Abstract

The relationship between porosity, permeability and acoustic parameters of mortar samples measured by ultrasonic NDT is investigated. In order to enhance the sensitivity of the ultrasonic wave to microstructure, a high frequency range (0.3 to 1.3 MHz) is chosen. Samples are fabricated with mortar of 4 different water/cement ratio and half of them were gradually chemically degraded for 4 periods of time. The effect of water saturation is also studied. This procedure yields a wide range of porosity (from 10% to 35%) and permeability values (from 10 to 25 10^-18 m²). For sound materials the correlation between physical and acoustic parameters yields the expected trend: velocity decreases with porosity and permeability, attenuation increases for dry samples and decreases for saturated samples. Similar behavior was not clearly observed in degraded samples.

1 Introduction

The concrete cover is a protective barrier against aggressive agents that may penetrate into the structure and induce corrosion of rebars. Therefore, on site evaluation of the quality of this cover is essential to predict at an early stage the durability of the structure and define a strategy of its maintenance. Porosity and permeability are of main interest, as moisture and chemicals can penetrate through connected pores.

Acoustic and ultrasonic waves are directly influenced by its elastic parameters. In homogeneous media, the compression and shear wave velocities are related to elastic moduli:

(1)

where E is the dynamic Young's modulus, u the Poisson ratio and r denotes the density. As elastic moduli depend on porosity, it is possible that there is a relationship between porosity, permeability, and ultrasonic parameters. Velocity is expected to decrease and attenuation to increase as porosity increases (Ould Naffa et al., 2002). However, those trends may differ for saturated materials. Recently, Hernandez at al. (2000) obtained extremely precise estimates of porosity by ultrasonic NDT. The estimate is based on micro-mechanical model established by Jeong and Hsu (1996). However, such model has many parameters as inputs, which may not be a priori known. In addition, only sound samples were studied and porosity increase by induced degradation was not addressed.

The presented study intends to relate porosity and permeability of mortar samples with their ultrasonic parameters. Mortar is chosen instead of concrete in order to limit excessive attenuation of ultrasonic waves due to scattering by large grains. Mortar samples were fabricated with four different water/cement (w/c) ratios. Porosity and permeability of those samples were further varied by chemical degradation in ammonium nitrate. Ultrasonic parameters (pulse and phase velocity, attenuation) of compression and shear wave are obtained by broadband ultrasonic spectroscopy (Eggers,1996). Those measurements are made either in direct contact on dry samples or by immersion on water saturated samples.

2 Methods

2.1 Sample preparation
The samples are cylinders of 37 mm in diameter and 70 mm high. They are cored from larger cylinders preserved, over 28 days, in water saturated with lime at a constant temperature of 20°C and then rectified to obtain a perfect geometry. The mortar used is of a fine grain type, made up of Portland cement CPA CEM I 52.5 from Origny and Hostun sand. The mixture is prepared with different ratios of w/c. Table 1 below gives the proportions of the various constituents.

Porosity measurements are made by the gravimetric method for all compositions through dumping of samples in water. The permeability tests are based on the measurement of intrinsic permeability by gas injection while samples must be dried before the tests. A moderate oven drying at a temperature of 60°C was carried out. Drying was stopped as soon as the sample weight remained constant. A comparison of this method with the more aggressive over-drying method at 105°C was made. It appeared very effective and did not exhibit significant thermal microcracking.

2.2 Chemical degradation
In order to accelerate the leaching of cement based materials by water, a system for chemical degradation was designed, based on the immersion of samples in ammonium nitrate solution (6 Mol/l). The use of nitrate is justified by the fact that the solution degrades the cementing matrix in a way similar to water but with an accelerating factor of 100 (Loosveldt, 2002). Each sample is placed in the solution with an agitator for periods of 4, 9, 16 and 25 days. The degradation is monitored by measurement of pH and the solution in which the samples were immersed is modified when a stable pH near to 8,0 is reached (on average every 2 days). After degradation, one sample per w/c ratio is cut in half and the thickness of the degraded layer is measured. It ranges from 1.2 mm after 4 days to 7.3 mm after 25 days of immersion.

2.3 Permeability measurement
The general principle of the test is to carry out a continuous gas flow through the sample under steady state conditions. The pressure cell was designed to submit the sample to a constant gas pressure P_i at one end and atmospheric pressure P₀ at the other end. Figure 1 shows an overall diagram of the experimental apparatus used. The test specimen, whose circumferential surface is sealed by a Vitton membrane, is placed in a pressure-confining cell. A Gilson type pump maintains the confining pressure. The gas, more than 99% pure Argon, is injected via a buffer reservoir whose use will be described later.

