Direct Tensile Test Method for Shotcrete

Abstract

This study substantiates the need for direct tensile strength testing of shotcrete and fiber-reinforced shotcrete, rather than relying on indirect methods, to accurately reflect material performance under biaxial stress conditions when used for structural reinforcement. Experiments on field specimens confirmed that tensile strength values derived through direct testing differ significantly from those calculated based on compressive strength. The study presents a new testing methodology with optimized specimen dimensions (32, 40, 50, and 82 mm diameter cylinders with length-to-diameter ratios of 3.0) to mitigate eccentricity effects, ensuring normal-section failure. Results show that tensile strength values for fiber-reinforced shotcrete with brass-coated fibers (13–15 mm length, 0.3–0.5 mm diameter, 30 kg/m³ dosage) reached 68 MPa, compared to 60 MPa for standard shotcrete, while basalt-fiber reinforcement (6 mm length, 1% by weight) resulted in 42 MPa. The initial modulus of elasticity for unreinforced shotcrete was 280 × 10³ MPa, with fiber reinforcement slightly increasing this value to 287 × 10³ MPa. The findings support a direct approach to testing, providing a foundation for developing predictive methodologies for fiber-reinforced shotcrete properties based on reinforcement type and dosage. These results are essential for applications such as seismic strengthening, where accurate tensile characteristics are critical for performance under dynamic loading.

1. Introduction

1.1. Relevance of the Study

Buildings and structures built with traditional construction materials are designed to withstand project loads and meet operational conditions. When design parameters are adhered to throughout their lifecycle, load-bearing structures and joints provide the required levels of reliability and functionality. However, due to various factors, errors may occur, leading to damage to load-bearing systems and enclosing structures.

To ensure the required level of reliability, the load-bearing capacity of damaged structures must be restored using various strengthening methods.

Experience in surveying buildings with damaged structures [1,2,3,4,5,6] demonstrates that the primary causes of damage can be categorized as follows:

• (a). Design-related errors:

  • (a.1). Errors in geotechnical investigations during the design phase of construction projects (especially in determining the parameters of the site’s engineering and geological conditions);

  • (a.2). Errors in the analytical validation of the strength, deformability, and reliability of load-bearing structures, including issues in idealizing structural elements when forming analytical models in design software, and misinterpretation of analytical results;

  • (a.3). Errors in structural detailing. Common problems in reinforced concrete structures include incorrect solutions for transverse reinforcement of columns and beams, resulting in inadequate load-bearing capacity under shear forces (e.g., improper transverse reinforcement layout, unconventional reinforcement, and detailing solutions);

• (b). Construction-related errors:

Errors in construction practices, such as failure to follow masonry construction technology, leading to low adhesion strength between masonry materials (brick and mortar); or non-compliance with concrete curing requirements for cast-in-place reinforced concrete structures;

• (c). Damage due to improper operation of the structure or the building as a whole:

  • (c.1). Operation leading to material weathering, corrosion of structural materials, or other processes that degrade the structure;

  • (c.2). Operation of the building in violation of design specifications, including exceeding the design loads, which alters the stress–strain state of the structures, causing stress levels in certain elements to surpass the designed thresholds;

  • (c.3). Changes in the mechanical properties of foundation soils due to failure to implement design solutions for surface water drainage, resulting in uneven settlement of foundations and non-design deformations in structures above the foundation;

• (d). Accidental impacts, including climatic and seismic events:

These impacts typically have a dynamic nature and cause specific types of damage to structures, joints, and facilities as a whole.

It is important to note changes in the functional purpose of the object, leading to increased design loads (such cases usually do not involve vertical structures and will not be discussed further).

These causes can be represented in a diagram—see Figure 1 [1].

Various methods are used for the repair and strengthening of structures, including the following:

• (a). Modification of the structural system:

This involves introducing new structural elements to redistribute loads within the load-bearing system and create unloading effects.

• (b). Localized strengthening of individual elements:

Techniques include cross-section enlargement, additional reinforcement, and similar methods.

In general, methods for local strengthening (such as cross-section enlargement, external reinforcement, including carbon fiber reinforcement) have been established for a long time, with their development primarily driven by advancements in both the materials for the structures being strengthened and the strengthening materials.

Currently, two methods stand out as the most promising: strengthening with external reinforcement using composite materials and strengthening with shotcrete (including fiber-reinforced shotcrete). Strengthening with shotcrete or fiber-reinforced shotcrete enables both cross-section enlargement (increasing stiffness) and additional reinforcement (discrete or dispersed) to be engaged.

