Anisotropy of reinforced concrete from geophysical methods

Anisotropy is expressed as the direction-dependent change of material
 properties and it is a very important parameter to the correct determination
 of the concrete quality. For the aim of determining the concrete anisotropy,
 geophysical measurements in the study were carried out on the reinforced
 concrete samples with different strengths, before concrete strengths were
 determined from Uniaxial Compressive Strength test. Since the propagation
 direction of concrete pores and saturation type of it is important
 parameters in affecting the concrete anisotropy, prepared samples were cured
 as oven-dried, water-saturated, and dried in outside. Thus, the effects of
 curing conditions on the anisotropy of reinforced concrete were investigated
 by geophysical measurements. For this purpose, ultrasonic P and S wave
 measurements were made on two opposite surfaces of cubic samples with
 different reinforcement diameters. In addition, a total of 8 resistivity
 measurements were performed by taking two diagonal measurements on each
 surface in except of reinforced surfaces of the sample. The velocity and
 resistivity anisotropies of samples were determined by using the anisotropy
 relations given in the literature. As a result, it is determined that while
 reinforcement diameter has no distinctive effect on anisotropy, curing
 conditions are especially very effective on resistivity anisotropy.


Introduction
Some materials have different properties in different directions due to their anisotropic nature. In the earth sciences, studies related to anisotropy were generally performed on the rock or soil [1][2][3][4][5][6]. The physical properties measured in one direction may be different the other direction depending on the structure of rocks [7][8][9][10]. The presence of a systematic fracture in the non-homogeneous and non-isotropic environment is one of the reasons to anisotropy. For this reason, the degree of anisotropy depends on the amount of fracture [11,12] and also the type of filler in the fractures [13] of the rocks. Generally, major fractures in the materials and their impact on elastic properties have been studied by simplifying them as minor fractures [8,14]. The definition of fracture, which is important in terms of elastic properties, was made by [15] and [16] in non-homogeneous materials. Concrete, which is a composite material and considered as an artificial rock, has a heterogeneous and anisotropic structure due to its structure and components. Non-destructive (NDT) geophysical techniques are effectively used in the solution of problems in concrete or counstruction. These problems can be sortable as strength and fracture-crack condition of concrete, anisotropy of concrete, hydration degrees of concrete, reinforcement corrosion, number and location of reinforcement, radioactivity of materials or dominant period of construction [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].
As it is known, nondestructive tests can be used to determine the anisotropy of concrete in-situ or in the laboratory. Because the measurements taken with NDT on the concrete can be applied in different directions. In addition, with these methods, it is possible to determine concrete strength, number or placement of reinforcement and also the cracks, fractures or voids in the internal structure of the concrete [31,37]. Resistivity method from these methods can give information about fracture, degree of damage, moisture and anisotropy in the concrete [38]. According to many studies, there were strong relationships among to the porosity, water content, physical and chemical characteristics and resistivity of concrete [39][40][41][42][43][44]. Similarly, ultrasonic method can be used to investigate the structural properties of materials due to the anisotropic and nonlinear elastic behavior of composites [45]. Concrete age, cement types and water/cement ratio, concrete density, aggregate type, reinforcement, content of moisture [46,47], surface roughness, porosity [48], heterogeneity and anisotropy of the elastic medium in the propagation area are considerably influence on the ultrasonic wave velocities [49,50]. Ultrasonic seismic anisotropy was found to be several times larger than the resistivity anisotropy of the same material in conducted study by [51]. The effects of lateral changes on resistivity measurements generally appear to be more significant, and it should be particularly attempt to identify and eliminate them as much as possible. Although performing resistivity measurements is generally easier and faster, seismic measurements provide more accurate results for anisotropy. In addition, theoretical studies for resistivity anisotropy have not yet reached the level developed for seismic velocity anisotropy [51]. For this reason, this study has been giving important knowledge about both resistivity and seismic anisotropy of reinforced concrete materials.
In this study, the samples used for reveal the effect of anisotropy on reinforced concrete were designed as concretes with low, medium and high strength. Then, Ultrasonic P and S wave measurements were applied from two opposite sides of the samples and the resistivity method was applied so as to obtain a total of 8 apparent resistivity values (R), two of which were diagonal scale to each other from the 4 surface of the samples prepared in the specific time periods. Thus, ultrasonic and resistivity methods have been used to reveal the effects of anisotropy on the reinforced concrete samples depending on the difference of the curing conditions, cure time, concrete strengths (between 2 MPa and 70 MPa) and pore quantities (between 1.77 and 11.90 %). The study covered 243 reinforced concrete samples. A piece of reinforcement 250 mm in length and 10 mm, 14 mm or 20 mm in diameter was placed in the middle of the samples. Also, crushed stone aggregates and Portland cement were used during the preparation of the designs. The examples of mix ratio of prepared reinforced concrete designs were given in Table I. The reinforcement in the reinforced concrete affects the strength of the concrete. For this reason, it is important to consider the reinforcement while determining the strength of the concrete. Using geophysical methods, the presence of reinforcements in concrete and the effect of these reinforcements on concrete strength can be examined without causing any damage to the reinforced concrete structure. In this context, the study was carried out on reinforced concrete using geophysical methods. Also, curing conditions are effective on ultrasonic P and S wave velocities and resistivity values [31,37]. Mechanical properties of structural materials are strongly dependent on size and distribution of its pores [52,53]. Particularly in low-strength samples, the values obtained due to the high amount of pores and the water or air filling of these pores may be different. In addition, the orientation direction of the pores also affects on the measurement results obtained depending on the direction. For this reason, 9 reinforced samples with 3 different reinforcement diameters were prepared for each reinforced concrete design (total 9 designs) and 81 samples were separately subjected to water, oven and air curing during to 90 days.

