This study demonstrates the feasibility of using a simple method to measure the resonant
fundamental frequency for determining the MOE (dynamic Young’s modulus) of lime and
cement mortars.
The procedure follows the instructions stated in the UNE-EN ISO 12680-1 standard for
refractory products although in this study the instructions are applied to standardized RILEM
4x4x16 cm test samples made of lime and cement mortars.
The simplicity of the procedure as well as its correlation to other measured variables,
suggest that it can be widely applied in studies about the evolution of the physical
characteristics in lime mortars, such as mechanical strength, static Young’s modulus,
carbonation depth, etcPostprint (published version

Pérez, F

Rodríguez Cantalapiedra, Inma

Rosell Amigó, Juan Ramón

English

UPCommons. Portal del coneixement obert de la UPC

 SIMPLE METHOD OF DYNAMIC YOUNG’S MODULUS DETERMINATION IN LIME AND CEMENT MORTARS  1Rosell Amigó, J.R.*; 2Pérez F.; 3 Rodríguez Cantalapiedra, I.  1 Department of Architectural Technology II, School of Building Construction of Barcelona. (EPSEB), Universitat Politècnica de Catalunya, España 2 School of Building Construction of Barcelona (EPSEB), Universitat Politècnica de Catalunya, España 3 Department of Applied Physics, School of Building Construction of Barcelona (EPSEB), Universitat Politècnica de Catalunya, España  Joan.ramon.rosell@upc.edu   ABSTRACT  This study demonstrates the feasibility of using a simple method to measure the resonant fundamental frequency for determining the MOE (dynamic Young’s modulus) of lime and cement mortars.  The procedure follows the instructions stated in the UNE-EN ISO 12680-1 standard for refractory products although in this study the instructions are applied to standardized RILEM 4x4x16 cm test samples made of lime and cement mortars. The simplicity of the procedure as well as its correlation to other measured variables, suggest that it can be widely applied in studies about the evolution of the physical characteristics in lime mortars, such as mechanical strength, static Young’s modulus, carbonation depth, etc.     1.-Introduction  With respect to the mortars used for restoration, it is especially important to know its modulus of elasticity. Usually some of the cement mortars overstiffen the building causing changes in its structural performance.  Since those restoration mortars are formulated from air limes (with or without puzzolana) and hydraulic limes, it is interesting to know the procedure of the carbonating process, the mechanical resistance gain, the stiffness, etc.  One of the basic parameters in the resistance of the materials and therefore in the area of the buildings materials is the Young’s modulus, which indicates the deformation capability of a given material in its linear elastic span depending on the strain to which is subjected.  The common method used in laboratory settings is the static testing by which mechanical properties of mortar lime are determined. Bearing in mind the assumption of homogeneity of the investigated media, elastic properties are characterized by a constant-static modulus that determines the relation between the stress and the strain applied.    Another group of techniques involves the application of non-destructive acoustic waves that have been successfully used in other materials such as wood, natural stones and refractory products.   The method enabling the determination of the dynamic modulus is relatively simple, inexpensive and suitable also for field application.  This non-destructive testing minimizes the possibility of rupture of the material or test specimens which represents a saving on the one hand and on the other provides new results for testing in the estimation of the material parameters.   For some of the specific materials, such as natural stone [1] and refractory products [2], the application of analysis methods of its fundamental natural frequency or resonant frequency in order to determine its MOE (dynamic Young’s modulus) has been standardized although this standardization has not been made in the case of the mortars.    