The issue of strengthening masonry walls is of particular interest, as their load-bearing capacity is significantly lower than that of reinforced concrete walls. A crucial feature of masonry walls is their anisotropy: the compressive and (especially) tensile strength of masonry depends on the direction of the applied load [7,8]. This factor is most pronounced under intense dynamic (seismic) impacts, as confirmed by engineering analyses of earthquake consequences (Figure 2). Masonry structures are among the most vulnerable to seismic forces. This high sensitivity is attributed to the complex composition of masonry, which consists not only of the primary materials (brick and mortar) but also of the interaction points between these materials within the masonry joints.

Under intense dynamic (seismic) loads, masonry walls experience biaxial stress conditions. In such conditions, the principal tensile stresses often exceed the tensile strength of the masonry along the unbonded joints. The first to fail are the adhesive bonds within the masonry joints (where stresses exceed the adhesive strength, Radh), after which the masonry loses its monolithic integrity and associated load-bearing capacity.

Masonry structures similarly respond to uneven foundation settlements: a network of diagonal cracks forms within the walls, along with vertical cracks at the junctions of walls in different orientations. These types of damage lead not only to a reduction in load-bearing capacity but also to alterations in the building’s spatial load-bearing system.

Based on the authors’ experience in strengthening damaged masonry structures, the most effective method has proven to be the application of concrete or fiber-reinforced concrete overlays, applied using shotcreting technology (Figure 3).

An analysis of the performance of shotcrete or fiber-reinforced shotcrete in strengthening masonry and reinforced concrete structures [7,9,10,11,12] highlights the following key features:

• The creation of an external reinforcing element with higher strength characteristics, relative to the original structure, helps restore broken connections between the masonry’s base materials by incorporating the strengthening element (overlay) into the combined load-bearing system;

• A key requirement in implementing an external reinforcement structure using shotcrete or fiber-reinforced shotcrete is ensuring the integrated performance of the reinforcing element and the structure being strengthened;

• The degree of increase in load-bearing capacity of the existing damaged structure is determined by the strength characteristics of the reinforcing element and the adhesive strength characteristics of the interaction between the reinforcing element and the structure being strengthened.

Experimental studies [13] have shown that the adhesive strength of the interaction between the shotcrete or fiber-reinforced shotcrete reinforcement and the structure being strengthened (masonry or concrete) generally exceeds the tensile strength of the material of the strengthened structure—failure typically occurs not along the line of contact but within the surface layer of the strengthened structure’s material (Figure 4).

Based on the established conditions for the integrated performance of the strengthened structure and the shotcrete or fiber-reinforced shotcrete reinforcement, a model of the reinforced structure’s behavior has been developed [13] (Figure 5).

The strengthened structure generally exhibits reduced strength according to primary criteria (compressive and tensile strength). For masonry structures under biaxial stress conditions, the primary strength criterion is the adhesive bond strength between the base materials (brick and mortar) within the masonry joints. Under intense dynamic impacts, such as seismic forces, adhesive bonds break down across large volumes, reducing the load-bearing capacity of masonry walls in response to principal tensile stresses. In such cases, compensating for the insufficient load-bearing capacity of the masonry structure can be achieved through the combined action of the existing damaged structure and the shotcrete or fiber-reinforced shotcrete reinforcement.

Therefore, to justify the strength and reliability of the strengthened structure, it is necessary to use the actual mechanical properties of the reinforcing material (shotcrete or fiber-reinforced shotcrete) along with the adhesive bond strength characteristic of the interaction between the reinforcement and the strengthened structure’s material.

Determining the compressive strength of the external shotcrete or fiber-reinforced shotcrete overlay material is straightforward and is performed by testing cores extracted from both the structure and specially prepared slabs. Currently, developed methods for translating compressive strength obtained from non-standard samples to standard cylinders and prisms show good convergence, and the authors of this article see no need for further refinement.

The most critical property for shotcrete or fiber-reinforced shotcrete reinforcement is tensile strength and the corresponding modulus of deformation. Presently, tensile strength for real projects is often estimated based on compressive strength using various empirical correlations. This method is only conditionally applicable for shotcrete and is entirely unsuitable for fiber-reinforced shotcrete with dispersed reinforcement, as translating compressive to tensile strength using known empirical correlations is inaccurate due to the presence of distributed dispersed reinforcement. It is also impossible to determine the initial modulus of elasticity for tensile conditions with acceptable accuracy through indirect tests (compression, density, etc.).

Thus, there is a need for a direct method to accurately determine the tensile strength of shotcrete or fiber-reinforced shotcrete, taking into account the specific composition of the concrete.

