Reactive Powder Concrete Beams Research Articles

Minimum Shear Reinforcement for Reactive Powder Concrete Beams

The aim of this research was to determine the minimal requirements for shear reinforcement for reactive powder concrete (RPC) rectangular cross-sectional beams with a compressive strength of 157 MPa and a steel fiber volume content of 2.0% that remained constant for all the tested beams. Additionally, the recommendations of KCI-2012 and AFGC-2013 for the design of RPC beams as well as the shear design requirements of ACI 314-2014 when applied to RPC beams were studied. Utilizing a three-dimensional finite element program, a computational model was designed for forecasting the deformations and shear strength of the examined RPC beams. Both the shear-span-to-depth relationship (a/d) and the minimal reinforcement web ratio, represented by the distance between stirrups and the diameter of the stirrup bars, are the key study parameters in this regard. According to this study’s experimental findings, increasing the given reinforcement of the web ratio has little influence on both the ultimate shear strength as well as the diagonal cracking strength of the beams. Additionally, the findings demonstrated that the ACI 318-2014 maximum stirrup spacing requirement of 0.5 d can safely be extended to 0.75 d for beams that are relatively short. Compared to what ACI 318-2014 mandates, the suggestions of AFGC-2013 and KCI-2012 are more cautious and safe. According to the AFGC-2013 criteria, the mean proportion of Vfb to projected Vu,AFGC is roughly 58.3%, whereas the mean proportion of vs. and Vc is just 41.7%. The deformation response and ultimate shear strength of the examined RPC beams were well predicted by the designed model using finite elements when metal fibers were taken into account.

Structural behavior of RPC beams subjected to flexural and torsional effects

This research is concerned with the behavior of reactive powder concrete beams (RPC) under the combined effects of bending and torsion moments, with three main parameters: torsional to bending moments ratio (T/M), longitudinal reinforcement ratio ( ), and transverse reinforcement ratio ( ). 12 rectangular reinforced RPC beams with dimensions of (1500 200 150) mm were tested. The outcome demonstrated that increasing the longitudinal reinforcement ratio from =0.009 to =0.016 improved the ultimate capacity significantly by 34.16%, and 35.54% in cases of (T/M) =0, and 0.5 respectively, also it significantly improved moment-deflection response in the case of (T/M) = 1, and well improved torque-rotation response in cases of (T/M)=0.5, and 1. Increasing the transverse reinforcement ratio from = 0.0042 to =0.0075 improved the ultimate capacity significantly by 49.22% in case of pure torsion and slightly improved it in other cases. Also it significantly improved moment- deflection response in case of (T/M) = 1 and improved torque -rotation response in cases of (T/M)=1and ꝏ.

Structural behavior of RPC beams subjected to flexural and torsional effects

This research is concerned with the behavior of reactive powder concrete beams (RPC) under the combined effects of bending and torsion moments, with three main parameters: torsional to bending moments ratio (T/M), longitudinal reinforcement ratio ( ), and transverse reinforcement ratio ( ). 12 rectangular reinforced RPC beams with dimensions of (1500 200 150) mm were tested. The outcome demonstrated that increasing the longitudinal reinforcement ratio from =0.009 to =0.016 improved the ultimate capacity significantly by 34.16%, and 35.54% in cases of (T/M) =0, and 0.5 respectively, also it significantly improved moment-deflection response in the case of (T/M) = 1, and well improved torque-rotation response in cases of (T/M)=0.5, and 1. Increasing the transverse reinforcement ratio from = 0.0042 to =0.0075 improved the ultimate capacity significantly by 49.22% in case of pure torsion and slightly improved it in other cases. Also it significantly improved moment- deflection response in case of (T/M) = 1 and improved torque -rotation response in cases of (T/M)=1and ꝏ.

