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The tensile strength of a bolt represents its capacity to endure stress and pressure. In simpler words, it indicates the maximum force a bolt can bear without failing. High-tensile bolt grades are capable of withstanding more significant impacts, making them suitable for demanding tasks, such as supporting industrial machinery or securing heavy objects securely. This should not be confused with yield strength, which is the amount of tensile strength at which specific permanent deformation happens.
The tensile strength of bolts varies depending on their grade or material composition. High-tensile bolt grades refer to bolts designed to withstand heavy loads and extreme conditions. These bolts are typically made from alloy steels and undergo specific heat treatments and manufacturing processes to enhance their strength.
Bolt head styles reflect the bolt&#;s intended function while enabling the installation tool to grip the head. The different types of bolt heads include:
For a closer look at bolt heads, check out our guide, What are the Different Types of Nuts and Bolts?
Bolt grades, which indicate the strength of your fastener, are determined by the standard the bolt adheres to. There are three primary standards. Understanding bolt grades is critical to choosing the right one. Typically, identification markings on bolt heads include the grade and the manufacturer&#;s mark. Bolt grade markings are indicated by raised dashes or numbers.
You&#;ll also need to consider nuts and washers. To learn more about all of these fasteners and view bolt grade charts, see our guide, What Are the Different Types of Nuts and Bolts?
How to read bolt grades: there are three primary standards used worldwide, along with their bolt grade markings. The markings will tell you at a glance bolt strengths and grades.
Again, we refer you to our guide, which gives visual examples of each of the standards: What Are the Different Types of Nuts and Bolts?
The first standard is SAE, which stands for the Society of Automotive Engineers. SAE bolt head markings use a series of raised dashes, or radial lines, to communicate strength.
Typical applications of SAE bolt grades include:
Grade 2Low- to medium-strength carbon steel bolts used for non-critical joints:
Medium carbon steel bolts used when more strength is needed than offered by Grade 2:
High-tensile strength bolts used when superior strength and reliability are needed:
The American Society for Testing and Materials (ASTM) indicates bolt grades by the letter A and three numbers on the bolt head.
A quick word about ASTM A325 grade: ASTM A325 bolts have been withdrawn as a standard specification. It was a specification for structural bolts that were commonly used in heavy construction applications. However, the ASTM F/FM standard has replaced the previous ASTM A325 specification. The new standard incorporates several bolt types, including the high-strength structural bolt previously covered by ASTM A325.
The change was made to align with the International Organization for Standardization (ISO) standards and to create a harmonized global standard for structural bolts. The new standard, ASTM F/FM, includes several grades and types of bolts, including the high-strength structural bolt now designated as "A325."
Therefore, while the specific ASTM A325 standard has been withdrawn, the high-strength structural bolt that was covered by that standard is still available under the ASTM F/FM standard as the "A325" bolt type. The designation ASTM A325 is still used in common vernacular.
It&#;s worth noting the difference between SAE and ASTM bolt grades: ASTM A325 bolts are more often specified by engineers for structural steel connections on heavy construction projects. SAE Grade 5 bolts are favored in OEM applications. That doesn&#;t mean there isn&#;t any crossover.
Grade A307Low- to medium-strength carbon steel bolts used for non-critical joints:
Ensures the integrity and safety of structural connections:
Covers the mechanical requirements for alloy steel bolts, studs, & other externally threaded fasteners:
Metric bolt grades are known as &#;property class,&#; and are set by the International Standards Organization (ISO). This system uses two numbers separated by a dot expressed in raised or depressed numbers either on the top or side of the bolt head. The higher the ISO numbers, the stronger the bolt.
Stainless steel bolt grades refer to the grade of stainless steel to make bolts. Stainless steel bolt strength grades are typically made of 304, 316 or 410 stainless steel. They&#;re bolt heads are marked as either A2 or A4.
Commonly used high-tensile bolt grade include the following applications:
Even stronger than grade 8.8:
This high-tensile bolt grade can handle all of the above, plus:
304 stainless steel bolts are used for:
316 stainless steel bolts are typically used in:
Free CADs are available for most solutions, which you can download. You can also request free samples to make sure you&#;ve chosen the right product for what you need.
If you&#;re not quite sure which solution will work best for your application, our experts are always happy to advise you.
You can also read our guides, How to Prevent Loose Bolts and How to Measure Bolt Size.
Whatever your requirements, you can depend on fast dispatch. Request your free samples or download free CADs now.