Preparation of Reinforced Concrete Samples
Tab. I Mixing ratios of prepared concrete designs. The samples in the water cure were kept in curing pools at 20±2 °C until the days when the measurements were taken. The samples cured in the air were subjected to an average temperature of 20 °C and humidity of 42-54 %. For oven dried samples, first, ultrasonic seismic and resistivity measurements were obtained and then samples were dried in the oven at 105 o C for 24 hours. Secondly, density, the ultrasonic seismic and resistivity values were determined in the dry condition. Finally, these samples were kept in the water curing pool until the day of their measurements in the determined time periods. The porosities (n) of the samples were determined by using water-saturated (γ s ) and dry densities (γ d ).

Determination of Anisotropy from Non-destructive Geophysical Methods
Ultrasonic and resistivity measurements were performed on the 7 th , 28 th , 41 st , 56 th , 65 th , 72 nd and 90 th days on reinforced concrete samples with different strength and kept in different cure conditions. The Ultrasonic P and S wave measurements were applied to two opposite sides of the samples by placing of two probes to the middle of the A-A′ and B-B′ surfaces. Furthermore, the resistivity measurement was performed to the 4 surface (A, B, A′ and B′ surfaces) of the samples by placing of resistivity meter on the X and Y directions (Fig.  1). Thus, how the curing conditions, reinforcement diameter and reinforced concrete strength affect the anisotropy was investigated.

