System of insufficiency of the modern theory of long-term resistance of reinforced concrete and designers’ warnings

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Aim of the research. The essence of the failure of the globally widespread theory of long-term resistance of reinforced concrete is defined and analyzed. Methods. This failure includes the following interconnected parts: 1) the set of ten basic fundamental properties of structural concrete is completely distorted (for example, instantaneous linear properties are Maxwell scheme); 2) mathematical rules are violated when recording the rates of elastic deformation and creep deformation, due to a misunderstanding of the Boltzmann principle (these violations distort the whole structure of the theory); 3) the rules of classical mechanics are violated, what is caused by substitution of fundamental properties of concrete with various “chain models” (for example, the principle of independence of action of forces, which is the fourth fundamental law of Galileo - Newton, is violated); 4) sections of the general “world theory of creep of reinforced concrete”, based on its algebraization, in their essence reject the fundamental law of natural science - Newton's second law: not only the inertial component is rejected, but also forces depending on speed (in this way the “world theory of creep of reinforced concrete” is degraded to the level of Aristotle’s mechanics); 5) unacceptably idealized creep theories and structural models that endow concrete with unrealizable properties, especially flagrant in zones of cracks, are incorporated in the normative calculations of structures; 6) solid design companies of the world show that concrete creep is not a scientific theory: this is a warning to designers. Results. The performed analysis is accompanied by necessary mathematical calculations and experimental estimates.