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The application of cable bolts was first introduced in the s as part of a temporary support system [ 1 ]. Due to the large demands of societal growth, the need for deep mining excavation has exceeded the technological and testing capabilities to facilitate a safe mining procedure. Civil tunnelling methods have ultimately been incorporated into deep mining excavations; thus, cable bolts are considered as a critical permanent support element [ 2 ]. Cable bolts are an effective method to provide reinforcement for the rock mass combined with a face support such as shotcrete and steel meshing [ 3 4 ]. A cable bolt is a flexible steel tendon made up of twisted steel wires that are inserted within a duct and anchored by a plate to the rock surface [ 5 ]. They are often used in conjunction with a pre-stressing and grouting system to provide additional tensile forces and have been used as the primary reinforcement method for deep mining excavation. Whilst there are many factors that contribute to the overall strength of the combined support system, the cable bolt is notably of greater influence when considering the reinforcement of the rock capacity [ 6 ]. Tahmasebinia et al. () [ 5 ] stated that whilst cable bolts are an effective method for reinforcement, there is much that is unknown about the nature of cable bolts subject to dynamic loading. This is due to the inaccessibility and restrictions of deep mining in situ testing and drop testing methods failing to capture in situ conditions. Bolts under static loading are well understood; however, in deep mining excavations, the presence of rock bursts induces sudden dynamic loading conditions and presents an additional potential failure mechanism. Therefore, it is important to understand cable bolt behaviour under dynamic loading conditions. This study conducted a parametric test examining the shear force, displacement and energy absorption capacity of a cable bolt subjected to loading through a double shear test using Finite Element Analysis (FEA) and the Finite Element Modelling (FEM) software ABAQUS/Explicit. As a relatively unexplored field of study, the insights obtained from this study will significantly improve industrial understanding of cable bolt behaviour under static loading. The goal of the study was to test and draw valuable conclusions about the influence of various parameters when subject to a static and dynamic load. The development of the model is detailed with explanations for each design criterion that was required in developing this model. Considerations of various design parameters are discussed, followed by a summary of the results of the testing according to each parameter. A discussion is provided to examine the fundamental implications of the results and its consistency with current literature. This compares experimental data against existing literature and experimental results. Finally, a discussion of the limitations of the testing is undertaken and final conclusions and recommendations for further investigation are presented.
Since the introduction of these analysis types, numerical analysis has become extremely popular due to its advantages of being cost-efficient and flexible, as it does not require specific testing facilities to carry out. Furthermore, as it is not a destructive form of testing, unlike blast, drop and the double shear tests, it is a safe methodology that can be easily repeated. However, numerical analysis results are only valid if verified using analytical and experimental data. Furthermore, similar to laboratory tests, numerical analysis is forced to make assumptions to produce accurate results, and thus it struggles to account for the in situ stresses of rock and the exact loading pattern of rock burst loading [ 8 ].
Numerical analysis has been utilised in studying and developing rock burst support systems since the s. In , the first finite different method model was developed to simulate the elastic pulse propagation problem in the Split Hopkinson pressure bar technique [ 39 ]. In the same year, Blake () [ 40 ] utilised finite element analysis to study and model pillar bursts, allowing him to predict probable rock burst locations. In , the first boundary element method was carried out to propose the complete plane strain concept and used to study pillar bursts [ 41 ]. Since the introduction of multiple different numerical methods, numerical approaches have been classified into three approaches, namely continuum, discontinuum and the hybrid approach [ 42 ]. Due to the complexity regarding rock burst phenomena, Wang et al. () [ 8 ] stressed the importance of selecting the correct numerical analysis methodology to achieve accurate results, where the specific engineering problem should define the numerical method selected. Thus, Wang et al. () [ 8 ] summarised the strengths and weaknesses of each numerical methodology, which has been adapted below in Table 1
The concrete blocks represent rock planes found in excavations, where the boundary blocks are fixed and a static load is applied to the middle block, applying a shear load to reinforcement bolts. Double shear tests can also conduct dynamic testing, where an impact load is applied to the centre block, such that the momentum of the applied load transfers the energy through the concrete block to the bolt under investigation. Like the drop test, the double shear test offers the opportunity to obtain repeatable results, and thus excels for quality control and comparative testing. Although it cannot accurately represent in situ conditions like blast testing, it can account for rock fault lines and thus is widely accepted as a rock and cable bolt shear test.
Another form of experimental testing is single or double shear test, which is used to replicate rock bolt shear strength in jointed rock masses. Although single shear tests are cheaper due to less operation and set-up costs, double shear tests are more reliable as they avoid utilising asymmetric loading [ 38 ]. Double shear tests can be arranged in varying ways; however, a typical set-up involves three concrete blocks reinforced with full grouted rock bolts that can be positioned in varying angles [ 38 ].
The WASM Dynamic Testing Facility was developed in Western Australia and involves dropping integrated rock mass and supporting elements on buffers to generate momentum energy transfer; Ref. [ 37 ] verified that it can be utilised to determine the energy absorption capacity of support elements. The WASM Testing rig is well instrumented as it is equipped with load cells, motion sensors and high-speed digital video cameras utilised for post processing. Due to its ability to test reinforcement and support systems unified, the WASM Testing facility is very active and used in the more recent publications [ 35 ].
The CANMET Drop Test Facility was developed in Canada, which functions by dropping a hammer, that can have a weight of up to three tonnes, from a height of two metres onto the test element, directly applying a dynamic load [ 36 ]. The testing rig can dynamically input up to 60 kJ of energy, and thus is used by suppliers to test existing and experiment new products dynamically.
