A novel approach to measure direct tensile strength on short-length cylindrical samples

A novel approach to measure direct tensile strength on short-length cylindrical samples | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A novel approach to measure direct tensile strength on short-length cylindrical samples M. Friedel, Y. Dong, H. Konietzky, A. Morgenstern, T. Wilsnack This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8337148/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract The determination of tensile strength via direct tensile tests sets special requirements to the sample geometry. Under certain circumstances these requirements cannot be fulfilled. The proposed new lab test approach allows to perform direct tensile tests on short-length cylindrical homogeneous samples, but especially on samples with interfaces. The proposed procedure is verified by numerical simulations. Validation is documented exemplary for a homogeneous sandstone sample and a composite sample with interface (salt rock and special concrete). direct tensile test tensile strength lab testing short-length cylindrical samples interface tensile strength composite materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Introduction Tensile strength is an important strength parameter in rock mechanics and rock engineering [1, 2]. The direct tensile test is the most accurate method to determine the tensile strength of rocks [3. 4]. Other methods, like for instance Brazilian tests [5–9] or 3-point-bending tests [10, 11], which are easier to perform and therefore more popular, deliver also tensile strength values, but they are not that accurate. They are mostly slightly higher and therefore not conservative. Direct tensile testing typically requires specially designed loading devices [12,13] to ensure stable force transmission and uniform stress distribution at the specimen ends, along with strict requirements on specimen dimensions [14]. Under some circumstances these demands cannot be fulfilled, for instance (a) the required sample length cannot be met (sample to short) or (b) the sample consists of two different materials along the long axis of the sample or (c) an interface or weak plane exist along the long axis. In these cases the new procedure described within this paper can be applied. 2. Equipment description The direct tensile testing apparatus employed for this study consists of an uniaxial tensile testing system supplemented by custom-designed metal clamps. The uniaxial tensile machine provides a precisely controlled axial tensile force, while the metal clamps (fixtures) ensure a uniform force transmission to the specimen throughout the loading process. The general test set-up in respect to the machine itself follows the ISRM suggested method [15] and ASTM [16], see also Perez-Rey et al. [17]. Figure 1 shows the used testing machine (a combined compression/tensile testing machine) with the following specifications for tensile tests: Tensile speed: adjustable within the range of 0.001-5 mm/min Maximum tensile force: 100 kN Measurement accuracy: ± 0.5% of full-scale range To overcome the specific limitations of the traditional direct tensile test method and to expand the test capabilities for certain sample constellations, a novel clamp (sampling holder) system is proposed as shown in Fig. 2 . The clamp system consists of two symmetrical metal clamps, each featuring a semi-circular groove to securely hold the cylindrical specimen. During loading, this design ensures stable and uniform tensile force transmission, effectively limiting strong local stress concentrations that could otherwise affect experimental accuracy. The semi-circular groove design not only minimizes potential specimen misalignment but also provides a large bonding (glue) area with identical adhesive tensile strength. The bonding strength of the glue (interface between rock sample and metal clamps) should be significantly higher than the rock strength. The inner radius of the metal clumps should be about 1 mm larger than those of the rock samples, which requires a thickness of the glue of 1 mm. The clamps are fabricated from high-strength alloy steel, selected for its superior mechanical properties and corrosion resistance. The key material specifications are as follows: Elastic modulus: E = 200 GPa (ensuring sufficient stiffness to minimize clamp deformation and its impact on test results) Yield strength: > 1000 MPa (preventing plastic deformation under maximum load conditions) Corrosion resistance: Suitable for various experimental environments, preventing degradation due to oxidation (corrosion) or impact by acids (a) (b) Photograph of metal clamps, (c) (d) Schematic of clamp design [mm] (a) Photograph, (b) Schematic [mm] The specimen dimensions (cores with 100 mm diameter) used for our system are illustrated in Fig. 3 . To ensure optimal bonding quality, the specimens are adhered to the metal clamps using a high-strength structural adhesive. The adhesive used must exhibit high bond strength, excellent durability, and negligible creep properties to prevent failure during testing. In this study, Hysol® 9466™ industrial grade epoxy adhesive was selected. Once mixed, the two component epoxy cures at room temperature to form a tough, off-white bondline which provides high peel resistance and high shear strength. The fully cured epoxy is resistant to a wide range of chemicals and solvents, and acts as an excellent electrical insulator. The Hysol® 9466™ glue has the following properties: Tensile strength: > 40 MPa Shear strength: > 25 MPa Curing time: 24–48 hours Operating temperature range: -40°C to + 150°C Young’s modulus: 3.2 GPa Shear modulus: 1.1 GPa After the bonding process, specimens are cured in a controlled temperature environment for at least 24 hours to ensure complete adhesive polymerization and development of maximum bond strength. Once cured, the specimen–clamp assembly is installed into the testing machine using ball-bearing mounted bolts, ensuring precise alignment of the loading direction with the specimen axis. This alignment is critical to eliminate bending or torsional loads. Upon test completion, to facilitate fixture reuse, the components with residual epoxy adhesive were placed in a controlled temperature furnace at 230°C for 3 hours to degrade the adhesive. The residue was then removed easily by non-abrasive manual scraping, ensuring no damage to the metal fixture surface, thereby providing contaminant-free interfacial contact surfaces for subsequent tests. 