- Email: [email protected]
Porosity estimation of aged mortar using a micromechanical model
Ultrasonics 44 (2006) e1007–e1011 www.elsevier.com/locate/ultras
Porosity estimation of aged mortar using a micromechanical model M.G. Herna´ndez *, J.J. Anaya, T. Sanchez, I. Segura Instituto de Automa´tica Industrial, (CSIC) La Poveda, 28500 Arganda del Rey, Madrid , Spain Available online 9 June 2006
Abstract Degradation of concrete structures located in high humidity atmospheres or under flowing water is a very important problem. In this study, a method for ultrasonic non-destructive characterization in aged mortar is presented. The proposed method makes a prediction of the behaviour of aged mortar accomplished with a three phase micromechanical model using ultrasonic measurements. Aging mortar was accelerated by immersing the probes in ammonium nitrate solution. Both destructive and non-destructive characterization of mortar was performed. Destructive tests of porosity were performed using a vacuum saturation method and non-destructive characterization was carried out using ultrasonic velocities. Aging experiments show that mortar degradation not only involves a porosity increase, but also microstructural changes in the cement matrix. Experimental results show that the estimated porosity using the proposed non-destructive methodology had a comparable performance to classical destructive techniques. 2006 Elsevier B.V. All rights reserved. Keywords: Ultrasound velocity; Material characterization; Micromechanics; Porosity
1. Introduction The durability of concrete structures is affected by chemical and mechanical factors, such as impact, abrasion, moisture, temperature variations or freeze-thaw cycles. Among factors with more negative influence, moisture plays a fundamental role due to water, either pure or carrying aggressive ions, moving through the concrete. The fluids can move through the material in different ways, but all transport processes depend primarily on the porous structure. A characterization of the degradation process due to humidity is made by accelerated ageing experiments in laboratory which causes the decalcification of cement paste and consequently a reduction in its mechanical properties. This procedure was characterized by means of non-destructive testing by ultrasound by several authors. For example, measurements of ultrasonic velocity and attenuation were made on degraded mortar, after 45 days degradation, a
*
Corresponding author. Fax: 34 91 871 70 50. E-mail address: [email protected] (M.G. Herna´ndez).
0041-624X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.05.195
decrease up to 24% velocity was observed, while attenuation increased up to 10 times [1]. While in [2], characterization using higher frequency Rayleigh waves (0.2–1 MHz) was presented. But in these papers, the relationship between ultrasonic parameters (velocity or attenuation) and porosity has not yet been established. When is necessary to characterize the porosity of cement based materials, e.g. mortar, the influence of the elastic and microstructural characteristics of different phases of the material (cement paste without pores, aggregates and pores) need to be considered. In [3], a micromechanical model of three phases has been presented to characterize the porosity. This model considers the microstructural characteristics such as the elastic constants, volume fractions and geometry, distribution and orientation of the phases considered. The application of this model to mortar samples makes it possible to estimate the volume fraction of pores with a mean error of 10%. This estimation is good if it is considered that in cement based materials, the destructive testing errors are often of the same order. The focus of this paper is to characterize porosity in non-degraded and chemically degraded mortar, obtained by accelerated calcium leaching. The leaching process
e1008
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
dissolves portlandite crystals (CH) and partially decalcifies calcium-silicate-hydrated (C-S-H) in the cement matrix. Combined experimental–theoretical investigations have been carried out on mortar samples with different water/ cement and sand/cement ratios. 2. Three-phase micromechanical model To study the influence of porosity on cement composites of three phases, the material is considered to be formed of a solid matrix (cement paste without pores) and two types of inclusions: pores and sand. From the formulation described in [3] the elastic constant tensor has been obtained as a function: C ¼ f ðC m ; C a ; C p ; mm ; ma ; mp ; hT a i; hT p iÞ
ð1Þ
where the superscripts ‘m’, ‘a’ and ‘p’ refers to a matrix without pores, aggregates (sand) and pores respectively. C denotes the elastic constant tensor, Tp and Ta represent Wu’s tensor in global coordinates for pores and aggregates, respectively, and the angle bracket h i denotes the average over all possible orientations. The tensor hTi is a function of the geometry, the distribution and the orientation of the inclusions and can be calculated using the method given in [4]. When the pores are considered as another phase, their volume fraction can be calculated as: mp ¼ 1 mm ma
ð2Þ
If it is considered that the three phases are isotropic, the elastic tensor C is reduced to two independent elastic constants, C11 and C44, in reduced notation, which are related to the longitudinal (VL) and transverse (VT) velocities as: sffiffiffiffiffiffiffi C 11 ð3aÞ vL ¼ q sffiffiffiffiffiffiffi C 44 vT ¼ ð3bÞ q where q is the material density, which can be calculated as: q ¼ q p mp þ q m mm þ q a ma
ð4Þ
From these expressions, we obtain a non-destructive method for determining the microstructural characteristics of a three-phase composite, such as porosity. 3. Experimental program 3.1. Description of the ageing process The degradation of cement based materials by ammonium salts has been studied by several authors [5]. The chemical attack of the ammonium nitrate leads to the development of a soluble calcium nitrate, a not very soluble and expansive nitro-aluminate of calcium (which formation must be avoided, because it can induce microcracking) and an emanating ammoniac, NH3.
