EA018263B1 - Method of probabilistic assessment of building parts physical deterioration - Google Patents

Abstract

The present invention relates to the research in the sphere of safety assessment of the use of buildings and their flexible parts and it involves developing a probability scale for building parts physical deterioration assessment. The method which includes assessment of averaged rate of building parts physical deterioration on the basis of quantitative assessment of the current technical status of its parts and an entire building in comparison with the initial status of technical and operating abilities of building parts and an entire building is presented. According to the invention a rise in probability of failure of a flexible building part or its destruction at the known time interval is taken up as a wear index of a flexible building part, average strength of the part at the beginning of operation and in the known time interval is determined, indexes of initial and maximum allowable part failure or destruction probability at a building part entire working life are estimated, by the results obtained by means of division of the remainder of average values of initial and maximum allowable density by 100% and by a building part working life value a percentage scale and a time scale which characterize a wear rate of the building, on the basis of which taking into account a rise in a building part failure or destruction probability the status of a building part is estimated by the expressionwhere φ- change in failure (destruction) rate over the period ΔT in the ratio 1 in a unit time; uand u- value of argument (strength index), for which it is necessary to determine failure (destruction) probability at the beginning and at the end of the period under review; Pand P- probability density distribution at the beginning and at the end of the period under review; b - upper limit of probability density distribution.2

Description

(57) The invention relates to research in the field of assessing the safety of the use of buildings and their elastic elements and involves the development of a probabilistic scale for assessing the degree of physical deterioration of building elements. A method is proposed that includes determining the average degree of physical deterioration of a building based on a quantitative assessment of the current technical condition of its elements and the building as a whole compared to the initial state of the technical and operational properties of structures and the building as a whole. According to the invention, an increase in the probability of its failure or destruction over a known period of time is taken as an indicator of the physical wear of an elastic element of a building, the average strength of an element at the beginning of operation is determined and after a known period of time, the values of the initial and maximum permissible probability of failure or destruction of an element for the entire service life according to the obtained values by dividing the difference between the average values of the initial and maximum permissible strength by 100% and the value of the service life the element is formed by the percentage and time scales characterizing the measure of wear of the building element, on the basis of which the state of the building element is assessed due to the increase in the probability of its failure or destruction by building the relationship

l where ψί is the intensity of the change in the probability of failure (destruction) for the period ΔΤ in fractions of 1 per unit time; u and u + v are the value of the argument (strength indicator), for which it is necessary to determine the probability of failure (failure) at the beginning and end of the period under consideration; R; and P _m the probability density of the distribution at the beginning and end of the period in question; B is the upper limit of the probability density of the distribution.

018263 B1

The invention relates to research in the field of assessing the safety of the use of buildings and their elastic elements.

A known method for assessing the physical deterioration of residential buildings [1, 2], including the concept of physical deterioration of the structure, element, engineering equipment system and the building as a whole, which is understood as the loss of the initial technical and operational qualities (strength, stability, reliability, etc.) as a result the impact of climatic factors and human life. Physical depreciation at the time of its assessment in [1] is expressed by the ratio of the cost of objectively necessary repair measures that eliminate damage to the structure, element, system or building as a whole, and their replacement cost.

Thus, the valuation method given in [1, 2] does not determine physical wear (reduction of strength, stability, reliability, etc.), but cost wear, at which 100% of wear occurs when the cost of the objectively necessary repair measures is reached, eliminating damage to structures, element, system or building as a whole, the cost of new damaged objects and their integration into the system or building during the inspection period. Therefore, this amount of depreciation depends on the prevailing market prices for construction products, materials and repair work during the survey period. Therefore, the evaluation method [1] of the so-called physical wear and tear to the physics of the process of loss of strength of building products and structures is very indirectly related, and the definition of the term physical wear (of a building, element) does not correspond to the meaning of this term.

There is a method of assessing the obsolescence of a building (element) [3, Appendix 1], which is characterized by the degree of mismatch of the main parameters that determine living conditions, the volume and quality of services provided to modern requirements. This method slightly affects the safety of the building, although it often plays a significant and even decisive role in choosing the type of repair, modernization and reconstruction.

A known method for assessing the physical deterioration of a building (element) is given in [3, Appendix 1], where it is said that the physical wear of a building (element) is a value that characterizes the degree of deterioration of the technical and related other operational indicators of the building (element) at a certain point time. Such a definition of the term physical deterioration has a comprehensive qualitative character without describing the specific possible quantitative estimates that are necessary for making technical decisions.