3. Numerical model To analyze the proposed testing scheme, 3-dimensional numerical simulations were conducted using FLAC 3D . The numerical model setup is shown in Fig. 4 , which includes sample, metal clumps, glue and optional a central material interface. To ensure an accurate representation of the experimental process, interface elements (INS) were introduced between the upper and lower clamps and the rock specimen to simulate the mechanical behavior of the bonding layer. Additionally, interface elements (INC) can be assigned optionally centric between two materials to simulate for instance a rock-concrete interface or to test a bonding material (see Fig. 4 ). For the clamps an isotropic elastic law was applied, because any kind of plastification or failure can be excluded. The elastic parameters correspond to the precisely defined material parameters of the metal clamps. For the tested material Mohr-Coulomb parameters were applied typical for salt rock, sandstone and a special concrete. The parameters for the interface representing the glue (INS) were taken according to the glue product data sheet (tensile strength and stiffness). Cohesion and friction at the interfaces are without relevance because the potential failure will be a pure tensile failure mode. At first numerical simulations were performed assuming an isotropic and homogeneous rock specimen (sandstone) without an interface and with a tensile strength of 1.6 MPa. The used parameters are shown in Table 1 . We duplicated the lab test procedure by applying the vertical loading velocity at the outer boundaries of the metal clamps and monitored the corresponding applied tensile force, the fracture evolution and identified the failure plane (tensile fracturing). Table 1 Material Parameters Specimen Parameters MgO-based Concrete Salt Rock Sandstone Young's Modulus (MPa) 30e3 20e3 30e3 Poisson's Ratio 0.30 0.25 0.30 Cohesion (MPa) 15 2.5 10 Friction angle (°) 40.0 37.0 30.0 Tensile strength (MPa) 2.0 2.0 1.6 Density (kg/m3) 2500 2160 2500 Interface Parameters INC INS Stiffness-Normal (N/m) 10e9* 1e12 Stiffness-Shear (N/m) 3e9* 0.3e12 Cohesion (MPa) 1.0* 10.0* Friction (°) 45.0* 45.0* Tensile strength (MPa) 1.0 1e9 Metal Clamp Parameters Young's Modulus (MPa) 210e3 Poisson's Ratio 0.28 Density (kg/m3) 7800 *Rough estimation (however, unimportant for the specific tests under consideration) 4. Validation for homogeneous material A well investigated sandstone was used to validate the proposed test procedure. This sandstone (Postaer Sandstone “Alte Post, Erste Bank”) has an uniaxial tensile strength (measured in classical direct tensile tests according to ISRM suggested methods (1978)) of 1.6 ± 0.6 MPa (47 samples). Figure 5 documents results according to the new proposed procedure. For isotropic and homogeneous sample it was observed that crack propagation initiates near to the clamps (see Fig. 7 ) producing a nearly horizontal fracture (see Fig. 5 ), primarily due to stress concentrations inside the rock near to the clamps. Figure 6 presents the force-displacement curves of three specimens up to tensile failure (see also Fig. 5 ). The peak (failure) loads are 17.64 kN for Sample A, 18.15 kN for Sample B, and 15.69 kN for Sample C. The corresponding tensile strength values, calculated by dividing peak force by fracture area, all fall within the previously mentioned range of 1.6 ± 0.6 MPa. This indicates that the results obtained by this study are consistent with previously reported mechanical properties of this sandstone. To investigate the behavior in more detail numerical simulations were performed. Due to symmetry conditions only the upper half of the experimental set-up was modelled to increase the computational speed. As shown later in Fig. 14 , the tensile stress distribution along the final tensile fracture plane is not homogeneous. Local peaks occur close to the clamps, which initiate the crack propagation already documented in Fig. 7 . This inhomogeneous stress distribution makes the determination of tensile strength less accurate. However, for practical applications and under consideration of the general scatter of rockmechanical data this level of accuracy may be sufficient. 5. Validation for composite material (material with interface) Exemplary, the tensile strength of the interface of a composite material (salt rock and MgO-based concrete) was determined. Figure 8 shows the sample before and after testing. Material parameters are given already in Table 1 . The numerical model for simulating the test contains an interface between the two materials. The interface tensile strength was determined by the new proposed test procedure and the numerical simulation is used to duplicate the lab test. The material interface has a much lower tensile strength compared with the two materials in contact. Therefore, the tensile failure develops along the interface as illustrated in detail by Fig. 8 (lab) and Fig. 9 (numerical model). The corresponding force-displacement curves of two lab tests are shown in Fig. 10 . By investigating the numerical simulation, it becomes obvious that the tensile stress distribution along the interface is nearly, but not absolutely perfect homogeneous (see Fig. 14 ). To investigate the tensile failure behavior in more detail the evolution of tensile stresses up to failure were analyzed by numerical simulations. For the intact homogeneous sample, due to the symmetry, only the upper half of the experimental set-up was modelled (see Fig. 7 and Fig. 11 ). Tests with central interface were modelled using the complete experimental set-up (see Fig. 4 and Fig. 9 ). The evolution of tensile stresses was monitored along line A (intact homogeneous sample) and line B (composite material with interface). These scanlines (see Fig. 11 ) mark the finale tensile fracture planes. Figure 12 and Fig. 13 illustrate the force-displacement curves for these two types of tests. Some points are marked in these figures, for which the stress profiles along the scanlines are illustrated in Fig. 14 . Figure 14 shows, that tensile stresses developing along a central weak plane (interface) are nearly perfect homogeneous in contrast to the homogeneous model, where peak stresses develop close to the clamps. The tensile strength of the interface can simply be calculated by dividing the peak force by the final fracture area. These results confirm that the proposed tensile