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The aim of the research The analyzed here theory is characterized by its authors as a new global harmonized format; it is “coordinated and promoted by international stan- dards institutes within the framework of the global harmonization scenario” [1]. This theory is being actively promoted now by well-known scientists to introduction into the field of internationally recognized regulatory and technical documents and main rules of application. This theory has been widely published and introduced into the FIB Standard, the ASI manual, and other documents [2; 3]. It is approved at various international conferences in the United States, Europe, and Russia, for example, at the First International Scientific and Technical Gvosdev Rea- dings (Moscow, October 2017). Therefore, the analy- sis presented below is important not only for scientific theory, but also for the vast international practice of reinforced concrete construction [4]. We identify and analyze errors in the areas of creep theory, where, as pointed by the leaders and authors of this theory, there is an “established consensus” [1]; we do not offer a different point of view or simplifications in standardization, since the elimination of the identified errors will significantly simplify the theory of long-term resistance of reinforced concrete. The methods About the inconsistency of the theory of creep of reinforced concrete: this system appeared and develops on a set of erroneous principles, rules and unauthorized methods; the inconsistency is aggrava- ted by numerous incorrect substitutions (random or deliberate) of the fundamental experimental properties of concrete; that is based on the inheritance of the principles of the inappropriate Boltzmann's theory of elastic aftereffect. The following comprehensively testifies to the fai- lure of the theory: the presence of a system of gross mathematical errors; violations of the principles and rules of classical mechanics and Eurocodes; inconsistencies with well-known experimental data; negative results of design practices, including global experience in designing unique structures by RAMBOLL structures (United Kingdom) [4]. The fundamental errors analyzed in this article are characteristic not only of concrete creep, but also of the rheology of the whole complex of aging materials. It is known that such materials include “concrete, wood, various polymers and plastics, rocks (also soils), ice, etc., (they) are characterized by the fact that their physicomechanical properties change over time, i.e. depend on the age of the material.” We first consider the set of fundamental experimental properties of concrete. Concrete, as a structural material, has substantially non-linear properties; they are well known from Eurocodes, and began to be introduced to the norms of many countries after the work of L. Baes (1927): 1. “Creep deformations are non-linear from the lo- west loading levels, linear creep area... exists.” So testify the founders of the theory A.A. Gvozdev, N.Kh. Arutyunyan, S.V. Aleksandrovsky, P.I. Vasilyev, figure 18]. As early as in 1931, the nonlinear creep of concrete is manifested in the results of the extensive experiments of R.E. Davis and H.E. Davis. The world format, considering only linear creep of concrete, describes something that does not exist. The character of the curves in figure 1 shows that any of the three curves (σ  0,29Rlim , σ  0,5Rlim , σ  0,75Rlim ) cannot be approximately replaced by a horizontal line σ  0,1Rlim : The values of specific deformations differ by 2-5 times, although we are talking only about a particular situation - simple creep. At variable stresses σt , it is necessary to additionally consider the transition from one curve to another curve. Figure 1. Change in the ratio of specific creep deformations at different initial stress levels Cσ(t, τ) to specific creep deformations at initial stress level C0,1(t,τ) Figure 1 shows a fragment of the extensive experimental data of NIIZHB widely published in various scientific journals; the same data can be obtained from the well-known works of A.D. Ross, R.A. Mel- nik, and other scientists. The ordinate axis in figure 1 shows the values of the ratio Cσ t,τC0,1 t,τ , that is, the ratio of nonlinear creep measures (specific creep deformations), found experimentally at differ- rent levels of constant stresses σ, to the creep mea- sure corresponding to the minimum experimental le- vel of stress σ  0,1Rlim . We remind that the creep measure C t ,τ according to G.A. Maslov is the “creep deformation by the time t from a single stress state that occurred at time τ”. Let us pay attention here to the inconsistency of attempts to describe the non-linear creep of concrete with the help of linear “chain models” arising from the data in figure 1. These attempts first appeared in the work of McHenry (1943) and are still ongoing in the world theory analyzed here. Additionally, we note that these attempts also lead to a violation of the foundations of classical mechanics. A.N. Rzhanitsyn, analyzing the experiments, paid attention: “creep curves change their appearance when constant stress changes”. This indicates, on the one hand, the presence of some parameter μ τ  in the specific creep curveCσ μ τ , ,τ  t  , and on the other hand, the unsuitability of the very common affine similarity condition Cσ  F σ τ ,τ  C t ,τ: F σ τ ,τ   is an experimental nonlinearity function; C t ,τ is a measure of concrete creep. 