Cracking characteristics evaluation for reinforcement basalt fiber reactive powder concrete beam using acoustic emission

New types of fibers such as basalt fibers are gradually being used to reinforce cement-based concrete materials. To provide a basis for the further popularization of basalt fibers and basalt fiber reinforced reactive powder concrete (BFRPC) materials, the bending mechanical properties and fracture properties of BFRPC beams were investigated by innovatively applying four-point bending test and multiple acoustic parameter analysis methods. On the one hand, the load vs. displacement curve and crack pattern of reinforcement BFRPC beam were obtained from the four-point bending test. On the other hand, Acoustic emission (AE) technology was used to monitor the cracking process of reinforcement BFRPC beam under four-point bending load, and the AE signal was analyzed to illustrate the cracking characteristics of reinforcement BFRPC beam. The results revealed that AE hits, amplitude, counts, duration, and energy have a similar changing trend with bending load. Cumulative hits and cumulative energy are positively linearly related to the displacement and quadratically related to the sum of crack widths, and the correlation coefficients are all above 0.95. Besides, the cracking process of reinforcement BFRPC beam can be divided into four stages by the variation of AE basic parameters with bending load. The main rebars yielding is an important turning point of the crack characteristic of reinforcement BFRPC beam. AE signal data varies greatly in different locations, and it has an obvious advantage to detect the formation of invisible cracks. The results of predicting concrete damage and cracking by AE signal data are consistent with the experimental phenomenon. The low-stress brittle fracture caused by tensile fracture was reduced, and the tensile resistance and flexural bearing capacity of the reinforcement BFRPC beam were increased. The results obtained in this paper support the damage assessment and structural health monitoring for cement base concrete materials under bending load.

Performing laboratory study of the behavior of reactive powder concrete on the shear of RC deep beams by the drilling core test

Abstract In the past decade, it has been observed that the applications of modern materials have developed a lot, especially effective reactive powder concrete (RPC), due to its superior performance properties. As a result of the superior resistance of RPC, it will give a longer construction life with less maintenance and more resistance to various environmental conditions and exhibits high-performance features such as high porosity, very high strength, and excellent corrosion resistance. The parameters studied in the present research were used to investigate the effect of maximum load, deflection, tensile and strain of concrete, first shear crack, crack pattern, and crack width. Considering the aforesaid cause and objective, one specimen of RPC RC deep beams has a rectangular cross-section of 150 mm in width, 500 mm in depth, and a total length of 1.2 m. One control specimen was tested for comparison. Moreover, 12 control specimens including cylinders and cubes were cast and tested to obtain the mechanical properties of the normal and RPC deep beams. Following the specimens’ processing, they were subjected to two concentrated load pressure tests through a hydraulic jack. Based on the results, the ultimate strength, deflection, and first shear crack capacity for the reactive powder concrete deep beam (RPCDB) have increased by 68, 10.5, and 62.5%, respectively, compared with concrete deep beam (CDB). Moreover, with respect to the width, the delay in the appearance of the first shear crack was reduced by 11 and 78%, respectively, compared with CDB at 65% of the final shear load. In addition, regarding the stress-strain results, RPCDB has increased by 118% at the maximum stress compared with CDB and in contrast, the strain scores for CDB increased by 22.5% at maximum stress compared to RPCDB.

Influence of Fiber Orientation on the Shear Properties of Steel Fiber-Reinforced Reactive Powder Concrete Beams

Steel fiber-reinforced reactive powder concrete (SFRPC) has good mechanical properties and is thus useful for engineering applications. Generally, the fibers in SFRPC are randomly distributed. To study the effects of the amount, length, and orientation of steel fibers on the shear strength of SFRPC beams, nonreinforced aligned steel fiber-reinforced reactive powder concrete (ASFRPC) beams were prepared using a large-scale electromagnetic field orientation device. Shear tests of specimens with a shear span ratio of 1.5 were performed under two fiber contents (1.0% and 2.0%) and three fiber lengths (20, 30, and 40 mm). The full-field strain during the loading process was obtained via the digital image correlation method, and the effects of fiber quantity and orientation on the shear strength of the beams were analyzed. The ASFRPC beams exhibited higher ductility but lower shear capacity than the SFRPC beams under the same conditions. The shear capacity increased with the quantity of steel fibers. According to the test results, the calculation formulas of the shear-bearing capacities of ASFRPC and SFRPC beams were established.