Non-Destructive Ultrasonic Method and Velocity Anisotropy
The ultrasonic method is based on the elastic wave theory. In the laboratory or in-situ, to determine the longitudinal (P) and transverse (S) wave velocities of the waves from the known length of the sample are determined by measuring the first break times at which these elastic waves pass through the sample [31]. Ultrasonic technique bases on the principle of measuring the transition time of artificially generated high frequency P and S waves in material. In the Ultrasonic method, the receiver and transmitter probes are placed on the opposite sides of the concrete element. Here, the contact surface between concrete and probes must be well provided. The voids in the concrete have an important effect on ultrasonic velocities. Because the passage of the waves through the concrete with void is slower than that of them concrete without void. High velocities indicate high strength of concrete and low velocities indicate low strength of concrete [31,54]. In this study, ultrasonic measurements were made by using OYO SonicViewer-SX(XP) equipment with 10-1000 kHz frequency range and using 200 kHz or 500 kHz P-wave and 100 kHz S-wave transducer. When the properties of a material are determined, if the value obtained from a vector measurement changes with direction, it is said that this material is anisotropic. Anisotropy parameter can be obtained by measuring the wave transition times in different directions of concrete element with ultrasonic systems. So, seismic anisotropy can be defined as the dependence of velocity to direction or angle. In contrast to the isotropic environment, the seismic velocities in the anisotropic medium vary depending on the direction of propagation according to the symmetry characteristics in the anisotropic medium ( Fig. 2) [55]. Both seismic P and S waves may show anisotropy. For both, the anisotropy may appear to be dependent on the direction of progress of the velocity (continuous). It can also be seen as a (discrete) dependence of velocity in the direction of polarization in S-waves. There is weak aniosotropy in case difference between the Vs measurements taken on two parallel lines is around 3-4 % [56].
The P wave velocity anisotropy in water-saturated rocks is weaker than that of dry rocks due to large changes in pressure [13]. On the other hand, S waves are not affected with the saturation type because the rigidity is no in water and gas. That is, S waves are only affected by the change in the properties of the solid. Depending on the fracture density, the Pwave velocities in water saturated samples were found to be greater than those of the dry samples. As the fracture density increases, the difference between saturated and dry samples is larger [13]. The amount of anisotropy depends on the intensity of the fractures in the rock [11,12] and the differences in water content due to the mechanical properties of the fractured rock and the presence of interconnected fractures affected by fillings in fractures [57,58].
The degree of anisotropy ( ) from the seismic velocities can be calculated from the following equation: The average velocity for the P and S wave velocities can be determined by taking the averages of the maximum and minimum velocities [59,60]: Anisotropy from P and S velocities can be rewritten as in Equations 4 and 5 by using Equations 2 and 3, respectively: Seismic anisotropy can be defined as the change of one or more geophysical properties in an inhomogeneous material depending on the measured direction [61]. Seismic method is interested in seismic wave propagation, and especially features related to seismic velocity changes. Moreover, S wave polarization is also an indicator of the presence of seismic anisotropy [62], [63] defined in his study with ultrasonic velocity measurements in dry and unsaturated conditions and on layered rocks on minerals such as amphibolite, gneiss, schist, quartz and so on., the velocity anisotropy between 2-6 % is as weak; the velocity anisotropy between 6-20% is as medium; the velocity anisotropy between 20-40 % is also as strong [64]. Found that P wave velocity anisotropy was 0.6-12 % in their study on three kinds of dolomitic limestone. They determined the parallel and perpendicular velocity differences in dry and water saturated conditions as 14 % and 8.3 %, respectively. The change of seismic P wave anisotropy due to temperature in low strength concretes has been demonstrated [65].
In this study, seismic anisotropy was investigated on reinforced concrete samples with different curing conditions and strengths using both P and S wave measurements. The novelty in this study can be listed as approaching concrete's anisotropy from S wave velocity, investigating anisotropy from both P and S wave velocities in reinforced concretes with different strength and investigating the effect of different curing conditions on anisotropy in reinforced concrete.