2.-Objective  The aim of our work is to obtain some preliminary results for evaluating the possibility of applying the non-destructive test based on the resonant frequency analysis of mortars samples RILEM 4x4x16 made from very simple and economic elements. With the aim to refine the determination of the mortars modulus of elasticity, some standards could be determined by the investigation.  Some of the tests we can use to calculate the relative reliability of those standards are:  - MOE (dynamic elasticity modulus of elasticity) determination test by impulse excitation of vibration and the subsequent analysis of the resonant basic frequency. - MOE determination test from the velocity at which ultrasonic impulses propagates through the sample. - Static flexural test to obtain the linear spam of the stretch-deformation graph. - Flexural and compressive fracture test.   3.-Mortars to test  Since the main objective of this work is to study the validation and reliability of the non-destructive testing methods, the mention of this point will be brief and only to illustrate results more clearly.  The natural frequency analysis test will be applied on standard specimens according to RILEM 4x4x16 cm. The mortars are of 8 different types depending on the conglomerates and sand dosage, but the study is centred on two types of conglomerates (hydraulic lime NHL-3,5 and air lime CL-90 and Portland cement CEM I-42,5) and two types of aggregate granulometric curves of calcareous origin (Table 1).   Water600 μm 3600 μm W/Sol.NHL 3,5 1: 2,7‐600 1 2,7 0,19NHL 3,5 1: 4‐600 1 4 0,19NHL 3,5 1: 2,7‐3600 1 2,7 0,15NHL 35 1: 4‐3600 1 4 0,14CC 1: 2,7‐600 0,6 0,4 2,7 0,24CC 1: 4‐600 0,6 0,4 4 0,22CC 1: 2,7‐3600 0,6 0,4 2,7 0,2CC 1: 4‐3600 0,6 0,4 4 0,18SandCodeCL‐90NHL‐3,5CEM I‐42,5BinderMax. Size  Table 1: Nomenclature and dosage  The quantity of water for the mixture has been defined by a settlement in a 155±5 mm shaking table according to standard [3] and the curing process has followed this schedule:  - 7 days in a saturated environment in a wet chamber (R.H. >95% and 18◦±1). - 21 days in laboratory environment (RH 50% ±5 and 20◦C ±2) - Drying in a mould dryer at 60◦C until even temperature.  4. Young’s modulus determination  In order to find the density of each of the mortar types that constitute the specimens,  it is necessary to determine its  weight with a precision balance of 0,01 g as well as its length, width and thickness with a gauge (as the slide-gage of 0,01 mm).  4.1. Longitudinal MOE by impact (MOE long)  The most important task is to obtain the fundamental mode resonant frequency when the specimen is subjected to an instantaneous pulse (beating) and to register the signal or the frequency spectrum that this beating produces. The analysis of the signal is made by a software obtained in Fakopp [4] and based in the fast Fourier transform (FFT) that directly identifies the value of the higher intensity frequency.  A drawing of the equipment is shown in Figure 1. It match the diagram of blocks of the device as shown in [2].          Fig. 1. Drawing and picture of the equipment  The device is composed of:  1. A plexor with an end made of steel or hardwood; its weight has to be suitable for preventing a physical movement of the specimens when the beating is produced. Appropriate plexor weight has to be a 5% of the specimen weight. The handle of the flexor has to be made of a nonrigid polymer material (methacrylate in this work).  2. Items for supporting the specimens or test samples. The role of the holders in this method is very important since they isolate mortar specimens from external vibrations and their position defines the vibration mode of the samples.  flex. Impactlong.impact0,224∙L 0,224∙L  Fig. 2. Image of the support and impact zones  The holders being used are made of triangular prisma-shaped extrusioned polystyrene of 35 kg/m³ density and with sides of 3 cm. The samples are supported by the edges of this prism.   