The SRK Drop Weight Test Facility was developed to determine surface support dynamic loading capacities in South African mines, with the capability of inputting 70 kJ of energy [ 35 ]. The advantages of this facility include its relatively inexpensive set-up cost and its ability to undergo consistent and repeatable tests due to its configuration. However, after further analysis, it was concluded that transmission losses of up to 50% input energy occurred [ 36 ]. The facility is no longer in operation.
The drop test is another dynamic experimental test method, which simulates dynamic loading patterns by dropping a known mass (with controlled drop speed and height) onto the support elements under testing [ 13 ] In general, drop tests are relatively simple to perform, provide the opportunity to obtain repeatable results and are suitable for quality control and comparative testing. However, impact and direct loading do not represent the true nature of rock burst loading. The lateral continuity of reinforcement support cannot be appropriately represented and in situ stresses that occur in burst-prone grounds cannot be accounted for accurately [ 11 ]. Globally, many different drop test facilities exist which all employ varying dynamic loading mechanisms.
This test is extremely limited due to being a destructive form of testing that requires vacant excavation walls that will become redundant, with suitable access. For a test that is situational based on site conditions and thus is not easily generalised, the test is extremely costly. Other limitations that can impact the accuracy of results include loss of access due to excessive damage and blasting misfires resulting in abandoning blast holes. Despite its limitations, in comparison with all other experimental testing, blast testing is the only test that can accurately imitate the in situ stresses and environment of rock in excavations.
Blasting is a form of experimental in situ testing that investigates rock mass discontinuity, stress conditions on rock burst damage and the influence of in situ dynamic loads on a ground support system by simulating a rock burst [ 33 ]. A blast test involves drilling blast holes parallel to an excavation face, that are separately charged and detonated sequentially such that dynamic loading can be applied. Mapping of the test site with a 3D photography system both before and after blasting is carried out to identify areas of rock bulking and ejection, and additionally measure deformations of both surface and reinforcement support elements [ 34 ]. However, due to movement of mapped control points after blasting occurs, errors in measurements of angles and displacements on digital images are likely to occur.
Methodologies of studying and testing ground support systems for burst-prone excavation can be summarised into five categories: analytical, experimental, empirical, data-based and numerical testing [ 8 ]. Data-based testing methods are accurate only if a large sample size is available; however, due to differing in situ rock stresses and conditions in differing excavations and the complexity of rock bursts, such data are not available [ 31 ]. Empirical methods are confined to the specific site they are conducted, limiting their ability to generalise and standardise results [ 32 ]. Each method of testing has its limitations due to the complexity of rock bursts, and thus only experimental and numerical testing are explored in further detail here, including blast testing, drop tests, double shear tests and applications of numerical modelling with these testing methods.
Many burst-prone mines in Canada favour the use of mesh and mesh straps due to the ability of mesh to undergo high deformity and not fail. A common weakness of mesh, where mesh overlaps, is solved by using straps, preventing mesh from failing as a retaining element without the failure of individual mesh wires [ 9 ]. The type of mesh used in burst-prone excavations has advanced over time, where steel wire weld mesh was the industry standard; however, after further investigation by Roberts, Talu and Wang () [ 30 ], it was experimentally and numerically proven that woven weld mesh and chain link mesh with closed wire loops have greater deforming and loading capacity under static and dynamic loading.
Fibre-reinforced shotcrete provides early support to prevent the early deterioration of the rock surface, but it begins to crack under minimal deformation. Thus, shotcrete in burst-prone grounds is not cost-efficient, as the surface will need to be retained by mesh [ 29 ].
Surface supports act as external support to excavations that are installed on the surface of excavations to hold and retain failing rock mass. In burst-prone environments, due to the dynamic loading of rock bursts, the interaction between surface elements and reinforcement elements is critical to ensure that no weak links are created [ 28 ]. Surface support elements can consist of fibre-reinforced shotcrete, mesh, straps and nuts/plates that connect reinforcing bolts to the surface support elements.
In addition to rock bolts, cable bolts research and usage in burst-prone grounds are increasing. Cable bolts perform like rock bolts, but cable bolts consist of flexible tendons with higher tensile strength to further strengthen rock mass [ 27 ]. Plain strand cables had poor load transfers properties when first introduced in ground support systems, which is reflective of their initial use as a secondary reinforcing member. However, after modifications such as indentation, double strands, birdcage strands, bulbed strands, fiberglass cable bolts and nut-caged cable bolts, the load transferring and energy absorption capacity has improved [ 2 ]. Currently, SUMO (9 wire strand) and Secta (7 wire strand) dynamic cable bolts with bulbed strands are popular in the Australian Mining industry.