As the material is supposed to be completely filled with gas, the measured permeability can be considered intrinsic (according to generalized Darcy's law) and not relative. This would have been the case if water (or other liquid) was significantly present in the porous network. The experimental apparatus enables permeability ranging from 10^-12 to 10^-21 m² to be measured (representing hydraulic conductivity between 10^-5 to 10^-14 m/s for water at 20°C). Measurement is carried out in a steady state flow with a moderate injection pressure of 1.5 MPa. To apply Darcy's law, the medium should be saturated with a single fluid phase and the flow must be laminar. We may assert that a laminar flow takes place if the Reynolds number is lower than 10³ (Coussy, 1990). This number can be evaluated by where r is the specific mass of the gas, h is the dynamic viscosity and V_c is the relative velocity with respect to the solid skeleton. l_c is a characteristic length which is of the same order as where is the intrinsic permeability tensor. With an expected permeability value of 10^-17m², an extremely small value of R (less than 10^-3) is obtained. This proves that the flow will be laminar. Such precautions allow the study to be placed within the conditions of Darcy's law, which is used for a one-dimensional flow. Argon is also assumed to be an ideal gas and this can be justified within the range of the pressure used (Iffly, 1956).

For x = 0, P (x) = Pi is the injection pressure and for x= h, P (x) = Po the draining pressure which is maintained at atmospheric level in this case. In this test, longitudinal permeability, noted K_x, will be measured.

In a steady injection state, the pressure variation in the sample is given by the well-known expression:

(2)

Darcy's law can be written for a one-dimensional flow:

(3)

where V_x is the gas velocity and m its viscosity(2.2 10^-5 Pa.s). The method of measurement is based on an assessment of the mean entry gas flow Q_m in the sample. The injection pressure of 1.5MPa and the very low value of the flow make the use of commercial flow transducers difficult; as a result, an indirect measurement method is developed, using a buffer reservoir at the entry point of the sample (Figure 2), in order to measure the volume flow rate entering through the sample. This method is carried out in three steps:

1. the gas is injected via the buffer reservoir, which is supplied with gas by an external source.
2. the reservoir is no longer supplied by the external source but gas, initially at pressure P_i, is continuously flowing into the sample. This involves a drop in pressure in the reservoir, which is limited to a low value DP_i (0.1 MPa) during a measured injection time Dt. Thereafter it is assumed that every thing occurs as if a steady state flow was taking place at a constant mean injection pressure P_m given by
3. the mean volume flow rate Q_m is calculated by where V_r is the volume of the buffer reservoir and the piping, Dr is the variation of the gas specific mass due to DP_i. As mentioned before the gas is assumed to be ideal and the test lasts sufficiently long for it to be under isothermal conditions. Consequently it can be shown that the mean volume flow is written (AFREM, 1996):

(4)

This method has been checked on many occasions when it was possible to directly measure the flow. A similar method for measuring gas permeability can be found in Dinku et al. (1997) under more complex conditions.The use of Darcy's law and of equation 3 from which P_i = P_m was taken, gives the following:

(5)

where S is the sample cross section.

Fig 1: Experimental device used for gas permeability measurements.

Fig 2: principle of mean flow rate measurement.

2.4 Ultrasonic measurements
Broadband ultrasound spectroscopy is used to obtain ultrasonic parameters of the studied materials. This technique can be applied either in transmission mode, with a pair of transducers, one emitter and one receiver, or in pulse-echo mode with a single transducer working as emitter and receiver. The emitted ultrasonic pulse is wideband, with a central frequency of either 0.5, 0.6 or 1MHz, and a roughly 60% bandwidth. As the analysis is performed in the frequency domain, ultrasonic parameters are estimated from 0.3 MHz to 1.3MHz. A Panametrics 5055 or 5058 Pulser-Receiver is used to excite the emit-transducer and amplify received ultrasonic signals. The amplified signals are then acquired by a digital oscilloscope card and stored on a PC for further analysis. Adequate coupling is required to transfer enough energy into the sample. Here, two coupling methods are used: direct contact and immersion.

