1. Introduction

As civil constructions have been increasing in recent decades, studies have investigated ways to facilitate the execution of major constructions that face difficulties due to unstable soils in which they are located. According to ^{Hachich et al. (2019}), the use of a containment system with diaphragm wall which consists of open trench in the ground filled with reinforced concrete stabilized by the synthetic use of polymeric fluids or bentonite clay is one of the alternatives to assist in the excavation of soils.

The use of synthetic polymer in excavations has great advantages over traditional forms of soil stabilization, such the use of bentonite. According to Mota (2010), the economic aspect is an advantage, because polymers although its cubic meter is more expensive than bentonite clay require less amounts of product to obtain better yields than traditional forms (bentonite clay). According to Mota (2010), the environmental factor is also noteworthy, mainly because of some properties of polymers, namely: their high solubility, chemical sensitivity, and ultraviolet ray actions that end up fragmenting their polymer chains and, therefore, preventing bioaccumulations. Thus, the use of polymers as stabilizers in excavations do not affect the environment (Mota 2010).

Studies conducted by Mota (2010) found that the highly concentrated synthetic polymer can be used specifically to chemically interact with all types of soil as the basis of its stabilization. Its molecular structure allows for total water solubility, without changing its primary role of active chemical bonding in the stabilization of soil particles.

The use of this polymer during excavations should follow the recommendations of ABNT-NBR 6122 (2019), with concrete density ranging from 2.1 to 2.8 g/cm³ and minimum cement consumption of 400 kg/m³, and stabilizing fluid as polymer with water pH between nine and 12, density from 1.005 g/cm³ to 1.1 g/cm³ and sand content up to 4.5%. According to ^{Djelal et al. (2020}) one of the pathologies found on the diaphragm wall is related to the mixture of polymer fluid during concreting, increasing the infiltration of groundwater from the soil after the execution of the panels, compromising the concrete ability to resist compression.

In loco diaphragm walls are extremely difficult to be assessed, especially regarding the addition of synthetic polymer, and its influence in the quality of the concrete. The ultrasound test is one tests that do not damage the concrete containment system as suggested ^{Silva (2020}). Studies conducted by ^{Savaliya et al. (2014}), through ultrasound test in concrete structures, demonstrate that the method is able to accurately detect pathologies, identifying defects and its specific location.

Considering the aforementioned aspects, our project used non-destructive ultrasonic wave propagation tests, directly and indirectly, simulating in loco inspection to verify its sensitivity in predicting mechanical (strength and stiffness) and physical (water absorption) properties of concrete made with different concentrations of synthetic polymer.

Thus, this research aimed to simulate pathological manifestations in diaphragm wall with different quantities of synthetic polymer in the concrete, proposing models of prediction of strength and stiffness obtained through ultrasound wave propagation tests to evaluate this containment system in loco.

2. Experimental program

For the research, concrete were made with CPII-F cement proportions following the ^{ABNT-NBR 11578 (1997)}: medium sand and gravel 01 (1:1.8:2.5), and the cement was measured in mass, aggregates by volume and water-cement ratio of 0.6, as specified for concrete structures as diaphragm walls (ABNT- NBR 6122, 2019). Considering the standard mixture, different percentages of synthetic polymer 0%, 20%, 40%, and 60% of granulated anionic polymer and high molecular weight > 21 million and long chains used for flocculation were added in relation to the cement mass (Figure 1a). The characterization of the aggregates was carried out according to the recommendations of the standards for fine aggregate NBR (^{NM 248, 2003}; ^{NM 52, 2009}; ^{NM 45, 2006}) and coarse aggregate ^{NBR (NM 248, 2003}, ^{NM 53, 2003}, ^{NM 45, 2006}). After 28 days, the samples were subjected to the immersion absorption test, according to the specifications of ^{ABNT-NBR 9778 (2015)}.

Table 1 shows the characterization of aggregates within the limits of acceptability, according to ^{ABNT - NBR 7211 (2009)}.

The addition of synthetic polymer presented a behavior similar to the addition of water to the concrete, especially when assessing workability (Slump Test values) and density, that is, the increment in polymer quantity increased workability and reduced the density (Table 2).

After the Slump tests, 12 cylindrical specimens (100 mm in diameter and 200 mm in length) and one prismatic specimen (400 x 400 x 300 mm³) were molded for each mixture simulating part of a finished diaphragm wall, totaling 48 cylindrical and four prismatic specimens. After 28 days, the cylindrical samples were ultrasound-tested by direct wave propagation method (Figure 1b) and prismatic samples by indirect method (Figure 1c), representing the in loco inspection.

Figure 1 (a) Synthetic polymer, (b) cylindrical samples subjected to direct ultrasound test (c) prismatic samples subjected to indirect ultrasound test. Source: authors (2021). 

For the tests, ultrasound equipment (USLAB, Agricef, Brazil) and 45 KHz-frequency longitudinal transducers of flat faces were used. With the propagation times of ultrasound waves (t), it was possible to calculate, for each distance between transducers (L), the direct propagation velocity of ultrasound waves (V_D), using the equation proposed by ^{ABNT NBR 8802 (2019)}, as in Equation (1).

V=Lt (1)

After 28 days, the mass of each specimen was also determined using a precision scale, and with a digital caliper its dimensions were obtained to calculate the volume and the density. From the direct velocity and density of the concrete (ρ), the stiffness coefficient was determined (2).

CLL = ρ. VD2 (2)

The prismatic samples, which represent the feasibility of inspection of a finished diaphragm wall using the indirect wave propagation method, were tested according to the methodology proposed by the ^{ABNT-NBR 8802 (2019)}. The ABNT proposes a way of measuring the ultrasonic propagation velocity by indirect transmission mode (VI), whose procedure consists of calculating the velocity through a propagation time graph versus distance between transducers Figure (2).