2. Creep deformations of concrete are unsteady; nonstationarity is taken into account using the aging function φ τ  in the expression of creep measure C t ,τ  φ τ  f t τ, f t τ, “a function that takes into account the increase in time of the creep measure”. The function φ τ  determines the aging process 0 τ  t , φ τ   limC t ,τ. t In scientific literature there are many proposals for the form of recording function φ τ  , substantiated by extensive experiments [8]. In the world theory format considered here, the creep characteristic Φt,τ is used, associated with the creep measure by the relation Φt,τ   C t ,τE τ , Eτ is the elastic modulus. This shows that the use of creep characteristics leads to a greater number of empirical coefficients determined by different experiments. For example, according to N. Аrutyunyan  A1  ατ Φchar  τ  φ τ   E τ C0  E0 1 β e  ,  τ  where E0, β, α are additional elastic modulus constants complicating the aging function. This remark is of no fundamental importance; it points to the unjustified cumbersomeness of the unsuccessful choice. 3. Creep deformations of concrete are damped. As early as in 1955, A.A. Gvozdyev pointed out: “If the ef- fective voltage is still below the limit of long-term resis- tance, then the deformation is non-linear, but fading” [14]. 4. Creep deformations (years) and short-term defor- mations (minutes) of concrete in the experiments appear separately and independently of each other; their ave- rage speeds differ in 518 400 times. For this reason, the substitution of short-term non-linear deformations by deformations of linear “minute creep” is an error. This substitution leads to a violation of the classical mecha- nics principle of independence of action of forces. 5. Short-term deformations of concrete are nonlinear [5]; the σ-εM diagram has a drop-down section and a limited length, figure 2. This property of concrete has been known for more than a hundred years (Ritter, Frank, Zaliger, Bach, Süle, Gastev, Boguslavsky, Rosh, Sakhnovsky, Yoshida, Emperger, Schreier, Nilender, Onishchik, Podolsky, Baykov and others). The curve proposed by Sardzhin (Canada) is used in Eurocode 2. Figure 2. The distortion of the σ-ε diagram of concrete However, in the world format of creep theory, short-term deformations are replaced by Hooke's law. In scientific literature, this linearity of short-term deformations is justified by various unreliable methods. Numerous and thorough experiments of reputable scientists on nonlinear short-term deformation are disavowed. An erroneous statement appears about the “experimentally grounded” instantaneous elastic properties of concrete: “in experiments, instantaneous deforma- tions are linearly dependent on stresses”; “instantaneous deformations are linearly related to stresses and, accordingly, the modulus of elastic-instantaneous deformations does not depend on the value and sign of stresses”; “elastic-instantaneous should be understood as deformations that develop under action of a statistical load at a very high speed”; “concrete is often viewed as a largely inelastic material... Fortunately, it is not. Differences from Hooke's law for concrete are explained by the influence of time... By extrapolation, an instantaneous strain curve is obtained, which is clearly rectilinear.” With surprising persistence, they also fail to hope for chain models, erroneously converting plastic deformation εn, to the minute creep deformation. 6. Short-term deformations of concrete are non-stationary; in the short term chart σ-εM (fi- gure 2) parameters a, b, g are functions of time. For example: a  2 10 5 1e0,03τ  ; according to RBτ εB0  τ experimental data from VNIIG b 2 ,  Eτ 2  2 g   εB0 . RB  τ εB0  τ  7. There is non-linearity of deformation due to the low tensile strength of concrete, which rejects models of norms based on the condition of infinite extensibility of concreteσ τ . 8. Non-stationarity of stressesσ τ  emphasizes the inadmissibility of the use of simplifications in the form of algebraization of the theory of concrete creep [1; 8]. 9. The total deformation of concrete, which occurs under the action of stressσ τ , is the sum of creep deformations and short-term deformations. The substitution of the instantaneous nonlinear deformation εn by the minute creep deformation caused confusion in the results of experimental values, and also in the normalization of the creep characteristic φ∞. Depending on experimenter's arbitrary choice, the creep characteristic is determined in four ways. εn εcr εcr φ1  , φ2  , εl εl εcr εn φ2  , φ4  . εl εn εl where εn is instantaneous nonlinear deformation; εl is instantaneous linear deformation; εcr is creep deformation. For definiteness, we consider high levels of stresses σRB at which it is possible (for analysis) to assume that the deformations are equal to each other. In this particular case, we have essentially different values of creep characteristic (φ12, φ2 1, φ3 0,5, φ4 1): the difference is up to four times, which is unacceptable for use in design practice. 