Currently, common dynamic rock bolts used in the Australian mining industry include the Yield Lok Bolt and the J-Tech All Thread Bar, which are produced by Jennmar Australia. The Yield Lok Bolt typically consists of a smooth steel bar with a portion of threaded bar (for resin mixing) with an upset, a type of anchor that is coated in an engineered polymer. Like the cone bolt, the Yield Lok bolt absorbs energy via bolt shank slippage through ploughing in grout/resin. The J-Tech bolt consists of a bolt that has a small pitch thread along the entirety of its length with exceptional static and dynamic capacity.
The Cone Bolt was the first energy-absorbing rock bolt designed, which consisted of a smooth bar with a flattened conical shape on the far end of the bolt [ 25 ]. The original cone bolt was designed to be grouted using cement, but the cone bolt was later adapted to function with resin by adding a threaded section and mixing blade [ 26 ]. The bolt was designed such that when displacement occurs, the conical end ploughs through the resin or grout to conduct work and absorb energy released from the rock. After Lindfors () carried out dynamic testing on modified cone bolts, it was recorded that the bolts were only effective when ploughing occurred. Further dynamic analysis by Cai, Champaigne and Kaiser () [ 3 ] showed an average dynamic yield loading between 50 and 216 kN when a kinetic energy of 33 kJ was inputted, presenting a large spread of values due to different failure mechanisms, including ploughing, steel stretching or a combination of the two.
Conventional rock bolts have been categorised into three major categories, which are mechanical bolts, fully grouted rebar bolts and frictional bolts [ 23 ]. These types of conventional bolts are utilised to deal with rock instability in areas with relatively low in situ stress. However, in burst-prone mines, energy-absorbing rock bolts (also known as yielding bolts) are more suitable due to their shear resistance under dynamic loading conditions that rock burst creates.
Since the development of rock reinforcement systems, yielding bolts were only widely accepted from the early s. This was due to misbelief of the effectiveness of reinforcement bolts that were designed to purposely yield [ 16 ]. Despite W. Ortlepp () [ 20 ] conducting a field test in that clearly demonstrated the effectiveness of yielding reinforcement, it was not until multiple mines that were prone to rock bursting displayed the success of yielding reinforcement, such as the Big Bell Mine in Australia [ 21 ] and Brunswick Mine in Canada [ 22 ], did yielding bolts become widely used in burst-prone excavations.
Existing ground support systems in prone-burst areas are composed of a reinforcement system that utilises yielding energy-absorbent tendons and flexible surface support elements such as shotcrete, straps, lacing, mesh and screens [ 19 ]. These elements that have been incorporated into current designs have improved over time through experimental testing, numerical analysis and field experience.
Therefore, to design a support system that adequately negates the damage mechanisms of rock bursts, Kaiser et al. () devised three necessary support functions that must operate concurrently: reinforce the rock mass to strengthen it, such that it can support itself and control bulking [ 18 ]; retain broken rock mass to prevent unravelling and further failure by using surface supports; and holding rock, reinforcement and surface elements securely to allow for the dissipation of dynamic energy [ 16 ]. These three support functions have been further built upon, and Cai and Champaigne () [ 15 ] advise that an effective rock support system must also account for dynamic energy absorption capacity, large displacement capacity and large load carrying capacity simultaneously, and thus created seven rock burst design principles. As burst-prone excavations cannot always be avoided, especially as mining depth increases, the next best thing is utilising effective and capable ground support systems.
To manage and create ground support systems capable of mitigating rock burst damage, it is necessary to understand the damage mechanisms of rock bursts. Rock burst damage mechanisms and their causes have been classified into three types by Kaiser et al. (): rock bulking, where rock mass with high stress but low stored stress energy fractures; rock ejection, where rock with excess stored energy ruptures or remote seismic events transfer dynamic stress creating a strain burst; and seismically induced rock fall, where rock strength is inadequate to resist forces that are accelerated due to seismic waves [ 9 ].
Initially, W. D. Ortlepp and Stacey () [ 17 ] proposed a classification of differing rock burst types, categorising them into five main types, which were strain bursting, buckling, face crushing (now known as fault slips), shear ruptures and fault slips. However, these rock burst types have more recently been refined into three distinct categories by Kaiser and Cai () [ 9 ], which are strain bursts, where high stress concentrations at the edge of excavations exceed rock strength; pillar bursts, where support pillars fail violently due to large volume of rock failure; and fault slip bursts, where failure occurs due to slippage between existing faults and newly generated shear ruptures within the rock mass.
The first rock burst was recorded in South Africa at the Witwatersrand Gold Mines in the early s, where sudden failure of rock masses occurred. Since this incident, there has been a clear link between mining activities, particularly at greater depths, and rock burst incidents, where it has been established that rock bursts are highly associated with hard rocks and geological faults [ 16 ].
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This literature review thoroughly investigates the existing state of rock burst management such that contributions, evidence and gaps in the existing literature can be identified to provide a relevant understanding of current rock burst management. This includes a further analysis of rock bursts to understand what must be considered when designing a support system, the existing reinforcement and surface elements currently used in the industry, the current testing methods and facilities used to test support systems elements and the validity of numerical analysis as a means of testing ground support systems.