Chemical attack induces total leaching of portlandite and progressive decalcification of C-S-H. The leaching process causes some changes in mortar that can be divided into several steps. First, the leaching process of portlandite leads to an increase in the size and volume of capillary porosity. Second, leaching of C-S-H increases microporosity and could lead to microstructural changes in the C-S-H structure. The accelerated ageing of cementitious materials was acquired through total immersion of the samples in a ammonium nitrate dissolution, with a concentration of 300 g of ammonium nitrate per litre of solution. This procedure is similar to the degradation process of material in atmospheres with high humidity but increased 300 times. To study how the mortar becomes degraded in the time, several periods of degradation were observed (5, 10, 20 and 31 days). After the degradation process, the samples were washed with demineralised water and kept in water in order to avoid microcracking. These specimens were characterized by destructive and non-destructive testing, porosity and ultrasonic velocity measurements, respectively. 3.2. Materials Mortar samples were cast on prismatic moulds with a size of 40 · 40 · 160 mm. After 24 h, the specimens were demoulded and cured for 28 days immersed in water. Four series of mortar samples were cast with different sand/ cement and different water/cement ratios and the same cement, Type III/B. The water/cement ratio of mortar (s/c = 2/1) was determined from water adsorption tests on aggregates. The composition of mortars is given in Table 1. In order to facilitate the leaching process, each original sample of mortar was divided into four portions. 3.3. Destructive testing and results The porosity of the mortar samples was determined by the vacuum saturation method as described in RILEM CPC 11.3 [6]. In order to avoid microstructural damage, samples were dried at 80 C until they reached a constant weight. The open porosity of degraded and non-degraded mortar samples measured is shown in Table 2. It can be observed that there is a significant increase of porosity in the first stage of the leaching process. This increase slowed down as the leaching process advanced, as described in the literature. This fact is related to the consumption of portlandite and the leaching of C-S-H.