10. At stresses σ  Rsus , exceeding the limit of long-term resistance of concrete, creep deformation is undamped [14]. The combination of the listed fundamental pro- perties of concrete (established by the Eurocode) is unique in its complexity. This set demonstrates practical interests, the need to take them into account in a robust theory of calculation of reinforced concrete, the inadmissibility of neglect of each of the properties. These neglects constitute the insolvency system of the considered world theory, with numerical errors of up to 300% or more, with gross mathematical errors. The beginning of the creation of the theory of concrete creep was carried out in 1940 by the outstan- ding scientist hydrotechnician G.A. Maslov. He intro- duced the classical linear connection between the stress σ(τ) and the compliance function Φ (in the world theory Φ  I t t , ), which characterizes the displace- ment under a single force, by analogy with the potential systems of classical mechanics. He indicated the need to take into account the aging of concrete in the measure of creep and non-stationarity of the mo- dulus of elasticity. G.A. Maslov emphasized, strongly warned that the first step in building the theory was being taken: “to evaluate the creep effect in the operation of concrete and reinforced concrete (hydrotechnical) structures in the first approximation”; “at the present stage, our knowledge in this area has to be idealized... the physical side of the phenomenon”; “we accept as- sumptions..., simplifying mathematical calculations”. The initial and cautious assumptions of G.A. Mas- lov, his urgent warnings are forgotten in the modern world theory of long-term resistance to reinforced concrete. The set of fundamental properties of concrete, in- cluding those formulated in the Principles and Rules of Eurocode 2, and obligatory for use in world norms, is unprecedentedly distorted in modern international standards. In them, the theory of concrete creep is based on other properties and rules: on the erroneous principle of superposition; on non-existent linear pro- perties: on fictional “chain models”; unreasonable re- ferences to the classical Volterra theory are used; algebraization of theory is applied and other errors. We first consider the fundamental error in copying the principle of Boltzmann’s linear superposition. The overlaying principle is the basis of both the modern scientific theory of concrete creep, which received from foreign scientists the name “world harmonized format”, and the developments “in recent decades international standards institutes... for recommendations, norms and technical guidance do- cuments” [1-3]. In these works, it is indicated that McHenry in the USA (1943) “substantiated this tendency by experimental studies of the creep of hermetic specimens according to the principle of superposition characteristic of Volterra's theory.” We give the fundamental law of concrete creep in the original notation [1]: t εσ t  σ  t0 J t,t0  Jt,tdσ t , (1a) t0 where εσt is total strain from stress σ(t); Jt,t  1  φt,t is the compliance function; Ec t Ec t Ect is the non-stationary modulus of elasticity; φt,t is non-stationary creep characteristic, taking into account aging. In scientific publications it is usually integrated in (1) in parts, obtaining σ t t   1 φt,t εσ t     σ t t Ec t  Ec t dt. (1b) Ec t t0 φt,t We note that the term is a creep measure Ec t of concrete C(t,t′), used in publications in in the countries of the former USSR, which is preferable to using the creep characteristic in processing experiments. We emphasize that the aging of concrete is taken into account in φ(t,t′) and C(t,t′), and the modulus of elastic-instantaneous deformation Ec(t′) essentially de- pends on the age of concrete. Equations (1a) and (1b) are justified by two fundamental assumptions: the principle of linear connection between stresses and strains εσt,t σ  t J t,t; (1с) overlaying principle, verbally formulated in various presentation options in numerous well-known publications on the theory of concrete creep, reference books, for example, in [9]. Serious errors in (1a) make the normative theory inappropriate to the Eurocode, unreliable and uneconomical. With an annual volume of 4 billion m3 of application of concrete and reinforced concrete in the world, the losses from such norms and calculations are a significant amount. Recall also the tragedy of the collapse of Transvaal-Park (Moscow, 2004), caused by the problems of concrete creep. We first consider the terms in (1a), (1b), descri- bing short-term properties and deformations. Here, in the world format of the theory, a number of substitutions of properties are made from the fundamental set (1.-10.). The first substitution is a violation of property 5. Nonlinear instantaneous deformation εM  ε εl n , point M in figure 2, is replaced by the elastic deformation εl, point 1 in figure 2: i.e., the real curvilinear diagram of the Eurocode is thrown out and replaced by a fictitious line diagram (figure 2). Article 1.4 (5) of the Eurocode 0 prohibits such unauthorized actions, it indicates the need to justify such actions: it is necessary “to prove that they comply with the principles and, at least, not worse than them in terms of safety, operational suitability and durability, assumed using the relevant article of the Eurocode”. Meanwhile, the first substitution underestimates short-term deformations of concrete to 100%, and in the calculations of compressed structures the error in the ultimate load is up to 500%. The second substitution, unnoticed by scientists, distorts the Hooke elastic model, erroneous here, figure 2; it attaches to the classical linear connection σt E t  a non-existent and unreal body of a viscous fluid, with Newton's linear viscosity coefficient Ec2 t η t  &c : E  t σt0 t 1 εl  t  Ec  0  t0 Ec  t dσ t  t . σ t t  1  с  t0 σ t t E c  t dt. (2) E  t Formula (2) represents the first terms in (1a), (1b), and demonstrates the transformation of a classical nonstationary elastic body into Maxwell's viscoelastic medium. The essence of the second substitution follows from the principle of superposition, the fundamental principle in the construction of the law of creep (1a). The principle of superposition, being a kind of catachresis (abuse), simultaneously combines two