test method provides a reliable approach for determining interface tensile strength in composite materials. However, prequisit is, that the interface tensile strength is significantly lower than the tensile strength of the two materials. Figure 14 documents also that the orientation of the maximum tensile stress along the scanline is vertical in agreement with the loading direction. Experimental and numerical results exhibit good agreement. Upon reaching peak stress, the force-displacement curves suddenly drop, indicating an abrupt failure when reaching the tensile strength (brittle failure mode). Table 2 summarizes the results. Table 2 Summary of results (lab test vs. numerical simulations) Sample data and measured values Salt rock - concrete Sample D Salt rock - concrete Sample E Diameter (mm) 100.64 99.33 Length (mm) 98.83 98.02 Interface Surface (mm²) 9946.25 9736.33 Aspect Ratio (L/D) 0.98 0.99 Fracture Surface Area (mm²) 9946.25 9736.33 Experimental Fracture Load (kN) 9.86 9.33 Simulated Fracture Load (kN) 9.94 9.69 Fracture Load Deviation (%) 0.8 3.7 Experimental Tensile Strength (MPa) Numerical Tensile Strength (MPa) 0.991 0.999 0.958 0.995 The results of lab tests and numerical simulations (see Table 2 ) for the composite material interface (salt rock and MgO-based concrete) reveal a high degree of consistency with deviation of only 0.8% and 3.7%, respectively. 7. Conclusions The proposed new test procedure is well suited to determine the direct tensile strength of interfaces located centric inside the sample, but allows also the determination of a lower bound (conservative value) for homogeneous materials. In both cases the measured peak load has to be divided by the final fracture area. The proposed method overcomes specific challenges associated with traditional direct tensile tests, such as demands on sample geometry by allowing testing on shorter samples and especially those with interfaces (composite materials of material with intrinsic interface). The procedure is verified and validated by experimental testing and numerical simulations, demonstrating its effectiveness and reliability. By appropriate design of the clamps also samples with other diameter can be used. The tests are easy to perform and the sample holder can be used repeatedly without bigger efford. Declarations Author Contribution M.F. and H.K. conceived the study and designed the overall research plan. Y.D. led the investigation, performed the experiments and numerical analyses, and wrote the first draft of the manuscript. A.M. contributed to the numerical simulations. T.W. assisted with the laboratory measurements. M.F., H.K., A.M. and T.W. reviewed and revised the manuscript. All authors read and approved the final manuscript. References Alzo’ubi AK, Martin CD, Cruden DM (2010) Influence of tensile strength on toppling failure in centrifuge tests. Int J Rock Mech Min Sci 47:974-982. https://doi.org/10.1016/j.ijrmms.2010.05.011 Liang Z, Xue R, Xu N, Dong L, Zhang Y (2020) Analysis on microseismic characteristics and stability of the access tunnel in the main powerhouse, Shuangjiangkou hydropower station, under high in situ stress. 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Int J Rock Mech Min Sci 115:21-32. https://doi.org/10.1016/j.ijrmms.2019.01.007 Liu J, Wu Y, Liu J, He Y, Shen X, Du Y, Sun B (2025) Acoustic emission evolution and fracture mechanism of rock for direct tensile failure. Int J Rock Mech Min Sci 185:105974. https://doi.org/10.1016/j.ijrmms.2024.105974 Liu J, Lyu C, Lu G, Shi X, Li H, Liang C, Deng C (2022) Evaluating a new method for direct testing of rock tensile strength. Int J Rock Mech Min Sci 160:105258. https://doi.org/10.1016/j.ijrmms.2022.105258 Aliha MRM, Ebneabbasi P, Karimi HR, Nikbakht E (2021) A novel test device for the direct measurement of tensile strength of rock using ring-shaped sample. Int J Rock Mech Min Sci 139:104649. https://doi.org/10.1016/j.ijrmms.2021.104649 ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15:99-103. https://doi.org/10.1016/0148-9062(78)90003-7 ASTM International (2020) Standard test method for direct tensile strength of intact rock core specimens (D2936-20). ASTM International, West Conshohocken Pérez-Rey I, Muñiz-Menéndez M, Frühwirt T, Konietzky H, Jacobsson L, Perras MA, Atefi-Monfared K, Mas Ivars D, Sánchez Juncal A, Alejano LR (2024) Assessment of direct tensile strength tests in rock through a multi-laboratory benchmark experiment. Rock Mech Rock Eng 57:3617-3634. https://doi.org/10.1007/s00603-023-03751-z Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 04 Mar, 2026 Reviews received at journal 21 Feb, 2026 Reviews received at journal 28 Jan, 2026 Reviewers agreed at journal 28 Jan, 2026 Reviewers agreed at journal 27 Jan, 2026 Reviews received at journal 13 Dec, 2025 Reviewers agreed at journal 13 Dec, 2025 Reviewers agreed at journal 12 Dec, 2025 Reviewers invited by journal 12 Dec, 2025 Editor assigned by journal 12 Dec, 2025 Submission checks completed at journal 12 Dec, 2025 First submitted to journal 11 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8337148","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":560035525,"identity":"f5fde28e-760b-4665-b627-aa2c29312a24","order_by":0,"name":"M. 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1","display":"","copyAsset":false,"role":"figure","size":634325,"visible":true,"origin":"","legend":"\u003cp\u003eCompression/tensile testing machine TIRAtest-2800\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/1234e6645322d1ef41ab2b24.png"},{"id":98451161,"identity":"c56468e6-7066-49e8-b2f1-0bb081b18192","added_by":"auto","created_at":"2025-12-17 17:31:53","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":384832,"visible":true,"origin":"","legend":"\u003cp\u003eMetal clamps\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/d58a3afa1b4303ae4c71fe1f.png"},{"id":98450993,"identity":"2cbe1b05-e06d-48c5-8698-361f386d2a1e","added_by":"auto","created_at":"2025-12-17 17:31:09","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":361871,"visible":true,"origin":"","legend":"\u003cp\u003eThree-dimensional representation of specimen inside clamp system\u003c/p\u003e\n\u003cp\u003e(a) Photograph, (b) Schematic [mm]\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/c231420ce5b26558458b7caf.png"},{"id":98622587,"identity":"6c2ea16d-2926-44a8-a8a1-305f023e2e36","added_by":"auto","created_at":"2025-12-19 