Flexural Behavior of Reinforced Rubberized Reactive Powder Concrete Beams under Repeated Loads

Non-biodegradability of rubber tires contributes to pollution and fire hazards in the natural environment. In this study, the flexural behavior of the Rubberized Reactive Powder Concrete (RRPC) beams that contained various proportions and sizes of scrap tire rubber was investigated and compared to the flexural behavior of the regular RPC. Fresh properties, hardened properties, load-deflection relation, first crack load, ultimate load, and crack width are studied and analyzed. Mixes were made using micro steel fiber of the straight type, and they had an aspect ratio of 65. Thirteen beams were tested under two loading points (Repeated loading) with small-scale beams (1100 mm, 150 mm, 100 mm) size. The fine aggregate is replaced by 5, 10, and 15%, respectively, with crumb rubber. While replacement of silica fume was 10, 20, 30, and 50%, respectively, with very fine rubber. Also, chip rubber was added to the mixture as coarse aggregate with 5, 10, and 15%. Five tested beams were chosen as case studies to analyze and compare the results of the ABAQUS software with the experimental results. The results showed that the flexural behavior of RRPC beams that contains rubber was acceptable when compared with the flexural behavior of the RPC beam (depending on load-carrying capacity). The crack width was decreased by including waste rubber and steel fibers. There is a satisfactory agreement between the results of the numerical analysis and the results of the experimental testing. Slight ultimate load differences are targeted between the effects of the monotonic loading and the repeated loading.

Structural Behavior of Reactive Powder Concrete under Harmonic Loading

Industrial buildings usually are designed to sustain several types of load systems, such as dead, live, and dynamic loads (especially the harmonic load produced by rotary motors). In general, these buildings require high-strength structural elements to carry the applied loads. Moreover, Reactive Powder Concrete (RPC) has been used for this purpose because of its excellent mechanical strength and endurance. Therefore, this study provides an experimental analysis of the structural behaviors of reinforced RPC beams under harmonic loads. The experimental program consisted of testing six simply supported RPC beams with lengths of 1500 mm, widths of 150 mm, and thicknesses of 200 mm under harmonic loading with varied frequencies between 10 and 20 Hz. Different steel fiber ratios of 0%, 0.5%, 0.75%, 1.0%, 1.5%, and 1.75% were provided in the concrete mixes to explore the effect of steel fibers on the dynamic behavior of these beams. Except for the steel fiber volume fraction, all of the examined specimens shared the same material attributes and reinforcing details. The outcomes proved the positive effect of adding steel fibers on the dynamic response under the effect of harmonic loading. The optimum volume fraction of steel fibers was characterized by a percentage of 1.5%. Moreover, the vibration amplitude was more affected by the steel fibers than the support reactions. The inertial force increased as the harmonic loading duration increased. This increase in the inertial force by the load duration was enhanced after adding the steel fibers. However, this enhancement started to decline after increasing the steel fiber content to 1.75%.

Study of the behavior of reactive powder concrete RC deep beams by strengthening shear using near-surface mounted CFRP bars

Abstract The applications of modern materials especially reactive powder concrete for improving concrete structures have been significantly growing in recent years. Great conduct properties creep, shrinkage, little permeability, ultra-high strength, and expanded safety against corrosion are the important features of Reactive Powder Concrete. In addition, the use of the Near-Surface Mounted technique in recent decades has helped strengthen and repair shears-reinforced concrete (RC) for deep beams using carbon fiber replacement reinforcing bars. The parameters studied in the present research investigated the impact of the maximum load, deflection, stress–strain curve of concrete, first shear crack, crack pattern, and crack width. Considering the aforesaid cause and objective, one specimen of Reactive Powder Concrete RC deep beams has a rectangular cross-section of 150 mm in width, 500 mm in depth, and a total length of 1.2 m. One control specimen was tested for comparison. In addition, 12 control specimens (cylinder and cubes) are used for experimental investigation on the mechanical properties of normal and Reactive Powder Concrete deep beams. Following the specimens’ processing, they were subjected to one concentrated load pressure test through a hydraulic jack. Moreover, six core drill specimens were taken from those deep beams to obtain the real mechanical properties of those beams, including maximum stress, modulus of elasticity, density, stress–strain curve, and Poisson’s ratio, after subjecting them to the pressure machine. Depending on the results, the ultimate strength, deflection, and first shear crack capacity for the specimens (RPCDB1P-4NSM & RPCDB1P-8NSM) have increased by (21, 25), (47, 27), and (133, 150)%, respectively, compared with (CDB1PC20). Moreover, the specimens above have reduced the first shear crack width by (9, 33.25)% respectively compared with (CDB1PC20) at 65% of the ultimate shear load.