concepts that are incompatible in meaning: stationarity and non-stationarity of the mechanical properties of concrete. Borrowing the Boltzmann scheme, the principle of superposition borrows the nonstationarity of the corresponding material properties of this scheme, that is, rejects the fundamental nonstationary linear properties of concrete 6., replacing them with statio- nary properties. The principle of superposition is ap- plied in non-stationary linear properties (1c), under the conditions of the fundamental meaning of this nonstationarity. The mathematical essence of the error arises from the second substitution in the values of deformations of concrete, detected as follows. The rate of elastic deformation is 1  1 ε&l  t  σ& t  σ t . Ec  t t E c  t Integrating, we obtain t 1 t  1 εl  t εl  t0  t0 E tc   dσ t  t0 σ t t E t c   dt. Integrating the first term in parts, we find σt σ t0 εl  t εl  t0    Ec  t Ec  t0 t t  1  1 0 σ t t E c  t dt t0 σ t t E c  t dt. t Hence the short-term deformation is equal to σ t εl  t  ; (3) Ec  t it is also seen that the first term under the integral sign (1a) is excessive, and the use of superposition principle σ t0 t 1 εl  t    dσ t  Ec  t0 t0 Ec  t σ t t  1   σ t dt (4) Ec  t t0 t E c  t in (1a) and (1b) is deeply mistaken. Let us make a numerical estimate of the error ari- sing in determining the instantaneous elastic deforma- tion distorted by the principle of superposition. Using  t   0 const in (3), (4) we obtain σ0 and εl  t0  σ0  const. Comεl  t  Ec  t Ec  t0 parison of these deformations is shown in figure 3. Figure 3. Comparison of εl(t0) and εl(t) Curve 2 in figure 3 corresponds to the VNIIG data on the change of the elastic modulus Ec(t) with time. Errors in the value of the elastic deformation at t = 360 days reach ≈ 300%. Distortions of instantaneous nonstationary nonlinear deformations εn, their attempts of an untenable description, will be considered later. The last term under the integral sign in the law (1b) is the third substitution of the fundamental property 1 of nonlinear creep: the non-existent property of linear creep is used instead. It can be seen from data of figure 1, that the error from such a substitution is up to +400% with t  40 days. If the average curve corresponding to σ  0,5Rlim with its experimental parameters is taken as a basis, then the error from such a distortion will be from +200 to -200%. The fourth substitution is demonstrated by the last part of the integral (1b) t φt t,  t0 Ec  t dσ t , describing the development of creep deformations with σ(t’) variables. The principle of Boltzmann’s linear superposition, corresponding to the stationary properties of creep of the material, is copied with the name of the principle of superposition; that is, substitution of the fundamental property 2 of concrete occurs in this case. This substitution, on the one hand, leads to the loss of three components in the basic law (1a), caused by the rate of change of the coefficient of compliance 1 φt t,  σ t  Ec  t t 1 φt t,  E&c  t σ t  σ  t φ t t,  2 , Ec  t t Ec  t at that they are comparable in importance to the remai- ning term. These losses cause significant discrepancies between theory and experiments, described in the scientific literature. They lead to the incorrect expression of the creep kernel, even within the framework of the non-existent linear creep theory of concrete. The principle of superposition distorts this li- near theory, causing the appearance of additional nonexistent bodies. The number of such bodies depends on the form of the functionφt t,  , which describes the non-stationary creep characteristic in the basic law (1). We write this function in the well-known, widely used in scientific literature, as φt t,  φ  t 1eγt t    , (5) Eс  t Ec  t where φt is a function considering aging of concrete. In the famous monograph of I.E. Prokopovich the creep characteristic φ(t,t′) of foreign scientists is designated asCt,τ these are identical values. In the case of (5) the basic law (1a) forms four superfluous (fictitious) bodies: two bodies of the Voigt type and two viscous elements connected in series with each other. The deformations of these bodies are equal t 1 γt t   , ε1f  t  t0 σ t η1f  t e dt Eс t η1 f  t  ; (6) φ&   t t 1 ε2f  t  σ t dt, t0 η2f  t Eс2  t 1 η2 f  t  & ; (7) Ec  t φ  t t  1 γt t   , ε3f  t  σ t e dt t0 η3f  t Eс2  t 1 η3 f  t   & ; (8) Ec  t φ  t t 1 ε4f  t  σ t dt, t0 η4f  t Eс  t η4 f  t   , (9) φ&   t where η1f, ... , η4 f are viscosity coefficients or coefficients of internal resistance of fictitious bodies; more- over, the bodies (8) of the Voigt and (9) of the viscous element expand when compressed. Creep deformations (6)-(9), caused by the influence of the superposition principle on the classical connection (1c), are fiction; they are also summari- zed with short-term fictitious deformation t  1 ε5f  t  σ t dt: (10) t E  t t0 с 5 εσf  t εif  t , i1 and introduce large errors in the total strain εσ (t), determined by the creep law (1b). This revealed fact of a significant erroneous complication of the theory, caused by the principle of superposition, shows the inconsistency of the judgments of leading scientists currently expressed about the mythi- cal advantages and benefits of this principle, evalua- ting it with the exact opposite: “and, on the other hand, this hypothesis greatly simplifies the phenomenolo- gical theory of creep and makes it simpler and more accessible for use in engineering calculations”; “аs applied to linear creep deformations, the superposition principle was first used by L. Boltzmann (1874), but only recently it was proved (B. Persoz) for non-linear creep deformations”. The fifth substitution violates the fundamental property of concrete 5. In the framework of the requirements of Eurocode 2 to the diagram of instantaneous deformation of concrete (figure 2) it is necessary to recognize the error of the creep theory, the removal of plastic deformation εn from the total instantaneous deforma- tion εM and its transfer into the category of creep deformation εcr(t): plastic deformation εn develops about 1-2 minutes (Aleksandrovsky, Bazant), and creep de- formation εcr(t) lasts for years; the rate of increase of nonlinear deformations is up to 2000 times the rate of increase of creep deformations (in 1 day); growth rate and time of elastic εl and nonlinear deformations εn have the same order; an error is the separation of these deformations by splitting the total quantity εcr in violation of the Eurocode 2 rules. Plastic instantaneous deformation εn is endowed with the name of fast-flowing or minute creep; total deformation of the usual εl(t) and fast-flowing creep εn is sought using a creep measure Ct,  Cопt, Cбпt,, presented in the form of two functions for ordinary and for fast-flowing creep. Such a technique artificially creates unnecessary mathematical difficulties, and a violation of the principle of independence of the action of forces that is fundamental in mechanics (more in section 5) arises; ridiculous results also arise in the design calculations. The mathematical complexity consists in the necessity of constructing an unnecessary integral, followed by defects in the principle of superposition, t  εn  t  σ τ  Cбп t,τ, τ1 τ whereas εн is easily found from the Sargin formula, other equations describing instant diagrams, for example, from Emperger's parabola εn  B2σ2 or from the dependence proposed by NIIZHB σ4  24  εn  3 0,1  . ERlim  2Rlim  Comparing these formulas with each other, we see the fallacy of the integral form, designed to find the fastflowing creep, its artificiality. Let us give an instructive example showing the absurdity of the results obtained using fast-flowing creep deformations. Consider the longitudinal bending of the compressed rack in the interval of one day after loading, when, in the main, only fast-flowing creep has time to appear. A long-term critical force in accordance with the well-known decisions of Rzhanitsyn, Rabotnov, Shesterikov, Prokopovich, is equal π2HI E to Pd  2 , where H  , φff - characterise 1 φ ff tic of fast-flowing creep. This critical force tends to infinity with a length l→0 (figure 4), what is rejected by both experiments and common sense. Figure 4. The schedule of calculation of compressed-curved concrete structures with an initial deflection If instantaneous nonlinear deformations are not added to creep deformations, then we have a tangential-modular (or reduced-modular) critical force with a finite value as l→0. Note that the renaming of plastic deformations εn (figure 2) in the creep deformation εl(t) and their uniform mathematical description  t t  u  t  E t 1 E u LE t,udu in the record of function LE(t,u) leads to distortion of the results of experimental research on concrete creep problems in all countries of the world (see [1]). As a result of such mixing, creep deformations mistakenly acquire initial “vertical segments”, distorting the values of creep deformations (up to 50%), distrac- ting concrete creep researchers and misleading experts in the theory of reinforced concrete. The erroneous assumption of “fast-flowing creep”, “minute creep” and “vertical segments” has distorted the direction of the development of the theory of creep of reinforced concrete. The introduction of this assumption in the norm is detrimental to reinforced concrete construction. Writing a concrete creep measure in the form of such a sum not only leads to mathematical complication of the creep theory, but also violates the principle of independence of the action of Newtonian mechanics. For clarity, we consider a simple and instructive case. We will write down the measure of creep in the form proposed by S.V. Aleksandrovsky (in his notation) Ct, A31et A41et, (11) where A3      const ; A4      const ;  0. “The presence of the second term in the formula... provides an initial steep rise in creep curves for small t-τ”. Differentiating the integral equation (1b) two times in t, taking into account (11), we obtain the second order differential (E = const) equation corresponding to that. &&  E  E& E &&    EA3 EA4&  1 EA3  EA4 . From this equation it is clear that there is a force proportional to the acceleration E   1 EA3  EA4 && t .  The remaining forces are proportional to ,&,&,&& insignificant. In Newtonian mechanics the presence of forces proportional to acceleration, indicates violation of the principle of independence of action of forces, and the impossibility of using expression (11) for concrete creep in practical problems, with variable for- ces σ(t). We will come to the same result if we use many other formulas to describe the creep measure in the form of two or more terms (Yashin, McHenry, Prokopovich, Ulitsky, etc.). The broad interpretation of the compliance factor in the form of “chain models” of type (11), beginning with the work of McHenry, is widely used for the sixth substitution of the fundamental property 1 of non-linear creep of concrete. McHenry, for example, writes a “chain model” in the form of C t ,τC0 1eγt t  Ce1 γ2t 1eγ3t t  . (12) McHenry himself admitted his attempt failed [6], which is not surprising. Here, as in the previous substitution, a violation of the principle of independence of action of forces appears; the principle of superposition here also forms a series of additional fictitious bodies that distort the creep core and the results of the theory. In addition, these defects, complementing each other, give unpredictable results for the theory. We assign numerous untenable attempts to describe the theory of creep with the help of the so-called condition of affine similarity of creep curves to the seventh substitution of property 1 for non-linear creep of concrete In this theory, the instantaneous properties of concrete are usually assumed to be non-stationary elastic, and the compliance function I(t,t’), depending on the parameter μ(t’), is written in the usual form 1 I t t,     Cσ μ t , ,t t . Ec t Further, it is erroneously considered that the parameter μ is the stress σ (the seventh substitution). 