From South African gold mine investigations, it was observed that approximately 70% of rock ejections due to rock bursts occurred due to failure of connecting elements, where the majority of reinforcement bolts were still intact [ 14 ]. Currently, a main objective of the international research effort is to analyse and design existing ground support systems as an integrated system rather than individual elements, such that support systems used in burst-prone excavations can reach their maximum potential capacity. This aligns with Cai and Champaigne ()&#;s [ 15 ] rock burst design principles, which place a heavy emphasis on addressing the weakest link of a support system and utilising an integrated system.
Rock burst management currently involves utilising capable ground support systems, which incorporate both surface support systems and reinforcement support systems. A surface support system, including steel mesh, rope lacings, shotcrete, etc., provides reaction forces to the face of the excavation [ 11 ], while reinforcement support systems, including rock bolts, cable bolts and anchors, are elements that are bored into excavation faces to enhance the overall strength of the rock mass [ 12 ]. However, current design procedures do not place enough focus on the connections between surface support and reinforcement systems, resulting in the failure of the support system before both the surface and reinforcement elements reach their full capacity [ 13 ].
The urgency to further understand and mitigate rock and coal bursts is reflective of the current international research effort, which includes countries such as Australia, China, South Africa and Canada, devoting resources to advance rock burst management and prevention [ 9 ]. Despite the number of resources invested in researching rock bursts over multiple decades, the mechanics of rock burst failure are not well understood, and therefore are difficult to control [ 10 ]. Therefore, as a safeguard to all workers, equipment and excavation operations, an effective rock support system is necessary and is currently deemed the most effective mitigation strategy.
A rock burst is defined by Kabwe and Wang () [ 7 ] as a mining-induced seismic event that causes destruction to excavations. It occurs due to dynamic rock failure, where the rapid release of stored strain energy with the rock results in displacement and violent ejection of rock mass [ 8 ]. Due to the complexity and unpredictability of rock bursts, it is considered as one of the most hazardous geological disasters, being responsible for excavation and equipment damage, injury and fatalities [ 8 ].
The method encompasses the entire design and calibration process of generating the FEA double shear test model. Prior to any testing, the calibration of the model was required. This is considered the most crucial aspect of numerical modelling. The development of the model includes creating of the geometric parts, inputting material properties, applying boundary conditions and interactions, assembling the model and meshing the parts.
To gain an understanding of the intricacies around cable bolts and their properties, the Australian Coal Industry Research Program (ACARP) and Jennmar papers were consulted. This provided a comparative model for which the model could be calibrated against for static loading, as ACARP had completed a similar study. The dynamic model was calibrated against Tahmasebinia et al. () [ 5 ], which a built upon Mirzaghorbanali et al. ()&#;s [ 2 ] work. Practical testing of bolts was obtained by extracting data from Jennmar, a steel bolt manufacturing company.
Jennmar Civil is a cable bolt manufacturing company that widely produces cable bolts designed for deep mining excavation. The bolts they manufacture have been an industry standard and are therefore referenced within the investigation. By modelling the cable bolts for the double shear test based on these bolts, the following tests yielded reliable results that are consistent with industry practice and manufacturing capabilities. The mechanical and geometrical properties were obtained from Jennmar. The bolts that have been considered by Jennmar are summarised below, in Table 2
Similarly to ACARP&#;s study, a Ø28 Indented (ID) SUMO cable bolt was used to calibrate the static model. Jennmar has developed various types of bolt configurations such as the Yield Lok Bolt, J-Tech bolt and the Sumo Cable Bolt, which have unique functions and purposes. The configuration of the bolt serves a unique purpose, with each possessing notable distinguishing factors. The Yield Lok Bolt contains a lock nut at the end which acts as a locking plate with the bolt and the rock face. This was designed for high seismic conditions due to its polymer ploughing design. The J-Tech Bolt is a more generic bolt model that is suitable with either resin capsule or grout. The threads can be made finer to achieve higher tension for a given torque. The Sumo bolt contains a bulb-like structure which is bird-caged throughout the entire bolt. This increases flexibility in handling, making it more advantageous around confined areas and contains smooth wires for optimum performance in shear.
The specific configuration and layout of the bolt contribute to each respective bolts&#; shear capacity and its overall behaviour under the double shear test. Within the scope of this investigation, the configuration is not a parameter that will be tested, and therefore, all bolts will be reduced to a single metal rod. This will also assist in the modelling procedure and will be further elaborated on in the following section.
To create the model, each individual geometric component was constructed. The double shear test comprises 2 key components, the box and the bolt. Mirzaghobanali et al. () modelled a double shear test which consisted of 300 mm cubic end blocks with a central block of 450 mm (L) × 300 mm (W) × 300 mm (H) and a mm cable bolt with no gap between the blocks. Tahmasebinia, Zhang, Canbulat, Vardar and Saydam () [ 5 ] followed a similar construction for the double shear test, but incorporated dynamic loading to further build upon the model. Both studies were developed from a relatively similar model and hence, the following model was similarly constructed.
