interpretation of experimental tests on small specimens of historical mortars, in: Structural Analysis of Historical Constructions 2012, Jerzy JasieĔko (Ed), DWE, Wrocáaw, Poland, pp. 716-723. [5] DIN 18555-9, Prüfung von Mörteln mit mineralischen Bindemitteln – Teil 9; Festmörtel: Bestimmung der Fugendruckfestigkeit, 1999. [6] UIC Code 778-3R, Recommendations for the inspection, assessment and maintenance of masonry arch bridges. Final draft, 2008. [7] DIANA. User’s Manual. TNO DIANA BV., 2016. [8] R. de Borst, Smeared cracking, plasticity, creep and thermal loading - a unified approach. Com. Meth. Appl. Mech. Eng. 62 (1987) 89-110. [9] R. de Borst, P. Nauta, Non-orthogonal cracks in a smeared finite element model, Engineering Computations. 2 (1985) 35-46. [10] H. A. W. Cornelissen, D. A. Hordijk, H. W. Reinhardt. Experimental determination of crack softening characteristics of normalweight and lightweight concrete. Heron, 31(2) (1986) 45–56. [11] P. Matysek. Identification of compressive strength and deformability of brick masonry in existing buildings. Ed. Cracow University of Technology, 2014.