Table 1 Composition of mortars used Mortar Sand/cement Water/cement
3/1 0.45
0.55
2/1 0.405
0.505
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
e1009
Table 2 Open porosity (in a percentage) of non-degraded and degraded mortar samples Groups
0 Days
5 Days
10 Days
20 Days
31 Days
3/1 3/2 2/1 2/1
15.04 18.23 17.87 21.01
20.16 21.42 21.32 24.76
21.34 22.39 22.01 25.78
22.42 23.7 24.63 27.17
22.75 24.56 25.24 28.36
0.45 0.55 0.405 0.505
3.4. Non-destructive testing Non-destructive characterization of samples was produced by ultrasonic testing. The ultrasonic longitudinal velocity was measured using a Krautkramer H2K, broad band transducer with 2 MHz of central frequency, emitting in longitudinal mode. Ultrasonic signals were acquired at 80 MHz of sampling frequency with SENDAS system, high precision equipment. Inspections were made with samples immersed in a water tank with controlled axis. With automatic inspection we obtained several advantages relative to the accuracy and uniformity of the signals, the number and distribution of inspections and time saving. Samples were aligned in the bottom of the tank and two ultrasonic transducers scanned all the surfaces of the samples with a spatial resolution of 1 mm in the horizontal and vertical direction. The experimental setup is shown in Fig. 1. A transmission inspection was made to calculate the ultrasonic velocity of the saturated samples. The following expressions were used: vL ¼
Xc tc twater þ X c =vwater
ð5Þ
where Xc represents the path length of the specimen, tc is the travelling time of the signal through the specimen, twater is the travelling time in water (with the specimen absent) and vwater is the velocity in water at inspection temperature. A zero crossing algorithm was used to know the travelling time of the ultrasonic signal. Due to the leaching process it was possible to modify the dimensions of the mortar samples, two pulse–echo inspections (from both sides) were made to know Xc exactly at each point. The measurements of transverse velocity, made only in non-degraded samples, were performed with normal incidence shear transducers (Panametrics V151). Measurements of ultrasonic velocity of non-degraded and degraded mortar samples are showed in Table 3, where
Fig. 1. Experimental setup.
it can be seen how the velocity decreases with the degradation times. 4. Estimate of porosity in mortar samples from a micromechanical model To apply the three phase model [3] to mortar samples, the following assumptions were made: • Mortar is a three-phase material formed by a matrix of cement paste and two types of inclusions, sand and pores. • The pores are modelled like cylinders of infinite length distributed randomly in the matrix. • The elastic constants of the pores are the elastic constants of contained water in these [7].
Table 3 Velocities of non-degraded and degraded mortar samples Velocity
Longitudinal (m/s)
Sample group
0 Days
5 Days
10 Days
20 Days
31 Days
0 Days
3/1 3/1 2/1 2/1
4521 ± 29 4485 ± 36 4605 ± 21 4330 ± 48
4324 ± 49 4205 ± 60 4464 ± 46 3879 ± 42
4245 ± 24 4103 ± 30 4360 ± 34 3825 ± 18
4130 ± 37 3935 ± 37 4121 ± 20 3691 ± 20
4046 ± 26 3786 ± 20 4056 ± 22 3640 ± 25
2.7382 ± 17 2.7030 ± 22 2.7849 ± 13 2.6138 ± 29
0.45 0.55 0.405 0.505
Transverse (m/s)
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
e1010
• The elastic properties of sand are assumed as grains of spherical geometry distributed randomly in the matrix. First of all, Young (Em) and Poisson (lm) elastic moduli were obtained, of the cement matrix for different mortar groups. For doing this, it is necessary to perform nondestructive measures (Vl, Vt, qa), destructive measures (q,
Young Module Matrix Variation 60 3/1 0.45 3/1 0.55 2/1 0.405 2/1 0.505
Em (GPa)
55
x), and to use the data obtained from the samples fabrication (Ca, ma). These last data could also be obtained from destructive tests. To calculate Young’s modulus and Poisson’s ratio of m sound mortars, Em 0 and l0 , the longitudinal and transverse velocities were used in equations (1)–(4) together with the known relations among the different elastic moduli. For degraded materials it is only necessary to know Young’s modulus, Em, assuming Poisson’s ratio of cement matrix remains constant (lm lm 0 Þ during the leaching process [8]. For this reason, in this case it was only necessary to use the longitudinal velocity. The results obtained for the different mortar samples are shown in Fig. 2. Em can be adjusted to a linear function such as:
50
p p Em ¼ Em 0 þ k ðm m0 Þ
45
where mp is the porosity, mp0 and Em 0 are the porosity and Young’s modulus of sound material, and the constant k depends on the mortar sample group. The tensor constants Cm are obtained from the Em and m l expressions. With these expressions and the equations (2)–(4), a function that relates the longitudinal velocity and porosity, for the four groups of mortar samples was obtained. The results are shown in Fig. 3. This function fits closely with the porosity measures obtained by destructive methods. Therefore, the method described permits the porosity of mortar samples that have been aged by leaching to be estimated.
40
35
30
25
0
5
10
15
20
25
30
Leacching time (days)
Fig. 2. Variation of Young’s modulus for the four groups of mortar samples.