1 I t t,   Ec  t  F σ t ,t C t t ,  . As the eighth substitution, it is considered possible to write the specific creep deformation Cσ μt, ,t t in a degenerate form (see also property 1). In accordance with the principle of superposition, we have the law of creep σt εσ  t   Ec  t t   1  t0 σ t t E tc    F σ t ,tC t t , dt. (13) Then a mathematical error appears, consisting in incorrect differentiation of the second integrand and the loss of the term F F   σ σ& t  t C t t ,  , (14)  what distorts the original superposition principle (13) and leads to appearing of the second (ninth substitution) principle of superposition in the basic creep law in the second integral term σ t t  1 εσ  t  c  t0 σ t t E c  t dt E  t t C t t ,  t0 σ t F σ t ,t t dt, (15) and appearing of the second fictitious force σc  t  σ t F σ t ,t , acting independently of the first force σ(t’) (related to development of instantaneous deformations). We note that the loss of term (14) distorts the meaning of experimental data on the nature of specific creep curves corresponding to different levels of loading, what follows from (15): nonlinearity function F σ t ,t removed from the essence of the curves Сσ and transferred to the force σ(t'), what formed a new non-linear relationship between stress and strain. We present one of the numerous formulations jus- tifying the erroneous law (15) in form of H. Leaderman: “...Boltzmann's principle of superposition of deformation with time was used... When deriving rheological equations for materials ‘with memory’ satisfying the closed cycle condition, Boltzmann postulated a linear relation between stresses and strains and used a hypothesis allowing to consider recovery. While the principle of superposition was reduced as a natural additional hypothesis. Later it was shown (Leaderman) that the principle of superposition does not require a linear connection between stresses and strains.” Comparing (15) and (1a), we emphasize that the nonlinear theory of concrete creep not only repeats the errors of the linear theory, but also adds two new significant errors to them: it incorrectly determines the parameter and function of nonlinearity of creep; supplements the linear erroneous principle of superposition with additional erroneous principle of superposition, which is nonlinear. The essence of the very principle of superposition, its connection with the Boltz- mann scheme and its “chain models”, was analyzed in detail in [15]. Recently, works have emerged that develop the “modification of the principle of strain superposition for nonlinear creep” in the form t  1  εt t, 0   ε t0  0 E τ C t ,τdσс  τ , (16а) t  where σсτ Sστ is known stress function σ(τ). The fallacy of this record is similar to that used in (1a). The total strain rate here is v t, &S   E1  C t,   S    dd E1      (16б) S   C t,   S   t C t, . This shows that in (16a) the last three terms of (16b) are lost. The significance of these terms is identical to the significance that we described above in paragraphs 1-3. It should be additionally taken into account that the identity of the nonlinear function S[σ(τ)] is also incorrect for short and long deformations. “Modification” not only saves the gross errors of the nonlinear theory (15), but also adds new ones: - instantaneous deformation, as before, is endowed with a mythical body of viscous fluid according to Maxwell's scheme, but the error is qualitatively preserved in the complicated structure shown in figure 3; - nonlinear creep is based on the untenable and non-existent condition of affine similarity, however, the nonlinearity function is now determined not from creep experiments, corresponding to figure 1, and from experiments on short-term loading (figure 2), and has no relation to the creep measure C(t,t'). The results The mathematical analysis of the existing errors of the modern theory of long-term resistance of reinforced concrete is carried out: in the values of instantaneous deformation, the error is up to 300%; in va- lues of long deformation - up to 250%. There are many substitutions due to the non-stationarity property 8 of the stress σ(τ). With such substitutions, the creep law is empirically converted to the form of some algebraic expression. Stresses here are replaced by a variety of values: constant stress; conditional “average equivalent stress over a period of time t t0 ”; stress is replaced by a certain function (linear, parabolic), depending on the creep characteristic of concrete, the mean-theorem is also involved; other empirical untenable substitution. N.Kh. Arutyunyan, S.V. Alek- sandrovsky repeatedly show the inconsistency of alge- braic creep theories: the condition of a unambiguous algebraic connection between C(t,τ) and σ(τ) is “devoid of physical meaning”; such a connection “leads” to implausible results.