As the various types of bolts that were to be modelled are complex in geometry and possess a unique layout, the bolts were simplified to be a single cylindrical smooth bolt. Although this does not accurately reflect the actual design of the bolt type, this was a reasonable simplification to avoid excessive modelling complexities. Each bolt was of mm length with a diameter of 18, 20, 23, 25, 28 or 31 mm. Figure 1 illustrates the 28 mm bolt.
Mirzaghobanali et al. () [ 2 ] differentiated between the geometry of the end and middle blocks; the blocks here are considered as having the same geometry. The blocks are representative of the individual rock layers within the geological rock profile and remain fixed at the ends, allowing only the middle block to move in the vertical, y, plane. The blocks were 500 mm (L) × 500 mm (W) × 500 mm (H). A hole with a diameter equal to the bolt under investigation was extruded through the centre of the cube in the ZY plane. Figure 2 illustrates the concrete box with a 28 mm extruded hole.
To aid ABAQUS in developing an efficient mesh, localised subdivisions were introduced by creating partitions around areas of concern. Focal areas where partitions were created included contact points, and areas where loading would be applied. ABAQUS develops a mesh by seeding the part, followed by auto-meshing. This develops a generic meshing model which cannot specifically refine meshing around boundary locations. This is further discussed in mesh generation.
Material properties were defined for the steel bolt and concrete. The parametric study included the analysis of varying steel yield and ultimate strength. Therefore, as part of the calibration, the primary material properties that were included in the ACARP C paper are referenced. The ID SUMO Cable Bolt material properties are summarised below in Table 3
ABQAUS requires yield strength,
fy
, and ultimate strength,fu
, as a pressure load. To convert force loads to a pressure, the yield strength was divided by the undeformed cross-sectional area.The steel bolt has been defined to fracture; hence, elastic, plastic and shear damage material properties were defined. Furthermore, the steel density, Young&#;s modulus and Poisson&#;s ratio were also defined. The basic steel properties have been obtained through the OneSteel 7th edition steel catalogue [ 43 ]. Please see Table 4
σ * = b ε * + ( 1 &#; b ) ε * ( 1 + ε * R ) 1 R
(1)
To replicate actual stress&#;strain plastic deformation, the Giuffre&#;Menegotto&#;Pinto model with isotropic strain hardening was utilised to describe the transition from the elastic slope to the plastic deformation region. Zafar and Andrawes () [ 44 ] adopted this equation to model steel behaviour of various steels.
σ T = σ E ( 1 + ε E )
(2)
ε T = ln ( 1 + ε E )
E
represents engineering stress/strain and the subscriptT
represents true stress/strain. As part of achieving calibration, this was necessary to ensure the accuracy of testing as it was compared with the experimental results obtained from ACARP Project C. A comparison of the engineering and true stress&#;strain curve for the calibrated model can be seen below inThe steel elastic and plastic behaviour was calculated in accordance with the AS: Steel Structures codes. To accurately reflect the actual behaviour of steel undergoing plastic deformation, the true stress and strain must be utilised. The engineering stress&#;strain relationship fails to factor in the constantly changing cross-sectional area of the material and hence is simply applied to the initial cross-sectional area prior to any deformation. The following equations were utilised to account for the reducing cross-sectional area, thus giving the true stress and true strain equations [ 45 46 ].where the subscriptrepresents engineering stress/strain and the subscriptrepresents true stress/strain. As part of achieving calibration, this was necessary to ensure the accuracy of testing as it was compared with the experimental results obtained from ACARP Project C. A comparison of the engineering and true stress&#;strain curve for the calibrated model can be seen below in Figure 3
To induce a fracture, ABAQUS requires shear damage properties for damage for ductile metals to be defined and hence, a fracture energy is required. Fracture energy is defined as the required energy per unit area to change a fracture surface from an initial unloaded state to complete separation [ 47 ]. This is calculated as the work carried out to achieve fracture and effectively calculate the area underneath the respective stress&#;strain curve [ 48 ]. A Python code was written to determine the specific fracture energy for all steel grades (see Appendix A ). The fracture energy for the calibrated model was calculated as 336,302 N/mm. The fracture energy will vary according to the steel grade.
Concrete was selected as a substitute material for the rock layers as they possess relatively similar material properties. The various blocks are representative of layers of rocks which the cable bolt penetrates. Within the actual geological profile, the nature of the rock, faults and strength of the rock will affect the behaviour of the cable bolt subject to shear; this model provides a simplification of this and therefore, the same concrete properties have been applied across all three blocks. The following concrete properties have been calculated in accordance with AS: [ 49 ]. Please see Table 5
The concrete damage plasticity (CPD) is defined in ABAQUS to model concrete and other quasi-brittle material inelastic behaviour. It assumes that there are two primary failure mechanisms, tensile cracking and compressive crushing. As the load is applied from the load cell and is transferred to the bolt, the concrete is expected to absorb energy and hence experience a compressive and tensile force. Sumer and Aktas () [ 50 ] defined the uniaxial tensile and compressive stress&#;strain relationships which were used to determine the concrete damage properties. This was consistent with Xiao, Chen, Zhou, Leng and Xia ()&#;s [ 51 ] understanding of CPD and therefore was utilised in this model.