1.2. Testing Methods

A standardized methodology for testing shotcrete and (especially) fiber-reinforced shotcrete in tension is currently lacking. At present, the following approach is used:

Different countries’ standards include their own tables of strength characteristic correlations (for example, Table 1 is an excerpt from the standards of the Russian Federation [14], presenting values of strength and modulus of elasticity for specific concrete classes, which should be used in calculations).

Based on the analysis of the presented table from the Russian Federation’s national standards, the following conclusions can be drawn regarding the applicability of these data for shotcrete, which uses fine-grained aggregate (the aggregate size in shotcrete is significantly smaller than in traditional fine-grained concretes):

• Tensile strength is shown as independent of aggregate size, which may be insufficiently justified for standardizing shotcrete characteristics;

• It is likely that an error accumulates in determining the tensile strength of shotcrete as compressive strength increases;

• For shotcrete with strength above B50, data on the modulus of elasticity are not available;

• Using the table’s data to determine the characteristics of fiber-reinforced shotcrete is not feasible due to the substantial impact and variability of dispersed reinforcement distribution within the material.

At the same time, methodologies exist for determining tensile strength in conventional concretes (also used for testing fiber-reinforced concretes) [15,16,17], among which the following can be highlighted:

• (A). Testing notched beam specimens under concentrated load (Figure 6).

This method is detailed in EN 14651 [16].

Further, using a series of relationships, strength can be determined while accounting for the inelastic properties of concrete.

• (B). Testing notched beam specimens under moment in a normal section (Figure 7).

This method is detailed in ASTM C1609 [17].

Figure 7

Test scheme for notched beam specimens, according to ASTM C1609 [17].

[Figure omitted. See PDF]

• (C). Testing fiber-reinforced concrete (including shotcrete and fiber-reinforced shotcrete) in tension under flexure using a round panel with a centrally applied load.

The ASTM C1550 [18] method is illustrated by a general scheme in Figure 8.

Analyzing the presented methods, including those based on research [19,20,21,22,23,24], the following conclusions can be drawn:

• Existing “tensile” testing methods employ indirect (secondary) testing approaches, and the obtained tensile strength values of concrete depend on both the testing method and the specimen material characteristics;

• Strength characteristics are calculated using formulas with empirical coefficients, whose values depend on the testing method, which imposes certain limitations on the applicability of the above methods;

• Analysis of test results using existing methods shows a low level of reliability, leading to the application of high variation coefficient.

Regarding the use of dispersed reinforcement in shotcrete and based on recent research findings [25,26,27,28,29,30], it can be concluded that accurate methodologies for determining the mechanical characteristics of fiber-reinforced shotcrete (including the effects of fiber type and reinforcement percentage) are essentially lacking. For any new mix design, a full range of physical and mechanical property tests must be conducted for the specific type of dispersed reinforcement.

2. Materials and Methods

2.1. Specimens

To conduct detailed investigations into the comparative strength of shotcrete and fiber-reinforced shotcrete in compression and tension, as well as to develop a tensile testing mechanism, the following specimens were prepared:

Panels (with subsequent extraction of cores with diameters of 64 mm and 72 mm and cutting samples for modulus of elasticity testing)—see Figure 9a;

Cylinders (cast in tubes of various diameters—32 mm, 40 mm, 50 mm, and 80 mm)—see Figure 9b.

The technique for extracting samples from prepared panels is well-established and widely applied: cores are drilled using specialized diamond-coated coring bits (ensuring that impact forces are strictly avoided). It should be noted that during the coring of fiber-reinforced shotcrete, edge chipping was observed in areas where the coring bit encountered fibers. To prevent the formation of local microdamage in the surface layer of the extracted samples, specimens were prepared in tubes, which resulted in samples with undamaged outer surfaces.

Preparing specimens in tubes required specific technical adjustments, which were carried out by experienced specialists based on comparative testing of various methods and equipment. This process involved developing a technique that ensures uniform filling of the tubular molds with shotcrete, eliminating local decompaction of the concrete. As a result, samples were obtained with sufficient homogeneity, and subsequent testing demonstrated a uniform distribution of reinforcing fibers, matching the fiber distribution in the panel specimens. Notably, the specimens prepared in tubular molds provided consistent tensile testing results.

The approach of using tubular molds was driven by the need to maintain the surface integrity of the fiber-reinforced shotcrete, which tends to be compromised during core extraction. The specimens produced with tubular molds were monitored for the following parameters:

• Visual inspection for defects (cracks, discontinuities, etc.);

• Internal integrity assessed by ultrasonic testing;

• Fiber distribution pattern within the volume (evaluated after specimen failure during testing).