1 3 4 2  3. Signal register device. Non-contact signal transducers have been used in this study in order to prevent miscalculations caused by the flutters that could be generated by the slightest movement of the samples. Depending on the vibration frequency range of a given material, it will be necessary to choose a transducer able to correctly translate these frequencies. The transducers must be placed in the antinode points fixed in the standard.   4. Signal processing system and analysis software [4]. This is composed of: signal conditioner/amplifier, signal analyzer, display showing the frequency and the analysis of the obtained spectrum.  The image of the product we obtain is:                   Fig. 3. Screen image reproduction of the software used  From the value of the resonant frequency given in Hz, we can obtain the pulse velocity:  V = 2Lf  V = Velocity L = test sample length (160 mm) f = Resonant frequency  And using the density value, it is possible to calculate the MOE long value:  MOE long = ρ v2 ρ = density  The value we use as resonant frequency is the average value of six successive readings obtained with a maximum difference of 1% between them.  4.2. Flexural MOE (MOEflex) by impact  Holding the specimens in the corresponding face to the bottom of the mould (face 1), and rotating them 90 degrees and holding in a lateral side of the mould (face 2),  successive readings of the flexural resonant frequencies are made. Specifications described in standard [2] referring to the conditions of the holders, results calculations, etc., have been followed. It is considered a 0, 22 Poisson’s ratio.  4.3. Longitudinal MOE (MOEus) by ultrasound   A transmitting and receiving appliance of ultrasound C368 made by Matest, was used for this determination. This appliance has 55 kHz transceiver feelers.  It has been measured the required time by the ultrasonic pulse to go through the test sample in longitudinal direction (160 mm)  The velocity of the longitudinal propagation of ultrasonic waves through the specimen (V us) has been determined as:  V = L/t  t = time it takes the ultrasonic waves to go through the sample   Longitudinal MOE by ultrasound has been calculated with the expression:  MOElong = ρ v2  4.4. Static MOE by flexotraction  The procedure to determine static Young’s modulus has been to manipulate specimens with strain gages and carry out flexural test by means of load increments until the signal stabilization of tensile strength and unital strain (* *). Linear regression in the initial zone of the graph (Figure 5) allows determining the Young’s modulus. With the purpose of facilitating a larger flexural zone, pure and constant, a proof loading system in two points has been used (Figure 4).  40strain gage20 40 40 40 20  Fig. 4: Image of the load and supports working points   y = 8185,x ‐ 0,008R² = 0,99900,20,40,60,811,21,41,61,80 0,00005 0,0001 0,00015 0,0002 0,00025Traction  Stress MPaStrainCC 0.6:0.4:2.7 600 (2)  Fig. 5: Strain-traction stress graph in the linear-elastic zone  5. Experimental results and discussion  Table 2 represents the results of the non-destructive test for the MOE determination.  Absolute errors for the MOE long and MOE flex determination have been omitted since only in one specimen the value exceeded 1%.  Values of the coefficients of variation expressed in % (C.V. %) of the results of each mixture, in general lower than 5%, prove the specimens’ homogeneity and the reliability of the measurements.  