3/1 0.45
3/1 0.55
30
30 r=0.99
Porosity (%)
Porosity (%)
r=0.78 25 20 15 10 3800
25 20 15
4000
4200
4400
10 3000
4600
3500
2/1 0.405
4000
5000
30
r=0.97
r=0.95 25
Porosity (%)
Porosity (%)
4500
2/1 0.505
30
20 15 10 3500
ð6Þ
4000
4500
Longitudinal Velocity (m/s)
5000
25 20 15 10 3000
3500
4000
4500
Longitudinal Velocity (m/s)
Fig. 3. Predicted and measured porosity for the four groups of mortar samples.
5000
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
e1011
5. Conclusions
Acknowledgement
The leaching process in cement-based materials has two effects: an important increase in the capillary porosity and a significant degradation in the elastic properties of the cement matrix. In this work the variation of elastic constants in the cement matrix in mortar samples subject to a leaching process was studied. In order to estimate this variation, the micro-mechanical model [3] and destructives measurements of porosity were used. The variation of Young’s modulus of the cement matrix obtained with this model linearly fitted to the porosity variation. By introducing this linear fit in the micromechanical model a close estimate of the porosity of aging mortar samples in relation to the longitudinal ultrasonic velocity (error fitting <5% for the four sample groups) was obtained.
The financial support of the Spanish Ministry of Education and Science (project DPI 2003-08628-C03-00) are acknowledged. References [1] S. Ould Naffa et al., Ultrasonics 40 (2002) 247. [2] B. Piwakowski et al., Ultrasonics 42 (2004) 395. [3] M.G. Herna´ndez, Cement and Concrete Research 36 (2006) 609. [4] T.T. Wu, International Journal of Solids Structure 2 (1966) 1. [5] C. Carde et al., Cement and Concrete Research 26 (1996) 1257. [6] RILEM CPC 11.3. Materials and Structures 17 (1984) 391. [7] M.G. Herna´ndez et al., Ultrasonics 42 (2004) 865. [8] G. Constantinides et al., Cement and Concrete Research 34 (2004) 67.
Porosity estimation of aged mortar using a micromechanical model M.G. Herna´ndez *, J.J. Anaya, T. Sanchez, I. Segura Instituto de Automa´tica Industrial, (CSIC) La Poveda, 28500 Arganda del Rey, Madrid , Spain Available online 9 June 2006
Abstract Degradation of concrete structures located in high humidity atmospheres or under flowing water is a very important problem. In this study, a method for ultrasonic non-destructive characterization in aged mortar is presented. The proposed method makes a prediction of the behaviour of aged mortar accomplished with a three phase micromechanical model using ultrasonic measurements. Aging mortar was accelerated by immersing the probes in ammonium nitrate solution. Both destructive and non-destructive characterization of mortar was performed. Destructive tests of porosity were performed using a vacuum saturation method and non-destructive characterization was carried out using ultrasonic velocities. Aging experiments show that mortar degradation not only involves a porosity increase, but also microstructural changes in the cement matrix. Experimental results show that the estimated porosity using the proposed non-destructive methodology had a comparable performance to classical destructive techniques. 2006 Elsevier B.V. All rights reserved. Keywords: Ultrasound velocity; Material characterization; Micromechanics; Porosity
1. Introduction The durability of concrete structures is affected by chemical and mechanical factors, such as impact, abrasion, moisture, temperature variations or freeze-thaw cycles. Among factors with more negative influence, moisture plays a fundamental role due to water, either pure or carrying aggressive ions, moving through the concrete. The fluids can move through the material in different ways, but all transport processes depend primarily on the porous structure. A characterization of the degradation process due to humidity is made by accelerated ageing experiments in laboratory which causes the decalcification of cement paste and consequently a reduction in its mechanical properties. This procedure was characterized by means of non-destructive testing by ultrasound by several authors. For example, measurements of ultrasonic velocity and attenuation were made on degraded mortar, after 45 days degradation, a
*
Corresponding author. Fax: 34 91 871 70 50. E-mail address: [email protected] (M.G. Herna´ndez).