16:58:36","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":242144,"visible":true,"origin":"","legend":"\u003cp\u003eNumerical model setup incl. mesh\u003c/p\u003e\n\u003cp\u003e(a) Clumps incl. test material (b) Metal clamps\u003c/p\u003e\n\u003cp\u003e(c) Test material with interface (d) Interfaces representing glue and potential material interface\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/15bd93d4547693f64b3a43f9.png"},{"id":98451087,"identity":"e5cd0d8d-7ee6-4020-8e28-e7ca439bb141","added_by":"auto","created_at":"2025-12-17 17:31:34","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":574851,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSandstone sample before (a) and after (b) - (d) direct tensile tests\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/a5079386056ea444e62f7717.png"},{"id":98451076,"identity":"3de3835e-2dca-4976-901a-6e77b6aafeb4","added_by":"auto","created_at":"2025-12-17 17:31:27","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":93842,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eForce-displacement curves of sandstone samples obtained by lab test (see Fig. 5)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/e99ffbf6b4a95d1d4ef96e32.png"},{"id":98451100,"identity":"a9934b72-6e81-4720-b7f8-07653f704a7d","added_by":"auto","created_at":"2025-12-17 17:31:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":394843,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEvolution and spatial distribution of fracture evolution (tensile failure) for selected loading stages\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/5775733d7917f20152f66e6c.png"},{"id":98451122,"identity":"8c4fa252-8428-4324-b4c1-945d4e8cfa37","added_by":"auto","created_at":"2025-12-17 17:31:40","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":865276,"visible":true,"origin":"","legend":"\u003cp\u003eComposite sample (MgO-based concrete and salt rock) before (left) and after (right) direct tensile test (sample D, see also Tab. 2)\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/f7f7c87fc19663af4098d6f6.png"},{"id":98451129,"identity":"65f9d0fc-2ebc-419c-b1db-29df64c7a6b9","added_by":"auto","created_at":"2025-12-17 17:31:42","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":343647,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacementmagnitude [m] (left) and contact state (right) of the interfaces at the point in time of sample failure (sample D)\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/fc68da5a4cd47c894838a5ef.png"},{"id":98450990,"identity":"dccdb1cb-dee7-4cf4-b9b6-fc1e528f3ce5","added_by":"auto","created_at":"2025-12-17 17:31:09","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":91081,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eForce-displacementcurve obtained by lab tests for rock-concrete sample\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/1319a8a0e6888f0a8c2ec95a.png"},{"id":98451112,"identity":"59c1fe64-266a-4162-bdd5-156b528e1ba7","added_by":"auto","created_at":"2025-12-17 17:31:39","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":283152,"visible":true,"origin":"","legend":"\u003cp\u003eNumerical model with indication of scanlines used in Fig. 14\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/dfbda1067346a7f4db9149cb.png"},{"id":98451110,"identity":"4516c728-ff92-41f5-94ad-0179799a6579","added_by":"auto","created_at":"2025-12-17 17:31:39","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":97193,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eForce-displacement curves with four marked loading stages (T1-T4) obtained by numerical simulation (homogeneous materials)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/a30657716532b5f6d318eccc.png"},{"id":98451099,"identity":"aa3a3468-86b5-4c0d-aa7a-b296eea246e5","added_by":"auto","created_at":"2025-12-17 17:31:36","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":88138,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eForce-displacement curves with four marked loading stages (T1-T4) obtained by numerical simulation (composite materials)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/dd3ddc5afffd652d5a0e4791.png"},{"id":98451089,"identity":"b6a85255-1c94-4129-b452-92e0a4fe0a38","added_by":"auto","created_at":"2025-12-17 17:31:34","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":137395,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eVertical stress component (a) and maximum tensile stress (b) along scanline A for homogeneous material and scanline B for composite material (see Fig. 11)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/f88b9a065d9f8b86d23fe0a4.png"},{"id":98631328,"identity":"95bd939a-51a6-49b8-8b44-2f69f21b4a8b","added_by":"auto","created_at":"2025-12-19 17:19:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6133471,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8337148/v1/28ed336c-7d05-4f0c-87f8-33fef8358cc5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A novel approach to measure direct tensile strength on short-length cylindrical samples","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eTensile strength is an important strength parameter in rock mechanics and rock engineering [1, 2]. The direct tensile test is the most accurate method to determine the tensile strength of rocks [3. 4]. Other methods, like for instance Brazilian tests [5\u0026ndash;9] or 3-point-bending tests [10, 11], which are easier to perform and therefore more popular, deliver also tensile strength values, but they are not that accurate. They are mostly slightly higher and therefore not conservative. Direct tensile testing typically requires specially designed loading devices [12,13] to ensure stable force transmission and uniform stress distribution at the specimen ends, along with strict requirements on specimen dimensions [14]. Under some circumstances these demands cannot be fulfilled, for instance (a) the required sample length cannot be met (sample to short) or (b) the sample consists of two different materials along the long axis of the sample or (c) an interface or weak plane exist along the long axis. In these cases the new procedure described within this paper can be applied.\u003c/p\u003e"},{"header":"2. Equipment description","content":"\u003cp\u003eThe direct tensile testing apparatus employed for this study consists of an uniaxial tensile testing system supplemented by custom-designed metal clamps. The uniaxial tensile machine provides a precisely controlled axial tensile force, while the metal clamps (fixtures) ensure a uniform force transmission to the specimen throughout the loading process. The general test set-up in respect to the machine itself follows the ISRM suggested method [15] and ASTM [16], see also Perez-Rey et al. [17].