2.2. Testing Procedure

The tests were conducted in the following areas:

Compressive strength on control specimens extracted by coring from prepared panels (cores)—Figure 10;

Modulus of elasticity in compression on control specimens (prisms) extracted from prepared panels—Figure 10;

Tensile strength on specimens extracted by coring from prepared panels (cores)—Figure 11;

Tensile strength on specimens cast in tubular molds—Figure 11.

Compression tests were conducted following a standard methodology, which involves determining the failure load on cylindrical specimens with diameters of 64 and 75 mm to assess compressive strength. The tests (Figure 12a) were performed on a press using specimens prepared from cores (drying after coring, trimming to achieve a diameter-to-height ratio close to 1.0, and surface end grinding). Final strength values were adjusted using scale factors in accordance with the Russian Federation state standard GOST 10180-2012, “Concretes. Methods for strength determination using reference specimens” [31].

To determine the prismatic strength and modulus of elasticity, four prism specimens measuring 70 × 70 × 280 mm were prepared from a shotcrete slab. Frames were attached to the prisms to hold four dial gauges with a resolution of 0.001 mm. After aligning each specimen along its physical axis, the prisms were loaded within a range of 0.01–0.1 Rb. The load was applied in increments, with a 5 min hold at each step. Deformations upon load increase were considered elastic, while those accumulated over the 5 min hold period were considered creep deformations. The tests and subsequent analysis were conducted in accordance with the interstate standard GOST 24452-2023, “Concretes. Methods of prismatic compressive strength, modulus of elasticity, and Poisson’s ratio determination” [32].

The modulus of elasticity was determined at a load level corresponding to 30% of the failure load. It was calculated based on the test results as the ratio of the stress increment from a nominal zero to the external load level (30% of the failure load) to the increment in longitudinal strain of the specimen, measured by sensors on the edges.

For tensile tests, a scheme was chosen that directly corresponds to the behavior of shotcrete and fiber-reinforced shotcrete in strengthening elements of load-bearing structures (Figure 12b).

The tests were preceded by detailed planning and prediction of the failure patterns of the specimens, during which the following occurred:

• the use of micro-notches to initiate failure at a specific location on the specimen was abandoned;

• Special support “cups” (Figure 13) with an expanded bonding area were prepared for gripping the specimens, secured with adhesive.

3. Results

The compressive strength of concrete obtained from the tests averaged 60 MPa (mix 1), 68 MPa (mix 2—fiber-reinforced shotcrete), and 42 MPa (mix 3—fiber-reinforced shotcrete).

The mixes used were specialized dry shotcrete mixtures based on cement binders, calibrated aggregate (with a maximum particle size of 3 mm), and various additives (these mixes are widely used in the Russian Federation). Sample 1 was made without fiber reinforcement. Sample 2 was made with concrete reinforced with brass-coated fibers, a length (L) of 13–15 mm and nominal diameter (d) of 0.3–0.5 mm, at a dosage of 30 kg/m³ of concrete. Sample 3 used alkali-resistant basalt fiber, 6 mm in length, at 1% of the total mass.

The modulus of elasticity in compression is graphically presented in Figure 14. The characteristic values (excluding plastic deformations) can be defined as: E₀ = 280 × 10³ MPa (mix 1), E₀ = 287 × 10³ MPa (mix 2), and E₀ = 262 × 10³ MPa (mix 3).

The test results indicate that there is virtually no difference in the modulus of elasticity values between shotcrete and fiber-reinforced shotcrete with various types of fiber during the elastic deformation phase. The influence of the fiber is evident only in the elastic–plastic stage. Considering this, it is deemed justified that deformation diagrams should be constructed for each concrete mix and fiber type when determining the modulus of deformation for fiber-reinforced concrete.

The results of the compressive strength and modulus of elasticity tests are presented in Table 2.

A comparison of the obtained experimental results with the recommendations of the current national standards [14] is presented in Table 3.

Tensile tests to obtain tensile strength characteristics directly, and to evaluate the use of standard tables for determining tensile strength from compression test results, were conducted on a tensile testing machine. During these tests, the failure mechanism, failure load, and grip displacements (an indirect assessment of the tensile modulus of elasticity to aid in developing testing methodologies and conducting further research) were recorded.

Before testing, the specimens’ dimensions and weight were measured, and the ultrasonic pulse velocity in the longitudinal direction was recorded.