Thus, the currently used [1, 2, and 3] definitions of the concepts of moral and physical depreciation do not allow us to present a method for real-time assessment of the wear of an element of a building and the building as a whole.

As a prototype of the invention, the fundamental work of E.P. Matveeva [4, p. 44], in which physical deterioration is characterized as a quantitative assessment of the technical condition, showing the proportion of damage compared with the initial state of the technical and operational properties of the structures and the building as a whole. In [4], the values of the average degrees of wear of Moscow and St. Petersburg houses of mass development are given, reaching 40-50% at the age of buildings over 50 years old. And this is in the conditions of the necessary repairs.

Further in [4, p. 163] to theoretically evaluate the decrease in the reliability of the system in time Y (T), consisting of a set of building elements, the statement is used that the time to reach the critical set O under fairly general assumptions made for a wide class of practical problems has an exponential distribution, so that Y ( T) “exp (-T / T _cr ), where T is the current time and T _cr is the average time to reach a critical level. According to the authors of the invention, the average time to reach a critical level corresponds to the definition of overhaul [3, p. 10], which states that the overhaul of a building is a repair in order to restore its resource ....

Such a general approach to assessing a decrease in the reliability of the normal functioning of a building cannot characterize individual elements whose state can decisively affect the state of the entire structure of the building or its individual systems. But the main drawback of the concept of wear adopted in [4] is its extension to comparison with the initial state of technical indicators, including the strength properties of the building’s power elements. This means that average wear and tear in the amount of 50% doubles the design strength of the supporting structures of buildings, and, subject to possible fluctuations, significantly more. Then why, with an average level of depreciation of up to 50%, thousands of buildings in Moscow and St. Petersburg still have not collapsed?

Consequently, the main drawback of the concept of physical deterioration proposed in [4] is its attribution to the initial physical characteristics of the building and the absence of its (physical deterioration) assessment of taking into account the increase in time of the failure probability of each building element. According to the authors of the invention, to conduct a more objective assessment of the technical and operational condition of the building, its physical wear should be attributed not only to the initial physical characteristics of the building, but to an increase in time of the probability of failure or destruction of each element. This probability of failure or failure in the limiting state should not exceed Ν (Τ) = 0.5, which approximately corresponds to the average value of the estimated parameter without taking into account the inherent probabilistic spread of all quantities (coefficients) included in the determination of the calculated value of the parameter.

- 1 018263

The objectives of the proposed method for assessing the probable wear of building elements are to assess the dynamics of the values of the probability of failure or destruction of the elastic element of the building during their operation during the service life;

development of a probabilistic scale for assessing the degree of physical deterioration of building elements;

limits of the practically possible value of the used physical parameter of the elements according to the probability factor of failure or destruction.

The technical result corresponding to the stated objectives of the invention is achieved by a new method for the probabilistic assessment of the wear of building elements, including determining the average degree of physical wear of a building based on a quantitative assessment of the current technical condition of its elements and the building as a whole compared to the initial state of technical and operational properties of structures and buildings in General, according to the method according to the invention as a physical indicator of the wear of the elastic element of the building they increase the probability of its failure or destruction over a known period of time, determine the average strength of the element at the beginning of operation and after a known period of time, establish the values of the initial and maximum permissible probability of failure or destruction over the entire life of the element, according to the values obtained by dividing the difference between the average values of the initial and the maximum permissible strength of 100% and the value of the life of the element form the percentage and time scales characterizing the measure of wear of the building element Based on which estimation is performed of the building element state due to increase in the probability of its failure or destruction by constructing dependencies

where φ ₁ - the intensity of the change in the probability of failure (destruction) for the period ΔΤ in fractions of 1 per unit time;

Ф ₁ and Ф _{1 + 1} - probability of failure (destruction) of a building element at the beginning and end of the period under review, share 1;

and ₁ and _{1 + 1} - the value of the argument (strength indicator) for which it is necessary to determine the probability of failure or failure at the beginning and end of the period under consideration;

P ₁ and P _{1 + 1} - probability density of distribution at the beginning and end of the period in question;

B is the upper limit of the probability density of the distribution.

Elements of a building are structures or engineering systems that make up a building and are designed to perform specified functions [SNB 1.04.01-04, p. 3].

