Data Modelling of Physical-Mechanical Processes in Nano Concrete with the Ensemble of Pores

. This paper assesses the strength of nano concrete and methods of strengthening it by adding nanoparticles. Since concrete structures are exposed to the environment and external influences, there is a need to enhance resistance to destruction. Modelling of behaviour and the nature of changes in indicators of chemical shrinkage and destructive load is performed. Data analysis is executed based on the data of ordinary portland cement pastes and cement-fly ash pastes. The results are compared with admixtures to these materials of three nanomaterials: nanolimestone, nanosilica, and nanoclay. The percentage ratio for compressive strength for materials is established. The data processing and visualization of the results are presented using an interactive web page using dynamic mathematical calculations of approximation and interpolation based on the entered data. The data is processed using modern open-source libraries and stored in the database. The work aims to develop a methodological approach for modelling physico-mechanical processes in nano concrete, considering nanoparticles and an ensemble of pores.


INTRODUCTION
One of the primary materials in construction is concrete based on sand-cement mixtures. This material must withstand heavy loads and be stable under various weather conditions, so the compressive strength parameter can be considered an additional factor in improving the stability of concrete structures [1,2].
Forecasting the strength and durability of nano concrete is expedient to assess the levels of reliability and resource using optimisation methods. Fundamental processes in this context relate to mechanical loads and the pore medium. It is possible to simulate the penetration of the pore fluid into the solid-phase frame and the redistribution (filtration) of the fluid in the pore space of the material. The porous medium is characterised by integral parameters, such as the volume of the pore space, porosity and permeability [3,4,5].
The liquid (water) in the porous medium of nano concrete is considered implicitly and is also characterised by integral parameters: mass, density, pressure, and dynamic viscosity [3,4].
The work aims to model such physical and mechanical processes as compressive strength, water and calcium hydroxide content in nano concrete, considering nanoparticles and the ensemble of pores.
One of the tasks of this work is the development of a strength criterion for nano concrete, taking into account the ensemble of pores based on the approaches of surface physics and fracture mechanics. In addition, the evaluation of the quality of nano concrete, taking into account the physical and mechanical characteristics of the rigid frame and porous medium, is taken into account.
Another task is the formulation of criterion ratios based on evaluating the strength, reliability, strengthening parameter and residual resource of nano concrete, and taking into account the porous medium.

MATERIAL AND METHODS
The non-associated law of plastic flow with the Mises-Schleicher criterion is used to describe stress relaxation and accumulation of inelastic deformation in nano concrete, which is used to model the behaviour of brittle natural and artificial materials [5,6]: where Y -adhesion characteristic (elastic limit of the material in pure shear); int -stress intensity;  -coefficient of internal friction; s(eff) -average effective stress; Ppr -actual pressure value in the pore medium of the element.
The main defining relations connecting the averaged stresses and deformations of the solidphase frame of the element, as well as the fluid pressure in the pore (capillary) space of the element, are of the form [5,6]: As a criterion for the destruction of the frame and cement mixture, the Drucker-Prager criterion is used, which derives the expression for the effective Tercaghi stresses [5,8,9]: where β = σc/σt; σc and σt -the value of the compressive and tensile strength of the frame material. For nonporous basalt, the traditional formulation of the Drucker-Prager criterion is used, in which instead of σs(eff) (4) is used σs [5,8,9].
The Griffiths-Irwin-Orovan strength criterion is also used [10]: where   -compressive strength; LT -pore diameter; WPL -specific energy spent on plastic deformation of the near-surface (interfacial) layer of the body, provided that a new (juvenile) surface is formed in it; E,  -Young's modulus and Poisson's ratio of the frame, respectively.
In reinforced concrete, rust forms on the surface of the reinforcement. Corrosion products (in particular, rust) penetrate the pores. Parameter WPL is included in the expression Ia corrosion current [11]: where  -electrical conductivity of the electrolyte; ak -ohmic potential change between the anodic and cathodic parts (anode -top, cathodeedges of the crack (pores)); r -pore radius; Ias, w -constants that are determined from the experiment.
Ratios (1)-(6) and the quality criterion [11] will be used to estimate the parameters of the stressstrained state and the conditions for strengthening nano concrete.
The reliability parameter R (reliability) (security characteristic) based on the probabilistic approach is determined by the ratio [11]: where YRM -strength reserve; YSRM -strength reserve standard.
There is a transitional state between the rigid frame and the pore. The energy of adhesive bonds ad and its change ad depend on the energy characteristics of the frame and the pore medium. Formulate the interphase ratio of the strength criterion between the frame and the pore medium similar to the coating, taking into account the results of the article [12,13,14,15]: where m -change in interfacial tension; m -change of interfacial energy;  -the symbol of deviation (change) of the parameter or energy characteristic of the interfacial layer; Aad -change in adhesion performance; m  , m  , Aad  , ad  -empirical constants.
Similarly to the article [11], the qualitative criterion of quality for the structural element of nano concrete is given in the form of the ratio: where k1 -the coefficient of the level of reliability of nano concrete; k2 -the coefficient that characterises the level of strength of the rigid frame; k3 -the coefficient that characterises the resource of the porous medium; k4(Df), k5(nZ), k6(ve), k7(KS) -coefficients that characterise the defectiveness Df, strengthening of the material nZ, the limit of corrosion fatigue ve, taking into account the corrosion resistance of fittings KS; 1, 2empirical constants.
Ratios (1), (2), (4), (5), and (8) constitute a new version of the strength criterion for the system nano concrete frame -pore medium. The parameters of the expressions (1), (2), (4), and (5) can be determined based on the experiment, and the parameters of the ratios (8) are estimated based on the computational experiment.