Tests were conducted on cylindrical specimens with diameters of 32, 40, 50, and 82 mm, with a length equal to the specimen diameter multiplied by 3.0.

In tensile testing of specimens with diameters of 32 and 40 mm, similar failure mechanisms were observed (Figure 15): upon reaching ultimate tensile strength, brittle failure occurred (tests were conducted on shotcrete specimens) along a normal cross-section, located between ¼ and ¾ of the specimen length.

For specimens with diameters of 50 and 82 mm, brittle failure was also observed, but along an inclined section (Figure 16), due to misalignment between the loading axis and the geometric axis. The test results are presented in Table 4.

The results of tensile tests on shotcrete specimens and their comparison with tabulated values from Russian Federation standards are presented in Table 5.

4. Discussion

In studies of shotcrete properties, the following mechanical characteristics are critically important for modeling and calculating reinforcement elements:

• Compressive strength;

• Tensile strength;

• Initial modulus of elasticity in compression, as well as its variation considering the addition of discrete reinforcement and the level of loading;

• Initial tensile modulus of elasticity of shotcrete (especially crucial for fiber-reinforced concretes). It is also important to understand the modulus of elasticity’s variation at different stress levels.

The most significant aspect is determining the actual tensile strength of shotcrete and fiber-reinforced shotcrete—an essential characteristic widely used in structural reinforcement applications, including seismic strengthening. The analysis presented in this article highlights the importance of this characteristic for fiber-reinforced shotcrete, which resists tensile stresses without rebar and experiences tensile stresses under biaxial stress conditions. Additionally, conducting tests under dynamic loads of varying intensity and direction is essential, as it would allow for the justified application of shotcrete and fiber-reinforced shotcrete in seismic strengthening to the design seismic resistance level.

The existing practice of designing and controlling the physical and mechanical properties of materials (primarily based on structural concrete) includes controlling compressive strength and subsequently determining the corresponding tensile strength and initial modulus of elasticity. These algorithms are also partially applicable to shotcrete. Using existing relationships in national standards (Table 6), characteristic moduli of elasticity can be calculated, which were generally confirmed by the results of this study.

It is important to emphasize that studies have shown that tensile strength values for shotcrete and fiber-reinforced shotcrete, determined using the developed direct testing methodology, differ significantly from values calculated based on compressive strength. Therefore, the research results support the conclusion that applying results obtained from indirect methods (secondary tests) is inaccurate for strength calculations.

5. Conclusions

• a.. The necessity of determining the tensile strength of shotcrete and fiber-reinforced shotcrete through direct testing (without using indirect methods) is substantiated, as it aligns with the material’s behavior when reinforcing structures under biaxial stress conditions (as confirmed by tests on field specimens). Given the good reproducibility of test results, it is possible to develop a methodology for predicting the properties of fiber-reinforced shotcrete based on the type and percentage of reinforcement. This will be implemented as sufficient statistical data are accumulated for various compositions.

• b.. A testing methodology has been developed to directly determine concrete strength, with recommended specimen dimensions that minimize the influence of eccentricity, resulting in failure along a normal section.

• c.. The application of methods to determine the initial modulus of elasticity of shotcrete by compressive strength testing is justified. However, the initial modulus of elasticity of fiber-reinforced shotcrete, as well as the stress–strain diagram, should be verified through testing for each specific composition.

Author Contributions

Conceptualization, O.V.K.; Methodology, O.V.K.; Validation, O.A.S.; Investigation, O.A.S.; Data curation, O.A.S.; Writing—original draft, O.A.S.; Visualization, O.A.S.; Supervision, O.V.K.; Project administration, O.V.K.; Funding acquisition, O.V.K. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Causes requiring restoration of reinforced concrete and masonry structures.

Figure 2. Damage to exterior masonry walls due to seismic impacts.

Figure 3. Sample of masonry structures reinforced with a one-sided shotcrete overlay.

Figure 4. Results of the study on failure mechanisms at the interface between shotcrete overlays and masonry.

Figure 5. Model of interaction between structural elements with compromised internal bonds and the external reinforcing element: under compression and shear conditions (a), tension and shear conditions (b).

Figure 6. Test scheme for notched beam specimens, according to EN 14651 [16].

Figure 8. Test scheme for panel specimens, according to ASTM C1550 [18].

Figure 9. Shotcrete and fiber-reinforced shotcrete specimens for testing with diameters of 64 and 72 mm; (a) extracted from panels, (b) cast in plastic cylinder molds with diameters of 32 mm, 40 mm, 50 mm, and 82 mm.

Figure 10. General view of the test series of specimens for compressive strength testing.