0041-624X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.05.195
decrease up to 24% velocity was observed, while attenuation increased up to 10 times [1]. While in [2], characterization using higher frequency Rayleigh waves (0.2–1 MHz) was presented. But in these papers, the relationship between ultrasonic parameters (velocity or attenuation) and porosity has not yet been established. When is necessary to characterize the porosity of cement based materials, e.g. mortar, the influence of the elastic and microstructural characteristics of different phases of the material (cement paste without pores, aggregates and pores) need to be considered. In [3], a micromechanical model of three phases has been presented to characterize the porosity. This model considers the microstructural characteristics such as the elastic constants, volume fractions and geometry, distribution and orientation of the phases considered. The application of this model to mortar samples makes it possible to estimate the volume fraction of pores with a mean error of 10%. This estimation is good if it is considered that in cement based materials, the destructive testing errors are often of the same order. The focus of this paper is to characterize porosity in non-degraded and chemically degraded mortar, obtained by accelerated calcium leaching. The leaching process
e1008
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
dissolves portlandite crystals (CH) and partially decalcifies calcium-silicate-hydrated (C-S-H) in the cement matrix. Combined experimental–theoretical investigations have been carried out on mortar samples with different water/ cement and sand/cement ratios. 2. Three-phase micromechanical model To study the influence of porosity on cement composites of three phases, the material is considered to be formed of a solid matrix (cement paste without pores) and two types of inclusions: pores and sand. From the formulation described in [3] the elastic constant tensor has been obtained as a function: C ¼ f ðC m ; C a ; C p ; mm ; ma ; mp ; hT a i; hT p iÞ
ð1Þ
where the superscripts ‘m’, ‘a’ and ‘p’ refers to a matrix without pores, aggregates (sand) and pores respectively. C denotes the elastic constant tensor, Tp and Ta represent Wu’s tensor in global coordinates for pores and aggregates, respectively, and the angle bracket h i denotes the average over all possible orientations. The tensor hTi is a function of the geometry, the distribution and the orientation of the inclusions and can be calculated using the method given in [4]. When the pores are considered as another phase, their volume fraction can be calculated as: mp ¼ 1 mm ma
ð2Þ
If it is considered that the three phases are isotropic, the elastic tensor C is reduced to two independent elastic constants, C11 and C44, in reduced notation, which are related to the longitudinal (VL) and transverse (VT) velocities as: sffiffiffiffiffiffiffi C 11 ð3aÞ vL ¼ q sffiffiffiffiffiffiffi C 44 vT ¼ ð3bÞ q where q is the material density, which can be calculated as: q ¼ q p mp þ q m mm þ q a ma
ð4Þ
From these expressions, we obtain a non-destructive method for determining the microstructural characteristics of a three-phase composite, such as porosity. 3. Experimental program 3.1. Description of the ageing process The degradation of cement based materials by ammonium salts has been studied by several authors [5]. The chemical attack of the ammonium nitrate leads to the development of a soluble calcium nitrate, a not very soluble and expansive nitro-aluminate of calcium (which formation must be avoided, because it can induce microcracking) and an emanating ammoniac, NH3.
Chemical attack induces total leaching of portlandite and progressive decalcification of C-S-H. The leaching process causes some changes in mortar that can be divided into several steps. First, the leaching process of portlandite leads to an increase in the size and volume of capillary porosity. Second, leaching of C-S-H increases microporosity and could lead to microstructural changes in the C-S-H structure. The accelerated ageing of cementitious materials was acquired through total immersion of the samples in a ammonium nitrate dissolution, with a concentration of 300 g of ammonium nitrate per litre of solution. This procedure is similar to the degradation process of material in atmospheres with high humidity but increased 300 times. To study how the mortar becomes degraded in the time, several periods of degradation were observed (5, 10, 20 and 31 days). After the degradation process, the samples were washed with demineralised water and kept in water in order to avoid microcracking. These specimens were characterized by destructive and non-destructive testing, porosity and ultrasonic velocity measurements, respectively. 3.2. Materials Mortar samples were cast on prismatic moulds with a size of 40 · 40 · 160 mm. After 24 h, the specimens were demoulded and cured for 28 days immersed in water. Four series of mortar samples were cast with different sand/ cement and different water/cement ratios and the same cement, Type III/B. The water/cement ratio of mortar (s/c = 2/1) was determined from water adsorption tests on aggregates. The composition of mortars is given in Table 1. In order to facilitate the leaching process, each original sample of mortar was divided into four portions. 3.3. Destructive testing and results The porosity of the mortar samples was determined by the vacuum saturation method as described in RILEM CPC 11.3 [6]. In order to avoid microstructural damage, samples were dried at 80 C until they reached a constant weight. The open porosity of degraded and non-degraded mortar samples measured is shown in Table 2. It can be observed that there is a significant increase of porosity in the first stage of the leaching process. This increase slowed down as the leaching process advanced, as described in the literature. This fact is related to the consumption of portlandite and the leaching of C-S-H.