About the authors

Rudolf S Sanzharovsky

L.N. Gumilyov Eurasian National University

Author for correspondence.

D.Sc. in Technical Scien- ces, Professor, Senior Research Fellow

11 Kazhymukana St., Astana, 010000, Republic of Kazakhstan

Maxim M Manchenko

Krylov State Research Center


PhD in Technical Sciences, Senior Research Fellow

44 Moskovsky Prospekt, Saint Petersburg, 196158, Russian Federation

Muhlis A Hadzhiev

Azerbaijan University of Architecture and Construction


D.Sc. in Technical Sciences, Professor, Head of the Department of Building Structure

11 Ayna Sultanova St., Baku, AZ1073, Republic of Azerbaijan

Turlybek T Musabaev

L.N. Gumilyov Eurasian National University


D.Sc. in Technical Scien- ces, Professor, Academician, Director of the Eurasian Institute of Technology

2 Satpayev St., Astana, 010000, Republic of Kazakhstan

Tatyana N Ter-Emmanuilyan

Russian University of Transport


Doctor of Technical Sciences, Professor of the Department of Theoretical Mechanics

9 Obrazcova St., bldg. 9, Moscow, 127994, Russian Federation

Kirill A Varenik

Yaroslav-the-Wise Novgorod State University


PhD in Technical Sciences, Associate Professor

41 Big Saint Petersburg St., Velikiy Novgorod, 173003, Russian Federation


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Copyright (c) 2019 Sanzharovsky R.S., Manchenko M.M., Hadzhiev M.A., Musabaev T.T., Ter-Emmanuilyan T.N., Varenik K.A.

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