Experiment study on reactive powder concrete beams using spirals reinforcement under torsion

This paper investigates the torsional behavior of reactive powder concrete (RPC) beams using spiral reinforcement. The influences of parameters, including different spiral reinforcement configuration, spiral reinforcement ratio, and the steel fiber content on the torsional performance of the nine RPC beams, were investigated and discussed. The experimental results showed that the failure mode, ultimate torque, torsional stiffness, and energy dissipation of the RPC beams were not affected by longitudinal reinforcement alone, but it improved the ductility. Compared to commonly used stirrups, the locked spiral reinforcement exhibits more torsional ductility, stiffness, and ultimate torque of the RPC beams. But the torsional ductility, stiffness, and ultimate torque decreased when the spiral reinforcement was unlocked. The cracking torque and pre-cracking torsional stiffness of beams were less affected by the locking and unlocking of spiral reinforcement. Greater steel fiber content and spiral reinforcement ratio resulted in higher torsional ductility, torsional stiffness, energy dissipation and ultimate torque of the locked spiral reinforcement reinforced beams. The pre-yielding torsional stiffness and plastic dissipation capacity were strongly influenced by spiral reinforcement states and spiral reinforcement ratio. The pre-cracking torsional stiffness and energy dissipation of RPC beam were determined by the steel fiber content. Considering the torsional contribution of steel fiber and concrete tensile strength, a new formula for calculating the ultimate torque of RPC beam was proposed, and the calculated value was closer to the experimental value.

Effect of incorporating fibers in reactive powder concrete – A review

Modified form of High-Performance Concrete is a Reactive- Powder Concrete(RPC) which was first found by PierreRichard and Marcel Cheyrezy, they successfully built France laboratory using RPC. High compressive strength of over 200 MPa has been achieved, with flexural strength up to 40 MPa, and in certain cases crushing strengthup to 800 MPa with the introduction of hybrid fibre reinforcement. Cement OPC grade, silica fume, quartz sand, crushed quartz flour, water, a superplasticizer, and fibre reinforcement all contribute to making RPC.These materials have high durability characteristics as a result of their extremely low porosity, low permeability, limited shrinkage, and higher corrosion resistance. To increase package density, the powder combination of RPC should have a variety of granular particle classes. By dense packaging theory and grading optimization technique, the absence of coarse aggregate increased compactness. Because of its compactness, it reaches high strength. The rapid hydration of cement and silica fume at a high curing temperature of 100 °C as compete to 27 °C is something that causes the higher early strength. This paper discusses about the hybrid fibers incorporation in RPC under various curing conditions and its enhancement in strength than single fibers. Using micro and macro fibers dramatically improves the properties of RPC and thermal properties with various types of fiber. The mechanical characteristics of the RPC beam without the hybrid fiber, on the other end, are the lowest of all the mixtures. Apart from these characteristics, RPC can be utilized for industrial and nuclear waste storage facilities due to its ultra-dense microstructure, which provides ultra-high strength even at elevated temperature and water resistance. This paper infers that the addition of hybrid fiber in RPC considerably reduces the spalling of concrete at elevated temperatures and it exhibits superior strength and durability.

Experimental investigation on flexural strength behaviour of reactive powder concrete

The performance of a composite conventional beam and a reactive powder concrete beam with various forms of reinforcement, such as PVC tubes, stainless steel tubes, and normal reinforcement, is compared in this project through an experimental comparison. In this study, experimental research on four specimens of conventional concrete beams and four specimens of reactive powder concrete beams was conducted using the two point loading test method, and mechanical properties such as flexural strength of composite beams were tested for M20 grade of conventional concrete beams and reactive powder concrete beams. The flexural strength of reactive powder concrete beams combined with conventional composite beams. Comparing the composite Reactive powder concrete beam with normal reinforcement to the composite concrete beam with normal reinforcement, the flexural strength is enhanced by 8.78%. Comparing the composite Reactive powder concrete beam with stainless steel reinforcement to the composite concrete beam with stainless steel reinforcement, the flexural strength is increased by 7.58%. When compared to composite concrete with PVC reinforcement, the composite Reactive powder concrete beam has a 5.6% higher flexural strength.