Figure 11. General view of the test series of specimens for tensile strength testing.

Figure 12. Testing of control specimens: (a) compression; (b) tension.

Figure 13. Support “cups” for gripping specimens in tensile testing.

Figure 14. Tests for determining the modulus of elasticity in compression.

Figure 15. Tensile tests on specimens with diameters of 32 and 40 mm.

Figure 16. Tensile tests on specimens with diameters of 50 and 80 mm. (a) formation of rectilinear inclined crack, (b) formation of nonlinear crack with displacement.

Figure 17. Specimen failure pattern.

Table 1

Standard physical and mechanical characteristics of concrete, according to [14].

Concrete	Prism Compressive Strength (for 150 × 150 × 600 mm Prisms), MPa	Tensile Strength, MPa	Compressive Modulus of Elasticity, MPa × 10−3	Tensile Modulus of Elasticity, MPa × 10−3
B20	15.0	1.35	27.5	27.5
Same, fine-grained	15.0	1.35	22.0	22.0
B30	22.0	1.75	32.5	32.5
Same, fine-grained	22.0	1.75	26.0	26.0
B40	29.0	2.1	36.0	36.0
Same, fine-grained	29.0	2.1	28.5	28.5
B50	36.0	2.45	38.0	38.0
Same, fine-grained	36.0	2.45	-	-
B60	43.0	2.75	39.5	39.5
Same, fine-grained	43.0	2.75	-	-

Table 2

Test results of specimens.

Mix	Strength, MPa	Corresponding Strength Class	Modulus of Elasticity, MPa
1 Shotcrete	60	B45	28.0 × 103
2 Fiber-Reinforced Shotcrete (Mix 2)	68	B50	29.7 × 103
3 Shotcrete with Polymer Fibers (Mix 3)	42	B30	26.2 × 103

Table 3

Comparative analysis of modulus of elasticity in compression results.

Mix	Actual Modulus ofElasticity, MPa	Modulus of Elasticity from Tables [14], MPa	Deviation, %
1 Shotcrete	28.0 × 103	28.5 × 103	1.78
2 Fiber-Reinforced Shotcrete (Mix 2)	29.7 × 103	-	-
3 Shotcrete with Polymer Fibers (Mix 3)	26.2 × 103	26 × 103	0.8

Table 4

Tensile test results of specimens.

Diameter	Tensile Strength	Average Value	Note
32	2.32	2.41	Failure along a Normal Section (Figure 17)
	2.54
	2.39
	2.41
	2.4
40	2.65	2.48	Failure along a Normal Section (Figure 17)
	2.42
	2.55
	2.39
	2.4
50	1.4	1.57	Failure along an Inclined Section
	1.55
	1.2
	1.6
	2.1
82	1.9	1.48	Failure along an Inclined Section
	2.2
	1.1
	0.8
	1.4

Table 5

Comparative analysis of tensile strength test results.

Specimen Characteristics	Tensile Strength from Test Results, MPa	Tensile Strength Based on Compressive Strength Data, MPa	Deviation, %
Specimens Ø32 mm	2.41	2.1	14.7
Specimens Ø40 mm	2.48	2.1	18.1

Table 6

Methodology for determining the modulus of elasticity of concrete (in compression), according to standards of various countries.

Methodology	Determination of Modulus of Elasticity	Note
USSR	$E_b={\displaystyle \frac{5.5·{10}^5·B}{870+B}}$	B—Concrete Class
Russian Federation	$E_b={\displaystyle \frac{43000·B}{21+B}}$
Canada	$E_b=3320·\sqrt{f_c^{\prime }}+690$	f′c—Specified Cylindrical Strength
USA	$E_b=w·0.043·\sqrt{f_c^{\prime }}$

References

1. Simakov, O.A. Analysis of Factors Causing the Need for Strengthening of Reinforced Concrete Constructions. Build. Reconstr.; 2019; 1, pp. 76-84. [DOI: https://dx.doi.org/10.33979/2073-7416-2019-81-1-76-84]

2. Metodika Otsenki i Sertifikatsii Inzhenernoy Bezopasnosti Zdaniy i Sooruzheniy, MCHS Rossii. FTS Nauki i Vysokikh Tekhnologiy “VNII GOCHS [Methodology for the Assessment and Certification of Engineering Safety of Buildings and Structures, EMERCOM of Russia. FC of Science and High Technologies “VNII GOCHS”], Moscow. 2003; Available online: https://files.stroyinf.ru/Data2/1/4293831/4293831920.htm?ysclid=m320i770md8785211 (accessed on 25 February 2003).