Test  face  1 face 2NHL 3,5 1 7656 7334 7495 7024 7259 89521: 2,7‐600 2 8346 8063 8205 C.V. % 4,7 8521 C.V. % 10,0 8363 C.V. % 7,3 10100 C.V. % 7,03 7752 7614 7683 Media 7794 7488 Media 7678 7585 Media 7736 8975 Media 9342NHL 3,5 1 4450 4547 4498 3958 4228 59411: 4‐600 2 4612 4624 4618 C.V. % 2,1 4342 C.V. % 4,9 4480 C.V. % 3,3 5944 C.V. % 0,53 4584 4272 4428 Media 4515 4037 Media 4112 4233 Media 4314 5997 Media 5961NHL 3,5 1 10392 9723 10057 9742 9900 123661: 2,7‐3600 2 10279 10090 10184 C.V. % 3,4 9674 C.V. % 1,8 9929 C.V. % 2,6 13001 C.V. % 2,53 10934 10509 10722 Media 10321 10010 Media 9809 10366 Media 10065 12701 Media 12689NHL 3,5 1 8423 8004 8214 7876 8045 105911: 4‐3600 2 8741 8373 8557 C.V. % 2,9 7928 C.V. % 1,5 8242 C.V. % 2,2 10927 C.V. % 2,83 8316 7862 8089 Media 8287 7702 Media 7835 7896 Media 8061 10344 Media 10620CC 1 9791 9736 9763 9848 9806 121971: 2,7‐600 2 9781 9450 9615 C.V. % 3,0 9913 C.V. % 0,8 9764 C.V. % 1,8 11991 C.V. % 2,33 9255 9164 9209 Media 9529 9755 Media 9839 9482 Media 9684 11644 Media 11944CC 1 7771 7604 7687 8040 7864 101191: 4‐600 2 7510 7821 7665 C.V. % 1,1 7928 C.V. % 0,9 7796 C.V. % 0,9 10423 C.V. % 1,83 7657 7994 7825 Media 7726 8064 Media 8011 7945 Media 7868 10457 Media 10333CC 1 13511 12943 13227 14225 13726 164651: 2,7‐3600 2 12987 13647 13317 C.V. % 1,3 14212 C.V. % 2,0 13765 C.V. % 1,6 16710 C.V. % 3,23 13303 12672 12988 Media 13177 13739 Media 14059 13363 Media 13618 15713 Media 16296CC 1 13630 13164 13397 13814 13606 190631: 4‐3600 2 13493 13310 13402 C.V. % 2,2 13999 C.V. % 3,0 13700 C.V. % 2,6 18774 C.V. % 4,73 13038 12742 12890 Media 13230 13219 Media 13677 13055 Media 13453 17434 Media 18424MOEus (MPa)MEAN MOE impact (long.  & flex)MOElong. (MPa)MOEflex. (MPa) Table 2. Results of several MOE   The result of the correlation between MOE long and MOE flex is shown in Figure 6, where the accuracy and correlation between both types of determinations are evident.   y = 0,994xR² = 0,961y = 0,972xR² = 0,97304000800012000160000 4000 8000 12000 16000MOEflex.MOElong.MOElong. vs MOEflex.MOEflex. face 1 MOEflex. face 2  Fig. 6. Correlation between MOE long and MOEflex.  y = 1,167x + 847,1R² = 0,975y = 1,275x + 14,90R² = 0,92540008000120001600020000400080001200016000MOEus MEAN MOE impactCorrelation between diferents systems to determine MOENHL 3,5CC Fig. 7. Correlation between MOE impact and MOEus.  Figure 7 compares the results obtained by impact (average MOE long and MOE flex) with those determined by the velocity at which ultrasonic waves propagate. The correlation is excellent (R²of 0,97 and 0,92) although the values obtained by ultrasound are clearly higher (16 and 27%) than the impact ones. Results corresponding to the determinations of the elasticity modulus by static flexure (E flex) and stress values of the flexotraction and compression tests are shown in table 3. Coefficients of variation values of the results of each mixture are clearly higher than the previous ones. As for the Young modulus, variability fluctuates between 5 and 18%.  Test NHL 3,5 1 7354 1,34 5,41: 2,7‐600 2 10055 C.V. % 15,6 1,37 C.V. % 1,5 6,7 C.V. % 15,53 8590 Media 8666 1,33 Media 1,35 5,1 Media 5,71NHL 3,5 1 4684 0,78 2,61: 4‐600 2 4894 C.V. % 7,3 0,83 C.V. % 6,0 2,8 C.V. % 3,93 5392 Media 4990 0,88 Media 0,83 2,6 Media 2,64NHL 3,5 1 10765 1,9 6,01: 2,7‐3600 2 9167 C.V. % 8,0 1,75 C.V. % 4,4 6,3 C.V. % 3,43 10038 Media 9990 1,78 Media 1,81 5,8 Media 6,04NHL 3,5 1 8480 1,09 4,61: 4‐3600 2 7702 C.V. % 5,2 1,12 C.V. % 5,3 4,1 C.V. % 6,63 8405 Media 8196 1,01 Media 1,07 4,2 Media 4,28CC 1 10526 2,57 10,51: 2,7‐600 2 8185 C.V. % 14,7 2,13 C.V. % 9,4 10,5 C.V. % 3,03 8290 Media 9000 2,39 Media 2,36 10,0 Media 10,33CC 1 8914 1,97 7,71: 4‐600 2 10767 C.V. % 10,9 2,32 C.V. % 8,2 8,0 C.V. % 6,23 9020 Media 9567 2,13 Media 2,14 7,1 Media 7,60CC 1 12425 2,10 12,01: 2,7‐3600 2 C.V. % 5,5 2,11 C.V. % 5,5 13,4 C.V. % 7,33 13428 Media 12927 2,31 Media 2,17 11,6 Media 12,34CC 1 15468 2,88 12,11: 4‐3600 2 12040 C.V. % 17,6 2,51 C.V. % 10,4 10,9 C.V. % 6,93 11174 Media 12894 2,36 Media 2,58 10,7 Media 11,24Compresion Stress MPaE bending Traction stress Mpa   Table 3. Results of Eflex and flexotraction and compression strength.  