Non-Destructive Resistivity Method and Resistivity Anisotropy
Resistivity of concrete is greatly affected with porosity, moisture, and the resistance of the liquid in the pores (by the contamination of salt into the water in the pores). When the pores are filled with water containing molten salt, the concrete becomes electrically conductive. The resistivity in the concrete depends on the w/c ratio (conductivity in the pores), the volume and type of cement, temperature and moisture [37,47,66,67]. Also, there is a strong relationship between resistivity and durability according to the age of the concrete [37,68]. Moreover, the temperature has a great effect on the resistivity of the concrete [69,70]. Resistivity is a fast and successful method used to determine the strength, physical and chemical characteristics of concrete [37,44,69]. A good correlation can be interrelated with resistivity and durability indicators such as diffusion coefficient, permeability coefficients, capillary absorption and porosity. Resistivity depending on time and temperature can be used to determine the durability values of modern designs [69,71]. Thus, large areas of the structure are indirectly measured.
The concrete resistivity is related to the porosity and distribution of pore size in the concrete [72]. These properties are controlled by the degree of hydration of the cement paste in concrete. The moisture content of the concrete's resistivity can be varied within a wide range of 1 -10 4 kΩcm with the effect of temperature and concrete quality (composition, cement type, etc.) [73]. One of the most important problems in the measurement of concrete resistivity is that the properties of concrete are affected by the varying in the environment. Also, the resistivity decreases with increasing of the w/c ratio and moisture [74,75]. That is, the resistivity value is decrease with the higher of the moisture contents in the concrete.
Because the concrete is not homogeneous and isotropic, the resistivity's obtained from the measured voltage differences are not true resistivity values. Therefore, the measured resistivity values are called as apparent resistivity. The apparent resistivity gives significant results in determining the properties of the material taken on the measurement and therefore anisotropy can also be determined. Thus, the effect of anisotropy is mostly observed in stratified and inhomogeneous environments [76]. Anisotropy is a perceptible indicator of whether the presence of reinforcement and concrete integrity (homogeneous structure) is present [18,77]. In measurements taken on an unreinforced homogeneous concrete, the resistivity values give regular results regardless of the position and direction of the measurement. Anisotropy in reinforced samples compared to unreinforced samples varies considerably depending on reinforcement density and directions [76]. On the other hand, the position and direction of the reinforcements in the reinforced concretes considerably change the resistivity results. While anisotropy value of 0 % of the concrete is considered to be isotropic and unreinforced, larger values of anisotropy indicate the presence of reinforcement [18]. In addition, the anisotropy obtained with apparent resistivity values gives information about the presence and location of the fracture in the concrete [78,79]. C. Andrade said that concrete resistivity is sensitive to the porosity and degree of porosity connectivity [80]. Therefore, anisotropy affects the electrical properties of concrete. The changes of the resistivity in dry and humid environments differ than that in seismic velocities.
The resistivity value changes with the filling types (air, water or dust etc.) of the void or fracture in the material [38,81]. The resistivity (longitudinal) measured parallel to the fractures is obtained smaller than the resistivity (transverse) perpendicular to the fractures in the dry medium. The proportion of longitudinal and transverse resistivities increases with the filler in water-saturated medium (with a greater reduction of the mineralized water content in the longitudinal resistivity) [8]. While higher resistivity values are obtained via the electric current sent to perpendicular the fractures in the concrete, measurements taken in parallel will cause to obtaining lower resistivity values. J.W. Lane stated that apparent resistivity value obtained in the direction perpendicular to the fracture is greater than that obtained in parallel to the fracture by Schlumberger or Wenner arrays in any environment showed anisotropic properties cause of the presence of fractures [82]. Anisotropy strongly emphasizes the electrical differences according to the measurement direction [18]. Therefore, anisotropy (A n ) is obtained by proportioning the apparent resistivity values obtained from the measurements made perpendicular to each other at a certain point (R max and R min ). In this study, Resipod resistivity meter with wenner array was used for measurements and resistivity anisotropy (A R ) was determined by using follow equation of [83]: The average resistivity (R mean ) can be determined by taking the averages of the maximum (R max ) and minimum (R min ) resistivity values:

Destructive Uniaxial Compressive Strength (UCS) Test
UCS test is a destructive method used to determine the strength of concrete. In this method, the prepared samples are broken with the help of the hydraulic press. UCS values were found as ratio of applied load to the surface area of the sample. In this study, these tests were made by Form+Test Alpha compressive test equipment with 0.01-99.9 kN/s loading speed. After resistivity and ultrasonic measurements, 3 samples of each reinforced concrete design type were subjected to UCS test and the averages of these were taken on the 7 th , 28 th and 90 th days in order to reveal compressive strengths. In addition, when the reinforced concrete compressive strengths were obtained, the UCS test was performed by applying load to the non-reinforcement surface (with the reinforcement facing to the side surface).

Evaluations
In order to determine whether the ultrasonic P and S wave velocities and resistivity (R) values changed depending to direction, measurements were made on 4 surface of the all off samples for 90 days. Measured and calculated parameters related to anisotropy and figures obtained from them were presented for resistivity and ultrasonic method, respectively.

Evaluations of Velocity and Resistivity Anisotropy depending on Reinforcement Diameter and Curing Type
Anisotropy results determined from seismic P and S wave and resistivity for water, air and oven curing of all designs were showed in Table II-IV depending on reinforcement  diameter. According to Table II Table II-IV (D1-D9). P and S wave velocity values of the samples depending on the reinforcement diameter and curing conditions were obtained close to each other (Table  II-IV). Similarly, a distinctive effect of the reinforcement diameter could not be obtained on the resistivity values of the samples under water and oven curing conditions. However, the resistivity values of the samples in air cure differ especially in the D1, D2 and D3 designs with the effect of the reinforcement diameter (Table III).
Tab. II Statistical results of determined from seismic P and S wave velocities and resistivity for water curing depending on reinforcement diameter. Comparison of resistivity values in directions X and Y, ultrasonic P wave and ultrasonic S wave velocity values on surface of A-A′ and B-B′ were presented in Fig. 3 depending on reinforcement diameter and curing type. In the Fig. 3 According to this, while P wave and S wave values close to each other on surface of A-A′ and B-B′, especially resistivity values in air curing was different in X and Y directions. This may be explained with that the pores in the samples originate from the air filler and the resistivity is more sensitive to the dispersion direction of the pores. Therefore, curing conditions are especially effective on the resistivity.