\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the used testing machine (a combined compression/tensile testing machine) with the following specifications for tensile tests:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTensile speed: adjustable within the range of 0.001-5 mm/min\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMaximum tensile force: 100 kN\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMeasurement accuracy: \u0026plusmn; 0.5% of full-scale range\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eTo overcome the specific limitations of the traditional direct tensile test method and to expand the test capabilities for certain sample constellations, a novel clamp (sampling holder) system is proposed as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The clamp system consists of two symmetrical metal clamps, each featuring a semi-circular groove to securely hold the cylindrical specimen. During loading, this design ensures stable and uniform tensile force transmission, effectively limiting strong local stress concentrations that could otherwise affect experimental accuracy. The semi-circular groove design not only minimizes potential specimen misalignment but also provides a large bonding (glue) area with identical adhesive tensile strength. The bonding strength of the glue (interface between rock sample and metal clamps) should be significantly higher than the rock strength. The inner radius of the metal clumps should be about 1 mm larger than those of the rock samples, which requires a thickness of the glue of 1 mm.\u003c/p\u003e \u003cp\u003eThe clamps are fabricated from high-strength alloy steel, selected for its superior mechanical properties and corrosion resistance. The key material specifications are as follows:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eElastic modulus: E\u0026thinsp;=\u0026thinsp;200 GPa (ensuring sufficient stiffness to minimize clamp deformation and its impact on test results)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eYield strength: \u0026gt; 1000 MPa (preventing plastic deformation under maximum load conditions)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eCorrosion resistance: Suitable for various experimental environments, preventing degradation due to oxidation (corrosion) or impact by acids\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(a) (b) Photograph of metal clamps, (c) (d) Schematic of clamp design [mm]\u003c/p\u003e\u003cp\u003e(a) Photograph, (b) Schematic [mm]\u003c/p\u003e \u003cp\u003eThe specimen dimensions (cores with 100 mm diameter) used for our system are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. To ensure optimal bonding quality, the specimens are adhered to the metal clamps using a high-strength structural adhesive. The adhesive used must exhibit high bond strength, excellent durability, and negligible creep properties to prevent failure during testing. In this study, Hysol\u0026reg; 9466\u0026trade; industrial grade epoxy adhesive was selected. Once mixed, the two component epoxy cures at room temperature to form a tough, off-white bondline which provides high peel resistance and high shear strength. The fully cured epoxy is resistant to a wide range of chemicals and solvents, and acts as an excellent electrical insulator. The Hysol\u0026reg; 9466\u0026trade; glue has the following properties:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTensile strength: \u0026gt; 40 MPa\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eShear strength: \u0026gt; 25 MPa\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eCuring time: 24\u0026ndash;48 hours\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eOperating temperature range: -40\u0026deg;C to +\u0026thinsp;150\u0026deg;C\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eYoung\u0026rsquo;s modulus: 3.2 GPa\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eShear modulus: 1.1 GPa\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eAfter the bonding process, specimens are cured in a controlled temperature environment for at least 24 hours to ensure complete adhesive polymerization and development of maximum bond strength. Once cured, the specimen\u0026ndash;clamp assembly is installed into the testing machine using ball-bearing mounted bolts, ensuring precise alignment of the loading direction with the specimen axis. This alignment is critical to eliminate bending or torsional loads.\u003c/p\u003e \u003cp\u003eUpon test completion, to facilitate fixture reuse, the components with residual epoxy adhesive were placed in a controlled temperature furnace at 230\u0026deg;C for 3 hours to degrade the adhesive. The residue was then removed easily by non-abrasive manual scraping, ensuring no damage to the metal fixture surface, thereby providing contaminant-free interfacial contact surfaces for subsequent tests.\u003c/p\u003e"},{"header":"3. Numerical model","content":"\u003cp\u003eTo analyze the proposed testing scheme, 3-dimensional numerical simulations were conducted using FLAC\u003csup\u003e3D\u003c/sup\u003e. The numerical model setup is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which includes sample, metal clumps, glue and optional a central material interface. To ensure an accurate representation of the experimental process, interface elements (INS) were introduced between the upper and lower clamps and the rock specimen to simulate the mechanical behavior of the bonding layer. Additionally, interface elements (INC) can be assigned optionally centric between two materials to simulate for instance a rock-concrete interface or to test a bonding material (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFor the clamps an isotropic elastic law was applied, because any kind of plastification or failure can be excluded. The elastic parameters correspond to the precisely defined material parameters of the metal clamps. For the tested material Mohr-Coulomb parameters were applied typical for salt rock, sandstone and a special concrete. The parameters for the interface representing the glue (INS) were taken according to the glue product data sheet (tensile strength and stiffness). Cohesion and friction at the interfaces are without relevance because the potential failure will be a pure tensile failure mode.