Table 1 Composition of mortars used Mortar Sand/cement Water/cement
3/1 0.45
0.55
2/1 0.405
0.505
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
e1009
Table 2 Open porosity (in a percentage) of non-degraded and degraded mortar samples Groups
0 Days
5 Days
10 Days
20 Days
31 Days
3/1 3/2 2/1 2/1
15.04 18.23 17.87 21.01
20.16 21.42 21.32 24.76
21.34 22.39 22.01 25.78
22.42 23.7 24.63 27.17
22.75 24.56 25.24 28.36
0.45 0.55 0.405 0.505
3.4. Non-destructive testing Non-destructive characterization of samples was produced by ultrasonic testing. The ultrasonic longitudinal velocity was measured using a Krautkramer H2K, broad band transducer with 2 MHz of central frequency, emitting in longitudinal mode. Ultrasonic signals were acquired at 80 MHz of sampling frequency with SENDAS system, high precision equipment. Inspections were made with samples immersed in a water tank with controlled axis. With automatic inspection we obtained several advantages relative to the accuracy and uniformity of the signals, the number and distribution of inspections and time saving. Samples were aligned in the bottom of the tank and two ultrasonic transducers scanned all the surfaces of the samples with a spatial resolution of 1 mm in the horizontal and vertical direction. The experimental setup is shown in Fig. 1. A transmission inspection was made to calculate the ultrasonic velocity of the saturated samples. The following expressions were used: vL ¼
Xc tc twater þ X c =vwater
ð5Þ
where Xc represents the path length of the specimen, tc is the travelling time of the signal through the specimen, twater is the travelling time in water (with the specimen absent) and vwater is the velocity in water at inspection temperature. A zero crossing algorithm was used to know the travelling time of the ultrasonic signal. Due to the leaching process it was possible to modify the dimensions of the mortar samples, two pulse–echo inspections (from both sides) were made to know Xc exactly at each point. The measurements of transverse velocity, made only in non-degraded samples, were performed with normal incidence shear transducers (Panametrics V151). Measurements of ultrasonic velocity of non-degraded and degraded mortar samples are showed in Table 3, where
Fig. 1. Experimental setup.
it can be seen how the velocity decreases with the degradation times. 4. Estimate of porosity in mortar samples from a micromechanical model To apply the three phase model [3] to mortar samples, the following assumptions were made: • Mortar is a three-phase material formed by a matrix of cement paste and two types of inclusions, sand and pores. • The pores are modelled like cylinders of infinite length distributed randomly in the matrix. • The elastic constants of the pores are the elastic constants of contained water in these [7].