Evaluations of Anisotropy depending on Curing Time of Reinforced Concrete
Percent change in resistivity, P and S wave velocities anisotropies for water, air and oven curing depending on age of reinforced concrete were presented in Table V-VII. According to these, the resistivity, Vp and Vs anisotropy values were respectively obtained between 0.501-2.604 %, 0.394-4.932 %, 0.216-5.954 % for water curing; 0.586-2.777 %, 0.0-3.901 %, 0.536-3.365 % for oven curing and 1.033-10.579 %, 0.0-4.800 %, 0.246-4.326 % for air curing. As seen, especially resistivity anisotropies were obtained higher in air curing depending on filling with air of pores than that of water and oven curing ( Table V). The anisotropy values obtained from the resistivities of the samples in the water and oven curing did not showed a significant change depending on time (Table V and VII).
Tab. V Resistivity, P and S wave velocity anisotropies for water curing depending on age of concrete. The porosities of all designs and resistivity anisotropies for water, air and oven curing of all designs were showed in Fig. 4 depending on curing time of reinforced concrete. In the resistivity anisotropy values of the samples in air curing appeared especially to be an increasing tendency in low strength reinforced concrete designs (D1-D3) after approximately 41 st day. This trend was not seen in solid or very durability samples (D4-D9). This stiuation can be explained with the higher porosity and the concentration of pores in a specific direction in the weak strength reinforced concretes when compared to high strength reinforced concrete designs. As is shown in the Fig. 4, resistivity anisotropy of low strength reinforced concrete (for example D1) varied approximately between 0.809-1.567 %, 0.934-2.169 % and 2.283-8.186 % for water, oven and air curing, respectively. These anisotropies of high strength reinforced concrete (for example D6) varied approximately between 0.701-1.192 %, 0.762-2.668 %, 2.112-4.351 % for water, oven and air curing, respectively.   P and S wave velocity anisotropies for water, oven and air curing of all designs were showed in Fig. 5 and 6 depending on age of reinforced concrete. As is shown in the Fig. 5 and 6, P velocity anisotropy of low strength reinforced concrete (for example D1) varied approximately between 0.394-2.603 %, 0.8-3.511 % and 1.058-3.667 % for water, oven and air curing, respectively. These anisotropies of high strength reinforced concrete (for example D6) varied approximately between 0.533-3.315 %, 0.0-2.641%, 0.0-2.193 % for water, oven and air curing, respectively.

Design No
Similarly, S velocity anisotropy of low strength reinforced concrete (for example D1) varied approximately between 0.216-3.720 %, 0.442-2.841 % and 0.793-2.929 % for water, oven and air curing, respectively. These anisotropies of high strength reinforced concrete (for example D6) varied approximately between 0.277-3.366 %, 0.558-3.046 %, 0.297-4.326 % for water, oven and air curing, respectively. According to this, variations of the P and S anisotropies were obtained in a narrow range for all cure conditions and different strength designs (D1-D9). In addition, it was determined that P and S wave velocity anisotropy values increased with increasing of porosity.
When Fig. 4, 5 and 6 were examined in terms of reinforcement diameter, the anisotropy did not show a significant change depending on the reinforcement diameter. For this reason, the average results of the anisotropy values obtained depending on the reinforcement diameter were also presented with black line in Fig. 4, 5 and 6.