Figure 2 Determination of the propagation velocity of ultrasound waves by indirect method. Source: ^{ABNT-NBR 8802 (2019)}.  

The specimens were then subjected to a compression test in a EMIC machine to determine the strength (f_c - ^{ABNT-NBR 5739, 2018}) and the elastic modulus (E_ci - ^{ABNT-NBR 8522, 2017}). The results of the tests were used in the creation of models to predict the mechanical properties based on the propagation velocity of ultrasound waves.

The results of f_c and E_ci and the parameters of propagation of ultrasound velocity waves (V_D), (V_I) and (C_LL) were used to analyze regressions in order to verify the existence of statistically significant models between mechanical properties and acoustic properties, obtained through ultrasound wave propagation tests.

3. Results and discussions

The mechanical (fc and E_ci) and acoustic properties (C_LL, V_D, and V_I) of the concrete also reduced as polymer quantities increased, a fact related to increased porosity (amount of voids) of the concrete. Table 3 shows the tests performed on the 12 concrete samples for each studied mixture.

To avoid dispersion of the we used the mean of the results of strength, stiffness, and acoustic parameters for statistical analyses. The linear regression models evaluated by analysis of variance (ANOVA) were statistically significant at the 95% confidence level (P-value < 0.05), and the best models for predicting concrete strength (f_c) and stiffness (E_ci) properties were obtained based on the stiffness coefficient (C_LL) (Table 4).

The models found are within the ranges of coefficients of determination (R²) found in the literature regarding mechanical tests and wave propagation. For the prediction of f_c, the R² in the studies conducted by Mohamad et al. (2016) and ^{Silva et al. (2020}), ranged from 60 to 98% and, for E_ci, from 50 to 96%, (^{Giacon et al., 2010}; Mohamed et al., 2016, and ^{Silva et al., 2020}). Correlations between the stiffness parameters (C_LL) and the mechanical properties of strength (f_c) and elastic modulus (E_ci) obtained in ultrasound and compression tests were found by ^{Giacon et al., (2010)} and ^{Silva (2020)}, with linear models and R² values ranging from 85% to 97% for Ec_i and from 79% to 95% for f_c.

Absolute error values of the strength and elastic modulus of the concrete range from 25% to 50% when based on models with wave propagation parameters (^{Bungey and Millard, 2006}). In our research, the absolute errors found (9.70% to 20% - Table 4) are below those found in the literature, suggesting that the models for predicting strength and stiffness are valid in the evaluation of the quality of concrete used in diaphragm walls, using acoustic parameters of wave propagation.

Table 5 shows the results obtained from immersion absorption and the longitudinal velocity of the tested samples after saturation. Notably, the addition of synthetic polymer increased water absorption (Table 5), leaving more voids (pores) after the drying process. This aspect occurs because of the release of internal curing, which leads to the swell of polymer particles, changing the porous structure of cement (^{Araújo and May, 2019}).

Note that, due to the change in the absorbed volume of water, changes in acoustic properties are observed (Tables 3 and 5), Also, it can be noted that the velocitys of sound propagation decrease as the amount of polymer used increases; the voids found in dry concrete are a significant factor in the transmission of sound waves, since the ultrasonic pulse velocity is lower in the air than in solids (^{Godinho, et al., 2020}), thus explaining the increase in the amount of pores, reducing the propagation velocity of ultrasonic waves in the specimens.

The regression between ultrasound velocity and absorption showed a model with R² of 92% (Figure 3) and P-Value of 0.04 < 0.05, demonstrating that there is a statistically significant relationship between the parameters, with a 95% confidence level, obtained through ANOVA. The outcomes suggest that the wave propagation method is sensitive to the increase of water content inside the samples, caused by increased porosity after drying the synthetic polymer within the cement, decreasing its ultrasound velocity. Thus, the concrete will present more voids (pores) and, therefore, absorbing more water and presenting lower density and mechanical properties. Water is the main erosive agent in concrete, therefore concrete performance as a barrier to reduce the transport of potentially corrosion-causing agents is related to its porosity (Dudhal, 2016; ^{Liu et al., 2020}; ^{Matiko, 2000}).

Source: Authors (2021).

Figure 3 Regression model between immersion absorption and longitudinal velocity.  

The polymer aggregates and forms a film on the surface of cement particles during the hydration, avoiding additional contact between cement and water, increasing the cement porosity, thus affecting the compressive strength and elastic modulus of polymer-added concrete (^{Liu et al., 2020}).

Our research corroborates with the literature. Table 3 shows a 26% reduction for the mean values of f_c and 13% for the mean values of E_ci, after an 18% increase in absorption for concrete samples with the addition of 60% of synthetic polymer in relation to the samples without it (Table 5).

The models obtained can be used as a non-destructive alternative test to estimate mechanical and physical properties, such as water absorption in samples and diaphragm wall structures, verifying the infiltration of groundwater from the soil mass after the execution of the panels, a fact that may compromise concrete ability to resist compression.

4. Conclusions

The increment in the concentration of synthetic polymer used in the different concrete mixtures increased its workability, reducing its density and its mechanical (f_c and E_ci) and acoustic (V_D, V_I, and C_LL) properties.

The models of prediction of mechanical properties by ultrasound velocity were statistically significant, showing coefficients of determination higher than 80% and errors inferior to those found in the literature.

Thus, the sensitivity of the direct or indirect ultrasound wave propagation test is demonstrated, for concrete with physical and mechanical properties similar to those used in our research, and the correlations established here in concrete samples can be used to support the detection of in loco pathological manifestations.

Moreover, the increase in synthetic polymer content in the production of concrete directly interferes with the amount of water absorption and, consequently, in the acoustic properties of the material.