\u003c/p\u003e \u003cp\u003eAt first numerical simulations were performed assuming an isotropic and homogeneous rock specimen (sandstone) without an interface and with a tensile strength of 1.6 MPa. The used parameters are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. We duplicated the lab test procedure by applying the vertical loading velocity at the outer boundaries of the metal clamps and monitored the corresponding applied tensile force, the fracture evolution and identified the failure plane (tensile fracturing).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial Parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eSpecimen Parameters\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMgO-based\u003c/p\u003e \u003cp\u003eConcrete\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSalt Rock\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSandstone\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYoung's Modulus (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePoisson's Ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCohesion (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFriction angle (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e37.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTensile strength (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDensity (kg/m3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInterface Parameters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eINC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eINS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStiffness-Normal (N/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10e9*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStiffness-Shear (N/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3e9*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCohesion (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.0*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10.0*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFriction (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45.0*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e45.0*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTensile strength (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eMetal Clamp Parameters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYoung's Modulus (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e210e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePoisson's Ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDensity (kg/m3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e*Rough estimation (however, unimportant for the specific tests under consideration)\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4. Validation for homogeneous material","content":"\u003cp\u003eA well investigated sandstone was used to validate the proposed test procedure. This sandstone (Postaer Sandstone \u0026ldquo;Alte Post, Erste Bank\u0026rdquo;) has an uniaxial tensile strength (measured in classical direct tensile tests according to ISRM suggested methods (1978)) of 1.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.6 MPa (47 samples). Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e documents results according to the new proposed procedure.\u003c/p\u003e \u003cp\u003eFor isotropic and homogeneous sample it was observed that crack propagation initiates near to the clamps (see Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) producing a nearly horizontal fracture (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), primarily due to stress concentrations inside the rock near to the clamps. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents the force-displacement curves of three specimens up to tensile failure (see also Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). The peak (failure) loads are 17.64 kN for Sample A, 18.15 kN for Sample B, and 15.69 kN for Sample C. The corresponding tensile strength values, calculated by dividing peak force by fracture area, all fall within the previously mentioned range of 1.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.6 MPa. This indicates that the results obtained by this study are consistent with previously reported mechanical properties of this sandstone.\u003c/p\u003e \u003cp\u003eTo investigate the behavior in more detail numerical simulations were performed. Due to symmetry conditions only the upper half of the experimental set-up was modelled to increase the computational speed.\u003c/p\u003e\u003cp\u003eAs shown later in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e, the tensile stress distribution along the final tensile fracture plane is not homogeneous. Local peaks occur close to the clamps, which initiate the crack propagation already documented in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. This inhomogeneous stress distribution makes the determination of tensile strength less accurate. However, for practical applications and under consideration of the general scatter of rockmechanical data this level of accuracy may be sufficient.\u003c/p\u003e"},{"header":"5. Validation for composite material (material with interface)","content":"\u003cp\u003eExemplary, the tensile strength of the interface of a composite material (salt rock and MgO-based concrete) was determined. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the sample before and after testing. Material parameters are given already in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The numerical model for simulating the test contains an interface between the two materials. The interface tensile strength was determined by the new proposed test procedure and the numerical simulation is used to duplicate the lab test. The material interface has a much lower tensile strength compared with the two materials in contact. Therefore, the tensile failure develops along the interface as illustrated in detail by Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e (lab) and Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (numerical model). The corresponding force-displacement curves of two lab tests are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. By investigating the numerical simulation, it becomes obvious that the tensile stress distribution along the interface is nearly, but not absolutely perfect homogeneous (see Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTo investigate the tensile failure behavior in more detail the evolution of tensile stresses up to failure were analyzed by numerical simulations. For the intact homogeneous sample, due to the symmetry, only the upper half of the experimental set-up was modelled (see Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e). Tests with central interface were modelled using the complete experimental set-up (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e). The evolution of tensile stresses was monitored along line A (intact homogeneous sample) and line B (composite material with interface). These scanlines (see Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e) mark the finale tensile fracture planes. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e illustrate the force-displacement curves for these two types of tests. Some points are marked in these figures, for which the stress profiles along the scanlines are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows, that tensile stresses developing along a central weak plane (interface) are nearly perfect homogeneous in contrast to the homogeneous model, where peak stresses develop close to the clamps. The tensile strength of the interface can simply be calculated by dividing the peak force by the final fracture area.\u003c/p\u003e \u003cp\u003eThese results confirm that the proposed tensile test method provides a reliable approach for determining interface tensile strength in composite materials. However, prequisit is, that the interface tensile strength is significantly lower than the tensile strength of the two materials. Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e documents also that the orientation of the maximum tensile stress along the scanline is vertical in agreement with the loading direction.\u003c/p\u003e \u003cp\u003eExperimental and numerical results exhibit good agreement. Upon reaching peak stress, the force-displacement curves suddenly drop, indicating an abrupt failure when reaching the tensile strength (brittle failure mode). Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes the results.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of results (lab test vs. numerical simulations)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample data\u003c/p\u003e \u003cp\u003eand\u003c/p\u003e \u003cp\u003emeasured values\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSalt rock - concrete\u003c/p\u003e \u003cp\u003eSample D\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSalt rock - concrete\u003c/p\u003e \u003cp\u003eSample E\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiameter (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e99.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLength (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e98.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e98.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInterface Surface (mm\u0026sup2;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9946.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9736.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAspect Ratio (L/D)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFracture Surface Area (mm\u0026sup2;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9946.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9736.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperimental Fracture Load (kN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimulated Fracture Load (kN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFracture Load Deviation (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperimental Tensile Strength (MPa)\u003c/p\u003e \u003cp\u003eNumerical Tensile Strength (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.991\u003c/p\u003e \u003cp\u003e0.999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.958\u003c/p\u003e \u003cp\u003e0.995\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe results of lab tests and numerical simulations (see Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) for the composite material interface (salt rock and MgO-based concrete) reveal a high degree of consistency with deviation of only 0.8% and 3.7%, respectively.\u003c/p\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eThe proposed new test procedure is well suited to determine the direct tensile strength of interfaces located centric inside the sample, but allows also the determination of a lower bound (conservative value) for homogeneous materials. In both cases the measured peak load has to be divided by the final fracture area.\u003c/p\u003e \u003cp\u003eThe proposed method overcomes specific challenges associated with traditional direct tensile tests, such as demands on sample geometry by allowing testing on shorter samples and especially those with interfaces (composite materials of material with intrinsic interface). The procedure is verified and validated by experimental testing and numerical simulations, demonstrating its effectiveness and reliability. By appropriate design of the clamps also samples with other diameter can be used. The tests are easy to perform and the sample holder can be used repeatedly without bigger efford.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eM.F. and H.K. conceived the study and designed the overall research plan. Y.D. led the investigation, performed the experiments and numerical analyses, and wrote the first draft of the manuscript. A.M. contributed to the numerical simulations. T.W. assisted with the laboratory measurements. M.F., H.K., A.M. and T.W. reviewed and revised the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlzo\u0026rsquo;ubi AK, Martin CD, Cruden DM (2010) Influence of tensile strength on toppling failure in centrifuge tests. Int J Rock Mech Min Sci 47:974-982. https://doi.org/10.1016/j.ijrmms.2010.05.011\u003c/li\u003e\n\u003cli\u003eLiang Z, Xue R, Xu N, Dong L, Zhang Y (2020) Analysis on microseismic characteristics and stability of the access tunnel in the main powerhouse, Shuangjiangkou hydropower station, under high in situ stress. Bull Eng Geol Environ 79:3231-3244. https://doi.org/10.1007/s10064-020-01738-6\u003c/li\u003e\n\u003cli\u003eGraue B, Siegesmund S, Middendorf B (2011) Quality assessment of replacement stones for the Cologne Cathedral: mineralogical and petrophysical requirements. Environ Earth Sci 63:1799-1822. https://doi.org/10.1007/s12665-011-1077-x\u003c/li\u003e\n\u003cli\u003eKlanphumeesri