Evaluations of Velocity and Resisitvity Anisotropies depending on Uniaxial Compressive Strength and Porosity
Statistical results of seismic velocity ratio (Vp/Vs), and porosity depending on curing conditions of all designs were showed in Table VIII Comparisons of Vp/Vs and porosity depending on reinforced concrete strength were presented in Fig. 7. According to this, While Vp/Vs changed between 1.67 and 2.08, percent change in porosities were between 1.77 % and 11.90 %. Porosity values were obtained higher than 7% in low strength reinforced concretes. In addition, while the porosity values of the samples in the water and oven curing increase, there is no significant change in the Vp/Vs ratio. On the other hand, it is seen that the Vp/Vs ratio in air cure decreases with increasing porosity values (Fig. 7). This situation can provide the interpretation of the saturation type in the pores of the samples from the Vp/Vs ratio. As can be seen in Fig. 7, while Vp/Vs ratio values of high strength reinforced concrete samples in all curing conditions were obtained greater than 1.83, it was seen that the Vp/Vs ratio values of only low strength samples in air curing were lower than 1.83. The 1.83 value of the Vp/Vs ratio can be considered as the limit value for saturation with air or water.    Comparison of UCS and anisotropies of calculated from resistivity and P and S wave velocities were presented in Fig. 8 depending on curing conditions. According to this, resistivity anisotropy (0-11 %) of low strength reinforced concretes (D1-D3) increases more than that of high strength reinforced concretes in air curing. However, this resistivity anisotropy changed between 0-3 % in water and oven curing. Furthermore, P and S wave anisotropy were obtained between 0-6 % for all curing conditions. In addition, while porosity of low strength reinforced concrete (0-20 MPa) varied between 4-12 %, it was obtained between 0-8 % in high strength reinforced concrete . It was seen that UCS values decreased as the Porosity values increased under all curing conditions (Fig. 8).
In Fig. 9, relationships between porosity and anisotropies of P, S velocities, and resistivity were presented depending on curing conditions. When Fig. 9 examined, it was seen that resistivity anisotropy values also increased with the increase of porosity of low strength reinforced concrete especially in air curing. This situation is considered to be because of being higher of the air filling in low-strength reinforced concretes, which were mostly porous, and the resistivity method was more affected by the filling in the pores.

Conclusion
Anisotropy in the reinforced concrete can be nondestructively determined by geophysical methods. The reinforcement in concrete is occurred anisotropy, but the different reinforcement diameters have no distinctive effect on anisotropy. However, curing conditions and different strength of reinforced concrete are very effective on anisotropy. Furthermore, these effects are seen to be different for each method. While the seismic velocities obtained from the different surfaces of the reinforced concrete samples did not significantly change in the water, oven and air curing, the resistivity values obtained from different directions of the same samples were considerably obtained different in the air group samples, especially. This may be due to the fact that the pores in the samples were filling with the air and more sensitive to the dispersion direction of the pores. In very few samples of water and oven group, different resistivity values were obtained. This situation may be due to being in different directions and sizes of the pores of these samples. As a result, non-destructive geophysical methods give valuable results in terms of orientation and saturation of the pores.
The Resistivity, Vp and Vs anisotropy values were obtained between 0.501-2.604 %, 0.394-4.932 %, 0.216-5.954 % for water curing; 0.586-2.777 %, 0.0-3.901 %, 0.536-3.365 % for oven curing and 1.033-10.579 %, 0.0-4.800 %, 0.246-4.326 % for air curing, respectively. While the anisotropy values determined from the resistivity are lower than that of its obtained from seismic velocities for water and oven curing samples, they are the opposite case for samples in air cure. This is an indication that resistivity is more sensitive to air filling in the pores. For this reason, the resistivity method gave better results than ultrasonic method in determining anisotropy.
In air curing, resistivity anisotropy (0-11 %) increased with decreasing of reinforced concrete strength. In addition, while porosity of low strength reinforced concrete (0-20MPa) varied between 1-12 %, it was obtained between 1-8 % in high strength reinforced concrete . Also, while Vp/Vs ratio change between 1.67 and 2.0 in the all curing conditions, porosity values vary between 1 % and 12 %. Furthermore, while Vp/Vs values were found lower than 1.83, porosity values were obtained higher than 7 % for low strength reinforced concretes in air curing.
While Vp/Vs ratio change in between 1.83-2.0 in water and oven curing, it was especially obtained in low strength reinforced concrete between 1.67-1.83 in air curing. These values in air cure decreases with increasing porosity values. This situation can provide the interpretation of the saturation type in the pores of the samples from the Vp/Vs ratio. As a result, Vp/Vs=1.83 value can be considered as the limit value of saturation for low strength reinforced concretes.