1. Direct contact technique
   

A thin layer of coupling agent is applied between the transducer face and the sample. It can be either a silicone gel (Sofranel D couplant) for longitudinal waves or a highly viscous liquid (Sofranel SWC couplant) for shear waves. Pulse velocity is measured in transmission mode by estimating the time-of-flight of the first transmitted signal relative to a reference signal synchronous with the electrical excitation pulse:

(6)

where e is the sample thickness. A better precision would have been achieved by considering time delay between multiple echos inside the sample, but only one signal could be observed in degraded samples, due to excessive attenuation. Attenuation is measured in pulse-echo mode by the buffer rod method (Papadakis, 1973). This method allows unbiased attenuation estimates by eliminating the influence of transducer coupling that would occur in direct contact transmission mode. It consists in introducing a 10mm plexiglas buffer between the transducer and the sample. First, the backwall echo from the buffer is recorded without sample, yielding a signal with spectrum denoted A'(f). Second, the sample is coupled with a gel to the buffer and two signals are recorded: the buffer/sample interface echo and the sample backwall echo, with spectrum denoted respectively A(f) and B(f). Finally, the attenuation versus frequency is derived from the following equation:

(7)

where is the buffer/sample reflection coefficient. As we are mainly interested in relative variation of attenuation with w/c ratio and degradation, not in absolute attenuation values, no diffraction correction is made on attenuation curves. Attenuation was measured for longitudinal waves and on sound samples only, since no backwall echo could be observed when testing degraded samples, again because of excessive attenuation related to high porosity.

2. Immersion technique
   

In order to study the effect of saturation, mortar samples were dried and then vacuum saturated with distilled water. Broadband pulses are obtained in transmission mode, performing measurements for two samples of the same material but of different thickness immersed in water (one measurement gives the reference signal). The distance between transmitting (T) and receiving (R) transducers is kept constant and samples are set to face of the receiver to avoid errors due to unparallel arrangement of ultrasonic beam and axis of samples. Having the amplitude and phase spectra for the two samples of different thickness L₁ and L₂ (15 and 25mm)_, the propagation parameters, phase velocity vj and attenuation coefficient a as functions of frequency f, can be calculated as follow (Yew et al. 1979):

(8)

where A₁ (f) and A₂(f)are amplitudes, j₁(f) and j₂(f) are phases of the spectral components of the reference and measured pulses, n is the total number of wavelength for a given frequency which is contained in the distance L₂ - L₁ . One important advantage of the applied method is that it allows to disregard correction for lost of energy due to the reflected wave. The shear wave parameters can also be studied by tilting the sample until the refracted longitudinal wave is transmitted away from the receiving transducer (Yew et al., 1979). However, only longitudinal waves transmission through sound samples have been considered in the immersion study.

3 Experimental results

3.1 Porosity and permeability
Water porosity is measured for sound and degraded samples. As expected, global porosity increases with w/c ratio and time of degradation (Fig.3). The maximum porosity increase induced by 25 days degradation is about 15%. The question is whether this variation is caused merely by a volume increase of the degraded material or additionally by a porosity increase within the degraded material. From the measured thickness of the degraded layer, an estimate of porosity of this layer was made (Fig.4). It shows that porosity in the degraded layer is almost constant. Therefore, the observed global porosity increase is mainly due to degraded volume increase. Permeability was also measured on the same samples (Fig.5). The global trend versus w/c ratio and time of degradation is as expected, i.e. permeability increases in the same way as porosity, but this trend is not clearly observed for w/c ratio 0.5 and 0.6. At this time of our research, it is still unclear whether this is due to measurement inaccuracy or corresponds to a real structural change in the sample.

Fig 3: global porosity vs. w/c ratio '' sound sample; sample degraded for 4 (), 9 (×), 16 (D) and 25 days ().

Fig 4: porosity in degraded layer vs. w/c ratio velocity'' sound sample; sample degraded for 4 (), 9 (×), 16 (D) and 25 days ().

Fig 5: global porosity vs. w/c ratio '' sound sample; sample degraded for 4 (), 9 (´), 16 (D) and 25 days (O).

3.2 Attenuation and phase velocity of sound samples
Attenuation was first measured on sound, dry samples with the buffer rod method, with reliable estimates from 0.3 to 1.2 MHz. Results are presented in Figure 6 and 7 for both central frequencies 0.5 and 1 MHz.

Fig 6: attenuation vs. frequency for sound dry samples with 0.5MHz transducer.

Fig 7: attenuation vs. frequency for sound dry samples with 1MHz transducer.