From the comparative analysis of all the results, we can highlight the high correlation between flexural Young’s modulus and MOE by impact and ultrasound (R²of 0.94 and 0,92) (Figure 8). Linear relations between both methods can be established in the cases we have studied; they follow the expressions:  MOE impact = 1,17 · E - 1800 MOE ultrasound= 1,46 · E - 2000  E given in MPa     y = 1,169x ‐ 1796,R² = 0,942y = 1,463x ‐ 1996,R² = 0,91820004000600080001000012000140001600018000200002000 4000 6000 8000 10000 12000 14000 16000 18000MOE  E flex. NHL 3,5 & CCMEAN MOEimpact MOEus  Fig. 8. Relation between MOE and Eflex  6. Conclusions  The measurement method of the dynamic Young’s modulus by impulse excitation by vibration is extraordinary simple to use. When applied to mortars, it can be obtained results able to correlate with the other dynamic system studied (MOE by ultrasound) and with the determination of the static Young’s modulus from the flexotraction test.  Standardized specimens RI.LEM 4x4x16 used in the ordinary mechanical tests are suitable to measure the dynamic modulus of elasticity.  The simplicity of the procedure and the reliability of the measures, as well as the low cost of the equipment (laptop and microphone) suggest that it could have widespread applicability of this procedure as a control tool in mortar factories. In addition, the  method allows classifying mortars with greater simplicity according to their strain capacity and not only to their mechanical resistance.  The simplicity of the procedure as well as its correlation to other measured variables, suggest that this can be a methodology widely applied in studies on the evolution of the physical characteristics of lime mortars, such as mechanical strengths, static Young’s modulus, carbonation depth, etc. The aim of this paper is to demonstrate the importance of using non-destructive dynamic tests for solving stability problems of engineering projects. The experimentally obtained Young’s modulus in laboratory indicates than there is a correlation expressed in form of an analytical function that helps to determine the corresponding static modulus. The results have been achieved under simplified assumptions since the relation for Young’s modulus calculation is valid only for homogeneous and isotropic media while lime mortar, in general, does not comply with this condition.  Acknowledgments  We wish to thank Cal de Pachs, Ciments Molins, Omya Clariana, Alfredo Pérez and Parex Morteros for his collaboration in this study. Also to the Laboratori de Materials of IEPSEB from the UPC.   REFERENCES  [4] Fakopp: Acoustic tomography for tree evaluation, www.fakopp.com [1] UNE-EN 14146 Standard:  Test method for natural stone. Determination of the dynamic modulus of elasticity (with the measure of the fundamental resonant frequency). December 2004. [2] UNE-EN ISO 12680-1 Standard: Test methods for refractory products. Part 1: Determination of the dynamic Young’s modulus (MOE) by impulse excitation of vibration. September 2007. [3] UNE-EN 1015-3 Standard. Test methods of the mortars for bricklaying. Part 3: Determination of the fresh mortar consistency (shaking table). September 2000.           

Simple method of dynamic young's modulus determination in lime and cement mortars

This study demonstrates the feasibility of using a simple method to measure the resonant

fundamental frequency for determining the MOE (dynamic Young’s modulus) of lime and

cement mortars.

The procedure follows the instructions stated in the UNE-EN ISO 12680-1 standard for

refractory products although in this study the instructions are applied to standardized RILEM

4x4x16 cm test samples made of lime and cement mortars.

The simplicity of the procedure as well as its correlation to other measured variables,

suggest that it can be widely applied in studies about the evolution of the physical

characteristics in lime mortars, such as mechanical strength, static Young’s modulus,

carbonation depth, et

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Simple method of dynamic young's modulus determination in lime and cement mortars

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