Experimental and numerical studies on the fire resistance of prestressed reactive powder concrete beams

The prestressed reactive powder concrete beam (PRPCB) is an advanced structural member that can take full advantage of the ultra-high compressive strength of reactive powder concrete (RPC) and the high tensile strength of tendons. The fire safety of PRPCBs has been mainly studied at the material level, with relatively few experimental studies being conducted on the structural member level with the principal reason of serious fire-induced spalling. This paper proposed an innovative curing method to prevent RPC spalling under high stress and extreme heating rates. A total of eight full-scale beams were tested in ISO 834 fire, considering the parameters of the cover thickness of tendon, load ratio, partial prepressing ratio (PPR), and bonded and unbonded prestress classifications. Cross-sectional temperatures, mid-span deflections, effective prestressing, crack patterns, failure modes, and fire resistances of the beams were obtained. Subsequently, fine thermal–mechanical coupling nonlinear finite element (FE) models were developed and verified, and an extensive parametric study was performed to simulate the fire responses of PRPCBs. The results indicated that the load ratio, cover thickness, and sectional dimensions notably affected the fire safety of PRPCBs, and PRPCBs fabricated as under-reinforced beams at ambient temperature may fail as lightly reinforced beams under fire exposure. According to these parametric studies, Eurocode 2: BSEN 1992-1-2 might overestimate the fire resistance of PRPCBs with small sectional dimensions by up to 3–15%. Therefore, fire resistance suggestions for PRPCBs are presented in this paper.

Nonlinear analysis of flexural performance of reactive powder concrete beams reinforced with hybrid GFRP and steel bars

In this paper, flexural performance of reactive powder concrete (RPC) beams reinforced with hybrid glass fiber reinforced polymer (GFRP) and steel bars was investigated by finite element (FE) analysis, and predicted formulae of flexural capacity was proposed. First, based on the corresponding tests, the FE models of reinforced RPC beams were built, and the applicability of FE method with RPC material was verified. After that, the FE models of RPC beams reinforced with hybrid GFRP and steel bars was designed, and the flexural performance of such beams was investigated. The influence of GFRP bar ratio, steel bar ratio, and resultant force of hybrid reinforcements on the vertical load – deflection curves were observed. Finally, the formulae of the flexural capacity of the normal section of RPC beams reinforced with hybrid GFRP and steel bars was derived. By comparing the results of proposed formulae and FE analysis, it was found that they were in good agreement. Therefore, the proposed formulae can be used to predict the flexural capacity of such RPC beams with hybrid reinforcements.

Studying the effect of shear stud distribution on the behavior of steel–reactive powder concrete composite beams using ABAQUS software

Abstract Using the ABAQUS software, this article presents a numerical investigation on the effects of various stud distributions on the behavior of composite beams. A total of 24 continuous 2-span composite beam samples with a span length of 1 m were examined (concrete slab at the top and steel I-section at the bottom). The concrete slab used is made of a reactive powder concrete with a compressive strength of 100.29 MPa. The total depth of each sample was 0.220 m. The samples were separated into four groups. The first group involved 6 specimens with shear connectors distributed into 2 rows with different distances (65, 85, 105, 150, 200, and 250 mm). The second group had the same spacing of shear connectors as the first group except that the shear connectors were distributed with one row along the longitudinal axis. The third group consisted of six specimens with single and double shear connectors distributed along the longitudinal axis. The fourth group included six specimens with one row of shear connectors arranged in a staggered distribution along the longitudinal axis. Results show that the optimum spacing was 105 mm in all groups and the deflection in group four fluctuated up and down due to the non-symmetrical distribution of the shear connectors.

Experimental Study on Shear Behavior of Reactive Powder Concrete Beam

In order to study the shear behavior of high-strength reinforced Reactive Powder Concrete (RPC) beams, eight test beams were designed and fabricated for the shear test under symmetrical concentrated load. By observing the development and failure mode of diagonal cracks, the influence of shear span ratio, stirrup ratio, and longitudinal reinforcement ratio on the cracking load, shear capacity, and deflection of the test beam is analyzed. The results show that: in a specific range, the shear capacity increases with the increase of stirrup ratio and longitudinal reinforcement ratio and decreases with the increase of shear span ratio. The shear span ratio has the most significant influence on the component’s failure mode and deformation capacity. The increase of the stirrup ratio can improve the deformation capacity of the component in a specific range. It is conservative to use the code to design concrete structures to calculate the shear capacity of high-strength reinforced reactive powder concrete beams. It is suggested that the shear calculation formula suitable for high-strength reinforced reactive powder concrete should be adopted to make the theoretical calculation results closer to the measured values.