S (2010) Direct tension testing of rock specimens. Master of Engineering thesis, Suranaree University of Technology, Nakhon Ratchasima\u003c/li\u003e\n\u003cli\u003eTavallali A, Vervoort A (2010) Failure of layered sandstone under Brazilian test conditions: effect of micro-scale parameters on macro-scale behaviour. Rock Mech Rock Eng 43:641-653. https://doi.org/10.1007/s00603-010-0084-7\u003c/li\u003e\n\u003cli\u003eMarkides CF, Pazis DN, Kourkoulis SK (2012) The Brazilian disc under non-uniform distribution of radial pressure and friction. Int J Rock Mech Min Sci 50:47-55. https://doi.org/10.1016/j.ijrmms.2011.12.012\u003c/li\u003e\n\u003cli\u003eErarslan N, Williams DJ (2012) Experimental, numerical and analytical studies on tensile strength of rocks. Int J Rock Mech Min Sci 49:21-30. https://doi.org/10.1016/j.ijrmms.2011.11.007\u003c/li\u003e\n\u003cli\u003eLi D, Wong LNY (2013) The Brazilian disc test for rock mechanics applications: review and new insights. Rock Mech Rock Eng 46:269-287. https://doi.org/10.1007/s00603-012-0257-7\u003c/li\u003e\n\u003cli\u003eDan DQ, Konietzky H, Herbst M (2013) Brazilian tensile strength tests on some anisotropic rocks. Int J Rock Mech Min Sci 58:1-7. https://doi.org/10.1016/j.ijrmms.2012.08.010\u003c/li\u003e\n\u003cli\u003eLoukil M, Hassine WB, Limam O, Kotronis P (2019) Experimental determination of GFRC tensile parameters from three-point bending tests using an analytical damage model. Constr Build Mater 223:477-490. https://doi.org/10.1016/j.conbuildmat.2019.07.005\u003c/li\u003e\n\u003cli\u003eLiao Z, Zhu J, Tang C (2019) Numerical investigation of rock tensile strength determined by direct tension, Brazilian and three-point bending tests. Int J Rock Mech Min Sci 115:21-32. https://doi.org/10.1016/j.ijrmms.2019.01.007\u003c/li\u003e\n\u003cli\u003eLiu J, Wu Y, Liu J, He Y, Shen X, Du Y, Sun B (2025) Acoustic emission evolution and fracture mechanism of rock for direct tensile failure. Int J Rock Mech Min Sci 185:105974. https://doi.org/10.1016/j.ijrmms.2024.105974\u003c/li\u003e\n\u003cli\u003eLiu J, Lyu C, Lu G, Shi X, Li H, Liang C, Deng C (2022) Evaluating a new method for direct testing of rock tensile strength. Int J Rock Mech Min Sci 160:105258. https://doi.org/10.1016/j.ijrmms.2022.105258\u003c/li\u003e\n\u003cli\u003eAliha MRM, Ebneabbasi P, Karimi HR, Nikbakht E (2021) A novel test device for the direct measurement of tensile strength of rock using ring-shaped sample. Int J Rock Mech Min Sci 139:104649. https://doi.org/10.1016/j.ijrmms.2021.104649\u003c/li\u003e\n\u003cli\u003eISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15:99-103. https://doi.org/10.1016/0148-9062(78)90003-7\u003c/li\u003e\n\u003cli\u003eASTM International (2020) Standard test method for direct tensile strength of intact rock core specimens (D2936-20). ASTM International, West Conshohocken\u003c/li\u003e\n\u003cli\u003eP\u0026eacute;rez-Rey I, Mu\u0026ntilde;iz-Men\u0026eacute;ndez M, Fr\u0026uuml;hwirt T, Konietzky H, Jacobsson L, Perras MA, Atefi-Monfared K, Mas Ivars D, S\u0026aacute;nchez Juncal A, Alejano LR (2024) Assessment of direct tensile strength tests in rock through a multi-laboratory benchmark experiment. Rock Mech Rock Eng 57:3617-3634. https://doi.org/10.1007/s00603-023-03751-z\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"geoenergy-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [GeoEnergy Communications](https://link.springer.com/journal/44421)","snPcode":"44421","submissionUrl":"https://submission.springernature.com/new-submission/44421/3","title":"GeoEnergy Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"direct tensile test, tensile strength, lab testing, short-length cylindrical samples, interface tensile strength, composite materials","lastPublishedDoi":"10.21203/rs.3.rs-8337148/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8337148/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe determination of tensile strength via direct tensile tests sets special requirements to the sample geometry. Under certain circumstances these requirements cannot be fulfilled. The proposed new lab test approach allows to perform direct tensile tests on short-length cylindrical homogeneous samples, but especially on samples with interfaces. The proposed procedure is verified by numerical simulations. Validation is documented exemplary for a homogeneous sandstone sample and a composite sample with interface (salt rock and special concrete).\u003c/p\u003e","manuscriptTitle":"A novel approach to measure direct tensile strength on short-length cylindrical samples","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-17 17:10:00","doi":"10.21203/rs.3.rs-8337148/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-05T03:02:04+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-21T11:51:37+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-28T08:08:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"167102521886896618051133481422851767128","date":"2026-01-28T08:01:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"73579773326912659625530300082698568047","date":"2026-01-27T08:39:20+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-14T04:21:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"232043882929599892557054629548389871202","date":"2025-12-14T03:17:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"311465230755416171895075583664764080040","date":"2025-12-12T09:22:21+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-12T07:08:32+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-12T05:36:14+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-12T05:32:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"GeoEnergy Communications","date":"2025-12-11T13:06:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"geoenergy-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [GeoEnergy Communications](https://link.springer.com/journal/44421)","snPcode":"44421","submissionUrl":"https://submission.springernature.com/new-submission/44421/3","title":"GeoEnergy Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c1b03ec3-d4d1-4df5-bc52-2a87b56cc665","owner":[],"postedDate":"December 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-19T11:25:05+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-17 17:10:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8337148","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8337148","identity":"rs-8337148","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}