3. Volkov, A.S.; Dmitrenko, E.A.; Korsun, A.V. The Influence of Construction Defects on Bearing Capacity of Reinforced Concrete Constructions of a Frame Monolithic Building. Constr. Unique Build. Struct.; 2015; 2, pp. 45-56.

4. Zolotozubov, D.G.; Mukhin, K.O. Problemy Usileniya i Rekonstruktsii Butovykh Fundamentov Pri Pereustroystve Podvalov Zhilykh Zdaniy [Problems of Strengthening and Reconstruction of Rubble Foundations in the Reorganization of Basements of Residential Buildings]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Stroit. Arkhitektura; 2015; 2, pp. 75-91.

5. Orlovich, R.; Mantegatstsa, D.; Naychuk, A.; Derkach, V. Sovremennyye Sposoby Remonta i Usileniya Kamennykh Konstruktsiy [Modern methods of repair and strengthening of stone structures]. Arkhitektura Dizayn I Stroit.; 2010; 1, pp. 86-87.

6. Tamrazyan, A.G. Concrete and Reinforced Concrete: Problems and Prospects. Promyshlennoye Grazhdanskoye Stroit.; 2014; 7, pp. 51-54.

7. Kabantsev, O.V.; Tamrazyan, A.G. Modeling Elastoplastic Deformation Masonry Under Biaxial Stresses. Int. J. Comput. Civ. Struct. Eng.; 2015; 3, pp. 87-100.

8. Cajamarca-Zuniga, D.; Kabantsev, O. Particular Strength Criteria for Microstructural Analysis of Masonry. Key Eng. Mater.; 2023; 959, pp. 185-195. [DOI: https://dx.doi.org/10.4028/p-6IMwpA]

9. Tonkikh, G.P.; Kabantsev, O.V.; Simakov, O.A.; Simakov, A.B.; Baev, S.M.; Panfilov, P.S. Experimental study of seismic strengthening of masonry exterior concrete applications. Earthquake-resistant construction. Saf. Constr.; 2011; 2, pp. 35-41.

10. Tonkikh, G.H.; Kabantsev, O.V.; Simakov, O.A.; Simakov, A.B.; Bayev, S.M. Increase of Seismic Resistance Of Masonry Structures By One-Sided Applications From Shotcrete. Airpt. Adv. Technol.; 2011; 3, pp. 23-37.

11. Shedid, M.T.; El-Dakhakhni, W.W.; Drysdale, R.G. Behavior of Fully Grouted Reinforced Concrete Masonry Shear Walls Failing in Flexure: Analysis. J. Eng. Struct.; 2009; 31, pp. 2032-2044. [DOI: https://dx.doi.org/10.1016/j.engstruct.2009.03.006]

12. Haach, V.G.; Vasconcelos, G.; Lourenço, P.B. Experimental Analysis of Reinforced Concrete Block Masonry Walls Subjected to in-Plane Cyclic Loading. J. Struct. Eng.; 2010; 136, pp. 452-462. [DOI: https://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000125]

13. Kabantsev, O.; Simakov, O. Repair of Masonry after Dynamic Impacts. Calculation and Design Methods. Int. J. Comput. Civ. Struct. Eng.; 2023; 19, pp. 48-68. [DOI: https://dx.doi.org/10.22337/2587-9618-2023-19-4-48-68]

14. SP 63 13330.2018 Concrete and Reinforced Concrete Structures. General Provisions; Official Edition. Standartinform Ministry of Construction and Housing and Communal Services of the Russian Federation: Moscow, Russia, 2019; Available online: https://docs.cntd.ru/document/554403082 (accessed on 20 June 2019).

15. C192/C192M-18 Making and Curing Concrete Test Specimens in the Laboratory; ASTM International: West Conshohocken, PA, USA, 2018.

16. EN 14651:2005+A1:2007 Test Method for Metallic Fibered Concrete—Measuring the Flexural Tensile Strength [Limit of Proportionality (LOP) Residual], NEQ; Slovenian Institute for Standardization: Ljubljana, Slovenia, 2005.

17. ASTM C1609-10 Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete (Using Beam with Third-Point Loading); ASTM International: West Conshohocken, PA, USA, 2010.

18. ASTM C1550-10 Standard Test Method for Flexural Toughness of Fiber Reinforced Concrete (Using Centrally Loaded Round Panel); ASTM: West Conshohocken, PA, USA, 2010.

19. D1557-12 Standard Test Methods for Laboratory Compaction Characteristics of Soil Using Modified Effort (56,000 ft-lbf/ft3 (2700 kN-m/m³)); ASTM International: West Conshohocken, PA, USA, 2012.