Theory/calculation
The data processing process can be automated using computer programs. The most popular method of viewing information from anywhere is a web page. This way, users can perform calculations and visualise the results in real-time. Bootstrap and ChartJS libraries are used in this work, which is open source and free to use.
These libraries can dynamically configure graphic objects' display parameters and show realtime changes. When the user moves the mouse over the graph points, the digital representation helps the user see the current value. This simplifies data analysis and allows for the extension of the application. In addition, libraries with implemented mathematical algorithms can be used to model various processes, particularly for compressive strength. The data is stored in a database for constant data access and storage of intermediate calculation results. Figure 1 presents a visual view of the information processing results for various nanomaterials [1]. Thus, these results can dynamically change and add new ones as needed. To analyse a specific area, it is possible to increase the scale.
The top three graphs show the difference between the ordinary portland cement paste and three nanomaterials, nanolimestone (NL), nanosilica (NS), and nanoclay (NC). The second row of graphs shows the changes considering the cement-fly ash blended paste (OPCFA).

RESULTS AND DISCUSSION
As a result of data processing determined, the change in the compressive strength   and water and calcium hydroxide content for cement paste after curing parameter when using different mixtures. Comparative graphic characteristics of the parameter change make it possible to estimate the difference in the strengthening of materials each time.   Figure 3 shows the interpolation of these same materials considering the cement-fly ash blended paste (OPCFA). Such a mixture provides cohesion and filling of pores in the cement mixture, which is due to the lower indicators of chemically bound water compared to without the addition of this additive. The lower graph from the upper group of diagrams in this figure takes into account the cement-fly ash blended paste (OPCFA) and the upper ones with the addition of nanoparticles, respectively, in Figure 3a is the cement-fly ash paste with nanolimestone (OPCFANL ), in Figure 3b -cement-fly ash paste with nanosilica (OPCFANS), 3c -cement-fly ash paste with nanoclay (OPCFANC). Moreover, the indicators with H shown in the lower group of graphs in Figures 2 and 3 Figure 4 shows a linear approximation, which shows the linear nature of changes in this parameter. The percentage deviation from the linear approximation is 17.32% for the ordinary portland cement paste (OPC) is 11.62% with NS, 10.28% -NL, and 7.6% -NC. Among all nanoparticles, the compressive strength increases linearly in a cement mixture with nanoclay. The most significant difference is observed in the first points due to the use of a linear approximation. Figure 5 shows the overlay of the linear approximation on changes in the compressive strength parameter. On these graphs, compared to the cement-ash mixture and nanoparticles, the percentage difference between the linearly approximated straight line and the compressive strength change graph: cement-fly ash paste (OPCFA), 41.4% -cement-fly ash paste with nanolimestone (OPCFANL) (Fig. 5a), 17.71%cement-fly ash paste with nanosilica (OPCFANS) (Fig. 5b), 20.75% -cement-fly ash paste with nanoclay (OPCFANC) (Fig. 5c). It can be assumed that the square root function is more suitable for such materials.    As shown in Table 1, with the addition of nanoparticles, all materials have higher destructive load indicators and become stronger. The most significant average deviation from the usual mixture in strength with the addition of nanosilica to the cement mixture (OPCNS) and less with the addition of nanoclay (OPCNC). On average, when added to a conventional cement mixture, the addition of nanoparticles equals 13.45%.
With the addition of nanosilica (OPCFANS) to the cement-ash mixture, such a mixture becomes the strongest. Compared to the cement mixture with nanosilica, the same combination is still worse in terms of results since the values obtained for compressive strength in Figure 2 have higher values of compressive strength compared to those with the cementash mixture in Figure 3.
By selecting approximation, it is possible to summarise the characteristics of the change of these parameters. This mathematical analysis allows you to work out and analyse the results. Theoretical results can be simulated programmatically using the developed web page. Different pastes can be programmatically affected and compare theoretical results in this case. Table 1 shows the percentage difference for different pastes with additives in each period. It can conclude the strength based on the compressive strength indicators. For cement and cement-ash pastes and with nanosilica, nanoclay and nanolimestone nanoparticles, data analysis is performed using linear interpolation and approximation methods to determine the nature of the compressive strength parameter.
Since the linear approximation is possible for deviation values that are not significant, it can be assumed that the strengthening coefficient increases linearly for cement paste and the behaviour of the square root function (branch of the parabola) for cement-ash pastes for a period from 3 hours to 29 hours. However, if it is considered that the beginning is from 1 hour, then in the first hours, this parameter increases the most and, in general, resembles the branch of a parabola.
Another parameter of strength can be considered the water and calcium hydroxide content after curing.
The paper also mathematically shows the influence of the destructive load parameter on changes in the quality of nano concrete, which can be used to assess strength and corrosion processes.

1.
A new version of the nano concrete strength criterion is proposed, taking into account the en-ergy characteristics of the interphase layers between the solid framework and the micropore medium, which characterise the connections (adhesion) of the two media.
2. The relationship between surface physics and fracture mechanics is the basis of the methodology for assessing the quality of nano concrete and can be used to determine the resource of the material and the strengthening parameter, taking into account the criteria of strength, corrosion processes and metrological support.
3. Based on the obtained results, the strength, reliability, strengthening parameter and residual resource of nano concrete can be evaluated, taking into account the porous medium.