For the same w/c ratio, a significant dispersion of attenuation values is noticed. However, it appears that attenuation increases with w/c ratio, especially around 1 MHz. The porosity increase probably induces more heterogeneity and scattering. Assuming a power attenuation law, such as:

(9)

an increase of attenuation slope a ₀ and exponent y are observed between w/c ratio 0.3 (a ₀ = 3 dB/cm/MHz and y = 0.4 ) and 0.6 (a ₀ = 16 dB/cm/MHz and y = 1.5). Values of a ₀ and y were obtained by linear regression of the log-log plot of the attenuation curves around the central frequency.

Attenuation was also measured around 0.6 and 1 MHz on saturated samples by the immersion technique (Fig. 8 and 9). The obtained values are not identical, but comparable to the one for dry samples. It is interesting to notice that the observed trend versus w/c ratio is opposite to the one obtained for dry samples: attenuation decreases with w/c ratio, i.e. increasing porosity (except for w/c = 0.5 at 1MHz). As observed in section 3.1, higher porosity in saturated material means higher permeability and water content, thus possibly less scattering and better "conductivity" of ultrasound. This suggests that propagation mechanisms are significantly different in dry and saturated materials.

Fig 8: attenuation vs. frequency for water saturated samples with 0.6MHz transducer.

Fig 9: attenuation vs. frequency for water saturated samples with 1MHz transducer.

Longitudinal wave phase velocity measured on dry samples is shown in figures 10 and 11. Velocity decreases as w/c ratio, porosity and permeability increases. Except for the 0.5 w/c ratio, dispersion goes from positive around 0.6 MHz to negative around 1 MHz. According to Waters et al. (2000), dispersion in a medium with power law attenuation (Eq.9) and 1<y<3 is given by:

Fig 10: phase velocity vs. frequency for water saturated samples with 0.6MHz transducer.

Fig 11: phase velocity vs. frequency for water saturated samples with 1MHz transducer.

(10)

It turns out that phase velocity should increase with frequency as 1< y <2 and decrease as 2< y <3. For w/c = 0.3, exponent y goes from 1.28 to 2.35. The observed behaviour of phase velocity versus frequency thus agrees with the model described by Eq.10.

3.3 Pulse velocity of degraded samples
As it wasn't possible to estimate attenuation and phase velocity in degraded samples - due to excessive attenuation of signals - only pulse velocities are presented here. Figure 12 and 13 show the porosity versus velocity correlation for longitudinal and shear wave respectively. Again, the expected trend is observed: velocity of both waves decrease as porosity increase. However, a single regression line could not be obtained and, in some cases, velocity was found higher in the most degraded sample than in the sound sample. This may be due to the fact that ammonium nitrate remained inside the pores, thus masking the effect of degradation to the ultrasonic wave. Therefore, degraded samples should have been washed prior to ultrasonic testing.

Fig 12: experimental correlation between porosity and longitudinal wave velocity'' sound sample; sample degraded for 4 (), 9 (×), 16 (D) and 25 days ().

Fig 13: experimental correlation between porosity and shear wave pulse velocity'' sound sample; sample degraded for 4 (), 9 (×), 16 (D) and 25 days ().

4 Conclusions

This study intended to relate physical parameters (porosity and permeability) and acoustical parameters (pulse and phase velocity, attenuation) of sound and damaged, dry or water saturated, mortar samples. In sound samples, despite a significant dispersion of experimental results, the expected trends were observed. Phase and pulse velocity decrease with porosity and permeability. The attenuation behaviour depends on material saturation. It was found to increase with porosity in dry samples, with just the opposite trend in water saturated samples. An interesting result is the change from positive to negative dispersion as frequency increases. Porosity of samples was further increased by chemical damage. Due to excessive attenuation, only the pulse velocity of longitudinal and shear waves could be measured. No clear correlation could be obtained between porosity and acoustic velocity in damaged samples. This is probably due to experimental problems that could be solved by carefully washing the samples prior to ultrasonic testing.

This study also highlights the difficulty of obtaining accurate estimates of ultrasonic parameters, because of the high variability of the material under study. Solving this problem would require a fair amount of experimental data and an appropriate equipment to acquire weak signals. The present study shows how ultrasonic parameters are expected to evolve as physical parameters related to damage vary. This observation is significant from the viewpoint of the undertaken project focused on quantitative interpretation of data acquired on site using ultrasonic NDT techniques.

5 Acknowledgments

Thanks to Ms. Bahia Talbi and Mr. Michal Pakula for their assistance with measurements. Part of this work was supported by the "Réseau Génie Civil et Urbain"of the French Ministry of Education and Research.

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