Detailed meshing is crucial in developing an accurate model that will produce accurate results. Effectively, by reducing the size of the mesh, ABAQUS can process the behaviour of individual elements more precisely as interpolation is utilised across a lesser distance to calculate stresses and deformations, thus eliminating imprecise estimations. However, by increasing the fineness of the mesh, more elements are created, and thus the computational time is inevitably increased as the FEA needs to run more equations. Therefore, is it important to differentiate between parts of the model which require a fine mesh and parts that require a coarse mesh.
The inbuilt ABAQUS auto-meshing function generates a mesh based on the seeding size that is specified. This creates a mesh size of specified seed size that does not consider the irregularity of the mesh. Therefore, partitions were manually added around areas of greater concern such as contact points, areas of significant deformation and high stress concentrations to create an ideal mesh. Figure 4 displays the difference in mesh regularity between the auto-meshing function with and without any partitions.
As the mid-section of the bolt is the primary region of concern as it deflects, the mesh around this area was made twice as fine as the first and last third of the bolt. Furthermore, this was extended to the 50 mm gap between the concrete blocks. The mesh can be seen in Figure 5 below.
When modelling steel and concrete members with ABAQUS, one of the main issues is addressing convergence due to the extensive number of contacts. This is particularly prevalent in the double shear test model at the contacts between the cable bolt and the concrete boxes. Therefore, the 8-node linear brick element, C3D8R, with reduced integration and built-in hourglass control will be used. The linear brick element contains a single integration point at the centre of the brick with 8 nodes forming the 1 × 1 × 1 cube. The reduced integration model is ideal when subject to plastic behaviour [ 52 ]. However, in conjunction with this, it is necessary to apply hourglass control because of the reduced stiffness of the reduced integration model. This will aid the meshing process and the overall run time of the model. Figure 6 shows the schematic diagram of the C3D8R model whilst highlighting the effects of hourglass control.
Mesh size was determined by comparing the trends of numerical and experimental data. The coarsest mesh that would minimise computational time and produce accurate results was selected. Seeding sizes of 10%, 15%, 20% and 25% of the bolt&#;s diameter were selected as the fine mesh portion, whilst the outer boundary was assigned double this value for static testing. For dynamic testing, an optimal mesh was selected by considering seeding sizes of the dynamic load. The results of various seeding were compared against the experimental results and can be seen in Figure 7
The computational times for various seeding sizes were recorded in Table 6 below.
Final mesh sizes were chosen based on the effects of a finer mesh and computational times. Excess deflections were observed when meshes of 5% and 10% were applied to the sphere. Despite reduced computational times, the coarse mesh presented too many inaccuracies. A 2% mesh size was selected due to the excessive computational time of 1% with little difference in deflection. A summary of seed sizing of the calibrated model is given below in Table 7
Interactions were created between the contact points between the bolt and the box. One of the primary advantages of using ABAQUS is its ability to define contact interaction properties. Three general surface-to-surface interactions were created between the steel bolt and the concrete boxes. There are 3 defining characteristics that were utilised to determine which surface would be the master and slave.
The larger surface should be the master;
If approximately the same size, the stiffer body should be the master;
If similar size and stiffness, the surface with the coarser mesh should be the master.
In this instance, the concrete was determined to be the master as the surface is larger than the bolt and will have a coarser mesh overall since the deflection of the load cell is measured. A penalty contact method was applied with mechanical, tangential and normal properties defined (see Table 8 ). These values are applied to account for slip conditions and are necessary to reflect the natural pulling that will occur due to the cable bolt undergoing a shear force.
Rigid bodies have been applied to sections of the model. To apply the rigid body, a set of reference elements, in this case body elements, was captured by a single reference point. By defining elements of the model as a rigid body, the shape does not deform, and therefore is not impacted when the load is applied. Rigid bodies have been placed at the base of the end blocks and at the top block. Figure 8 below shows the rigid body elements of the static and dynamic model.
The double shear test involves fixing the end blocks and applying a vertical load to the middle block. Therefore, when simulating the double shear test in ABAQUS, it is necessary to apply boundary conditions to reflect this. The concrete end blocks were fixed in all directions and fixed in all rotational axes, whilst the middle block was fixed in all directions except the vertical plane and fixed in all rotational planes. The boundary conditions were applied on reference nodes that contained the whole surface face set as defined when applying rigid bodies. All boundary conditions were placed as an initial condition (see Figure 9 ).
To prevent the bolt from slipping, it was fixed at the ends in all displacement and rotational planes. A loading rate was defined for the middle block. The loading rate was applied to the central reference node of the load cell and assumed to be 100 mm/s. This was applied at Step 1 of the test as it was not an initial condition. For calibration purposes, this was set to 200 m/s, as defined by Tahmasebinia et al. () [ 5 ].