20. Yang, G.; Cheng, F.; Zuo, S.; Zhang, J.; Xu, Y.; Hu, Y.; Hu, X.; Wei, Y.; Gou, G. Constructing Quasi-Vertical Fiber Bridging Behaviors of Aramid Pulp at Interlayer of Laminated Basalt Fiber Reinforced Polymer Composites to Improve Flexural Performances. Chin. J. Aeronaut.; 2023; 36, pp. 477-488. [DOI: https://dx.doi.org/10.1016/j.cja.2023.10.013]

21. Yildizel, S.A.; Tayeh, B.A.; Uzun, M. The Evaluation of Calcium Carbonate Added and Basalt Fiber Reinforced Roller Compacted High Performance Concrete for Pavement. Case Stud. Constr. Mater.; 2022; 17, e01293. [DOI: https://dx.doi.org/10.1016/j.cscm.2022.e01293]

22. Yao, J.; Ge, Y.; Ruan, W.; Meng, J. Effects of PVA Fiber on Shrinkage Deformation and Mechanical Properties of Ultra-High Performance Concrete. Constr. Build. Mater.; 2024; 417, 135399. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2024.135399]

23. Min, W.L.; Jin, W.L.; He, X.Y.; Wu, R.J.; Chen, K.Y.; Chen, J.J.; Xia, J. Experimental Study on the Flexural Fatigue Performance of Slag/Fly Ash Geopolymer Concrete Reinforced with Modified Basalt and PVA Hybrid Fibers. J. Build. Eng.; 2024; 94, 109917. [DOI: https://dx.doi.org/10.1016/j.jobe.2024.109917]

24. Rao, L.; Wang, L.; Zheng, Y. Experimental Research on Mechanical Properties and Compression Constitutive Relationship of PVA Fiber-Reinforced Coral Concrete. Materials; 2022; 15, 1762. [DOI: https://dx.doi.org/10.3390/ma15051762]

25. Ali, B.; Raza, S.S.; Hussain, I.; Iqbal, M. Influence of Different Fibers on Mechanical and Durability Performance of Concrete with Silica Fume. Struct. Concr.; 2021; 22, pp. 318-333. [DOI: https://dx.doi.org/10.1002/suco.201900422]

26. Gholampour, A.; Danish, A.; Ozbakkaloglu, T.; Yeon, J.H.; Gencel, O. Mechanical and Durability Properties of Natural Fiberreinforced Geopolymers Containing Lead Smelter Slag and Waste Glass Sand. Constr. Build. Mater.; 2022; 352, 129043. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2022.129043]

27. Jawheer, A.A.; Mansoor, Y.A.; Al-Hadithi, A.I.; Hamad, O.A. Fuzzy Logic Progress to Predict of Mechanical Properties for Shotcrete Concrete Contianing Waste Plastic. Proceedings of the 2021 14th International Conference on Developments in eSystems Engineering (DeSE); Sharjah, United Arab Emirates, 7–10 December 2021; pp. 566-570.

28. Shah, S.A.; Gul, M.A.; Naqash, T.; Khan, Z.; Rizwan, M. Effects of Fiber Reinforcements on the Strength of Shotcrete. Civ. Eng. Archit.; 2021; 9, pp. 176-183. [DOI: https://dx.doi.org/10.13189/cea.2021.090115]

29. Al-Hadithi, A.I.; Abbas, M.A. Innovative Technique of Using Carbon Fibre Reinforced Polymer Strips for Shear Reinforcement of Reinforced Concrete Beams with Waste Plastic Fibres. Eur. J. Environ. Civ. Eng.; 2021; 25, pp. 516-537. [DOI: https://dx.doi.org/10.1080/19648189.2018.1532820]

30. Hossain, M.S.; Han, S.; Kim, S.K.; Yun, K.K. Long-Term Effect of Accelerator Content on Flexural Toughness of Steel Fiber Reinforced Shotcrete for Tunnel Construction. Case Stud. Constr. Mater.; 2021; 15, e00706. [DOI: https://dx.doi.org/10.1016/j.cscm.2021.e00706]

31. GOST 10180-2012 Concretes: Methods for Strength Determination Using Reference Specimens; International Standard: Moscow, Russia, 2012.

32. GOST 24452-2023 Concretes: Methods of Prismatic Compressive Strength, Modulus of Elasticity, and Poisson’s Ratio Determination; Interstate Council for Standardization, Metrology and Certification: Moscow, Russia, 2023.