Reactive Powder Concrete Beam's Behavior in Flexural : Review

Reactive Powder Concrete can be considered as a special type of concrete in which the coarse aggregate will be eliminated to get a homogenous microstructure with a maximum density for final result. Many researchers presented a state of the art review on reactive powder's production, mechanical properties, durability, development and applications. But the review about structural behavior is hardly to found. Because of importance of this type of concrete and its structural applications. This paper focused on review the researchers that deals with structural behavior of reactive powder concrete beams under bending load. Also review the proposed design equations related with reactive concrete behavior. Before starting a review of strength , stress-strain relation and ductility are presented because of their importance and effect on structure behavior of beams under bending. According to review of previous studies the type of fibers and its content as volumetric ratio, type of pozalanic materials and its content , amount of longitudinal steel reinforcement are main factors that affected the flexural behavior of reinforced Reactive Powder Concrete

Behavior of Reactive Powder Concrete Beams Exposed to Fire

In this paper, the effect of direct fire flame and steel fiber ratio on some mechanical properties and behavior of the relationship between load and deflection of rectangular reinforced concrete beams under the influence of fire exposure was studied. Concrete specimens were exposed to fire at temperatures ranging from (25- 400 ºC). Three temperature levels of (200, 300, 400 ºC) where chosen for exposure duration of 2.0 hours. After conducting the test, it was found that increasing the proportion of steel fibers in percentages 0.5% to 1% and 1.5% decreases the mid-span deflection at service load by 33%, 50% and 37.5 and increases the ultimate load by 36.36%, 41.6% and 53% respectively. After the beams are exposed to fire, it was noticed that the maximum crack width increases with increasing fire temperature.

Fire resistance evaluation and minimum reinforcement ratio for hybrid fibre-reinforced RPC beams under fire exposure

Reactive powder concrete (RPC) structural members are faced with the problem of fire resistance evaluation in fire safety design. In this study, the fire resistance of hybrid fibre-reinforced RPC beams evaluated through the existing design methods was compared with those measured in standard fire tests. The results showed that the existing design methods cannot provide satisfactory fire resistance evaluation for hybrid fibre-reinforced RPC beams, which highlights the need to propose a new prediction method. To fill this gap, an existing macroscopic finite-element model was extended to simulate the fire response of hybrid fibre-reinforced RPC beams. Based on the developed FE model, an extensive parametric study was conducted to study the effects of structural parameters such as the RPC cover thickness, load ratio, reinforcement ratio, span-depth ratio, beam width and compressive strength of RPC on the fire resistance of hybrid fibre-reinforced RPC beams. Then, through the regression analysis of the 663 FE simulation results, an equation, which is expressed in the form of continuous multiplication, was proposed to predict the fire resistance of hybrid fibre-reinforced RPC beams under standard fire exposure. The validity of the proposed equation was established through comparisons with the results from FE simulation and existing fire resistance tests. Additionally, the minimum reinforcement ratio required for RPC beams to achieve a specified fire resistance was proposed to prevent the brittle failure caused by the insufficiency of reinforcement under fire.

Numerical Simulation of Steel-Reinforced Reactive Powder Concrete Beam Based on Bond-Slip.

In this study, based on the concrete damaged plasticity (CDP) model in the ABAQUS software, various plastic damage factor calculation methods were introduced to obtain CDP parameters suitable for reactive powder concrete (RPC) materials. Combined with the existing tests for the bending performance of steel-reinforced RPC beams, the CDP parameters of the RPC material were input into ABAQUS to establish a finite element model considering the bond and slip between the steel and RPC for numerical simulation. The load-deflection curve obtained by the simulation was compared with the measured curve in the experiment. The results indicated that on the basis of the experimentally measured RPC material eigenvalue parameters, combined with the appropriate RPC constitutive relationship and the calculation method of the plastic damage factor, the numerical simulation results considering the bond-slip were in good agreement with the experimental results with a deviation of less than 10%. Thus, it is recommended to select a gentle compressive stress-strain curve in the descending section, an approximate strengthening model of the tensile stress-strain curve, and to use the energy loss method and Sidoroff’s energy equivalence principle to calculate the RPC plastic damage parameters.