Table 3 Velocities of non-degraded and degraded mortar samples Velocity
Longitudinal (m/s)
Sample group
0 Days
5 Days
10 Days
20 Days
31 Days
0 Days
3/1 3/1 2/1 2/1
4521 ± 29 4485 ± 36 4605 ± 21 4330 ± 48
4324 ± 49 4205 ± 60 4464 ± 46 3879 ± 42
4245 ± 24 4103 ± 30 4360 ± 34 3825 ± 18
4130 ± 37 3935 ± 37 4121 ± 20 3691 ± 20
4046 ± 26 3786 ± 20 4056 ± 22 3640 ± 25
2.7382 ± 17 2.7030 ± 22 2.7849 ± 13 2.6138 ± 29
0.45 0.55 0.405 0.505
Transverse (m/s)
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
e1010
• The elastic properties of sand are assumed as grains of spherical geometry distributed randomly in the matrix. First of all, Young (Em) and Poisson (lm) elastic moduli were obtained, of the cement matrix for different mortar groups. For doing this, it is necessary to perform nondestructive measures (Vl, Vt, qa), destructive measures (q,
Young Module Matrix Variation 60 3/1 0.45 3/1 0.55 2/1 0.405 2/1 0.505
Em (GPa)
55
x), and to use the data obtained from the samples fabrication (Ca, ma). These last data could also be obtained from destructive tests. To calculate Young’s modulus and Poisson’s ratio of m sound mortars, Em 0 and l0 , the longitudinal and transverse velocities were used in equations (1)–(4) together with the known relations among the different elastic moduli. For degraded materials it is only necessary to know Young’s modulus, Em, assuming Poisson’s ratio of cement matrix remains constant (lm lm 0 Þ during the leaching process [8]. For this reason, in this case it was only necessary to use the longitudinal velocity. The results obtained for the different mortar samples are shown in Fig. 2. Em can be adjusted to a linear function such as:
50
p p Em ¼ Em 0 þ k ðm m0 Þ
45
where mp is the porosity, mp0 and Em 0 are the porosity and Young’s modulus of sound material, and the constant k depends on the mortar sample group. The tensor constants Cm are obtained from the Em and m l expressions. With these expressions and the equations (2)–(4), a function that relates the longitudinal velocity and porosity, for the four groups of mortar samples was obtained. The results are shown in Fig. 3. This function fits closely with the porosity measures obtained by destructive methods. Therefore, the method described permits the porosity of mortar samples that have been aged by leaching to be estimated.
40
35
30
25
0
5
10
15
20
25
30
Leacching time (days)
Fig. 2. Variation of Young’s modulus for the four groups of mortar samples.
3/1 0.45
3/1 0.55
30
30 r=0.99
Porosity (%)
Porosity (%)
r=0.78 25 20 15 10 3800
25 20 15
4000
4200
4400
10 3000
4600
3500
2/1 0.405
4000
5000
30
r=0.97
r=0.95 25
Porosity (%)
Porosity (%)
4500
2/1 0.505
30
20 15 10 3500
ð6Þ
4000
4500
Longitudinal Velocity (m/s)
5000
25 20 15 10 3000
3500
4000
4500
Longitudinal Velocity (m/s)
Fig. 3. Predicted and measured porosity for the four groups of mortar samples.
5000
M.G. Herna´ndez et al. / Ultrasonics 44 (2006) e1007–e1011
e1011
5. Conclusions
Acknowledgement
The leaching process in cement-based materials has two effects: an important increase in the capillary porosity and a significant degradation in the elastic properties of the cement matrix. In this work the variation of elastic constants in the cement matrix in mortar samples subject to a leaching process was studied. In order to estimate this variation, the micro-mechanical model [3] and destructives measurements of porosity were used. The variation of Young’s modulus of the cement matrix obtained with this model linearly fitted to the porosity variation. By introducing this linear fit in the micromechanical model a close estimate of the porosity of aging mortar samples in relation to the longitudinal ultrasonic velocity (error fitting <5% for the four sample groups) was obtained.
The financial support of the Spanish Ministry of Education and Science (project DPI 2003-08628-C03-00) are acknowledged. References [1] S. Ould Naffa et al., Ultrasonics 40 (2002) 247. [2] B. Piwakowski et al., Ultrasonics 42 (2004) 395. [3] M.G. Herna´ndez, Cement and Concrete Research 36 (2006) 609. [4] T.T. Wu, International Journal of Solids Structure 2 (1966) 1. [5] C. Carde et al., Cement and Concrete Research 26 (1996) 1257. [6] RILEM CPC 11.3. Materials and Structures 17 (1984) 391. [7] M.G. Herna´ndez et al., Ultrasonics 42 (2004) 865. [8] G. Constantinides et al., Cement and Concrete Research 34 (2004) 67.