The model was assembled such that the bolt fit perfectly within the box with a 50 mm gap between each box. The purpose of this was to simulate a test whereby the frictional forces of the boxes would not impact the shear analysis. Each block was 50 mm apart from the next block. As the model was assembled as such, no frictional forces will contribute to the measured shearing force of the bolt which would be measured by the load cell.
A single step was generated for the analysis. To obtain accurate deflection information, it is important to allow the test to run for an acceptable time step. Initially, a single second time step was set up. This showed a deflection pattern that continually was rising, suggesting that a longer time step was to be utilised. This was changed to 1.5 s. The force vs. deflection graph agreed with the calibrated test study. It was also necessary to define the number of outputs that ABAQUS would return to provide effective data that did not span across a significant time step.
The analysis procedure of the static test was dynamic explicit. However, to conduct a valid test for this model, mass scaling was applied, so a quasi-static test was observed. Because the simulation includes rate-independent material behaviour, the natural time scale can be ignored. By artificially applying mass-scaling to the entire model, the mass is increased, thus omitting any consideration of the natural time scale and achieving a quasi-static analysis. Table 9 below tabulates the quasi-static mass scaling criteria. The maximum displacement can only be considered at the ultimate load resisted by the load cell as displacement reflects the load cell displacement.
Prior to performing any analysis, the model first required calibration. This is to show that the results that were obtained from the model are consistent with proven experimental studies and various academic literature. The static model was calibrated against the results obtained from the ACARP C paper using the double shear test on a 63 T Indented Sumo bolt with 0 tonne pretension and angled perpendicular to the shearing plane. Whilst the dynamic model was not calibrated against an experimental result, it was compared against Tahmasebinia et al. () [ 5 ] dynamic model, which measured impact loading against deflection.
The development of the model required the simplification of geometrical and material properties such as defining the cable bolt as a smooth single rod. Furthermore, as the experimental testing includes manufacturing defects within the steel that is measured, this contributes to the inaccuracies of simplifying the model. Whilst there are numerous factors that contribute to the simplified inaccuracies of the model, the output is deemed to be valid, and the model will be calibrated if the results display a similar pattern deflection force pattern, and the maximum results for displacement and force are within 25% of the calibrated data.
The Drucker&#;Prager model was initially investigated as a parameter to increase the overall accuracy of the model; however, it was omitted from testing as it significantly increased the computational time without significant variation in the results.
The calibration of the model involved an iterative process which required constant revision of the model by varying different parameters. The iteration process required careful consideration of how variables were applied. For example, a first pass iteration of the model did not consider applying boundary loads to the ends of the bolt, fixing them to be restricted in all translations and rotations. This resulted in slipping of the bolt and observing large deflections. The meshing process was considered to determine the appropriate balance between a fine and coarse mesh when examining the impact on the validation of the model.
D i s p l a c e m e n t S t a t i c , C a l i b r a t e d D i s p l a c e m e n t S t a t i c , E x p e r i m e n t a l = 73.5 92.82 = 0.79 = 79 % c a l i b r a t i o n F o r c e S t a t i c , C a l i b r a t e d F o r c e S t a t i c , E x p e r i m e n t a l = 647 795 = 0.81 = 81 % c a l i b r a t i o n
F o r c e S t a t i c , C a l i b r a t e d F o r c e S t a t i c , E x p e r i m e n t a l = 647 795 = 0.81 = 81 % c a l i b r a t i o n
The static calibration model was obtained from the analysis with results graphed against the experimental data. A visual assessment was conducted to compare the force vs. displacement pattern of the graph to ensure consistency, whereas a quantitative analysis was conducted to confirm that calibration was achieved. A comparison between the maximum displacement at ultimate force and maximum force of the model and experimental data was completed.
The calibrated force vs. displacement graph was plotted against the ACARP C experimental data. As seen below in Figure 10 , the calibrated model follows a similar curvature to the experimental data, particularly up to the ultimate load. A key difference, however, is the post-failure behaviour. The FEA data obtained show a gradual failure. This is inconsistent with existing steel behaviours which show that steel exhibits a much more brittle failure, shown in the experimental data. The corresponding displacement for the maximum force occurs at different stages. The FEA model was calibrated and validated to 80% and is deemed acceptable.
The different modes of failure have also been successfully replicated by the FEA model. Initially, a shear failure occurs where the force suddenly experiences a dip, followed by a gradual increase in applied force to induce bending. Finally, fracture is shown at the sudden drop where both shear and bending have both completely failed.
Once the model was calibrated, testing was conducted to obtain results for the parametric study. Testing involved examining the impacts of variables against deflection. The test involved examining 6 cable bolt diameters and 6 steel strengths, totalling 36 test variations. The parameters have been summarised below in Table 10
The results from the testing are presented in the next section, followed by a discussion of the validity and trends of the data. Finally, conclusions from the test are obtained and recommendations are provided for further study.
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