The method is based on the fact that the probability of failure or destruction, which underlies the determination of strength characteristics and defines the concept of reliability of a building element, is taken as a physical parameter that is the main parameter in the wear characteristics of building elements. Accordingly, the authors define such wear and tear as probabilistic wear.

The essence of the method for assessing the probable wear of building elements includes determining the initial level of probability of destruction or failure of a new element and its average strength, the maximum acceptable level of probability of failure or destruction and the minimum acceptable average strength with periodic determination of these parameters by various experimental methods during the life of the building element and analysis dynamics of change over time.

As a result of such monitoring, the current values of the average strength of the element, the probability of failure or destruction, and the intensity of their change are determined.

To compare the measured changes in the average strength values and fracture probabilities with the planned ones, a scale of average percent strength changes (MPa /%) is developed, for which the maximum permissible decrease in average strength and an increase in the probability of fracture (% /%) are taken as scale of changes in time, for example, for 1 year, the average values of strength and the growth of the probability of failure or failure (MPa / year and% / year). The scale of average percent changes in strength characterizes a measure of probabilistic wear, and the scale of changes in time characterizes a measure of temporary wear.

The phenomenon of physical wear and tear of any design, as well as of a material that is hard and substantially limited in ductility, is largely analogous to the concept and mechanism of the metal fatigue phenomenon described in [4, p. 585-586]. The basis of this mechanism is the idea of the polycrystalline nature of the material and the inevitability of its heterogeneity, which creates the possibility of microcracks. Moreover, in the case of stresses caused by static loads, such microcracks are not dangerous. If stresses are time-varying, which is typical for building structures (wind and snow loads, repair and holiday events of residents, etc.), then there is a tendency to the development of microcracks, which ultimately lead to fatigue failure of both individual elements and whole building structures. Such a fracture mechanism is analytically described in the Griffiths-Orowan theory. An explanation of the dependence of the fatigue endurance limits of metals on the dimensions of the cross-section of parts and other laws and characteristics

- 2 018263 give statistical theory of fatigue [4, p. 597]. The main factors affecting fatigue wear are considered [4, p. 598-601] the influence of the surface condition, including corrosion, as well as microroughness, loading and pause modes, overloads, training and temperature fluctuations. Each of these factors and their combination can have a significant impact on fatigue wear. So, plastic deformation of the surface layer can give an increase in the endurance limit by 10-20%. The presence of significant compressive residual stresses in the surface layer impedes the formation of fatigue cracks and therefore increases the endurance limit.

A significant effect on the strength properties of a material is exerted by its homogeneity [5, p. 454]. For example, for steel grade St.Z, the uniformity coefficient is taken in the amount of k0 = 0.85-0.90, which approximately corresponds to the coefficient of variation of strength near K _in »0.05 (5%). The values of the coefficients of variation in the values of concrete strength under construction conditions are K _in »0.1-0.2 (10-20%) and decrease with increasing average strength. To account for snow load in [5, p. 454] a load factor of 1.4 is recommended, which may vary. Therefore, with any method of calculating building structures, including the limit states, it is necessary to take into account the stochasticity of the material properties and loads on the building structure.

Given the significant stochasticity of the processes of destruction of materials and products, their wear should be evaluated from the point of view of increasing the probability of failure or destruction (lowering reliability) with increasing operating time. An example of what has been said is the case of a roof collapse in the gym of the Red-Polish School [7]. Stroynauk Unitary Enterprise 16 gymnasiums similar to the emergency were examined, and significant defects and damages were found in the supporting structures, including through cracks with an opening of up to 1.6 mm of inclined orientation in the support nodes of dummy reinforced concrete trusses with a span of 24 m - the main supporting structures of these gyms . In addition to these signs of wear, shear of concrete was found on the heads of the elongated truss racks under the supports of the coating slabs, as well as horizontal and inclined cracks in the interface nodes of the trusses with truss belts [7]. Thus, the collapse of one roof out of 17 gives about 6% (0.06) of the probability of destruction or 94% (0.94) of the reliability of functioning up to the point in time. For the safety factor adopted during the design of gyms, taking into account a possible excess of the roof covering mass by 25-30% compared with the design coefficient of variation in strength, it can be K _in »0.13 to implement 1 case out of 17. Here it is also necessary to take into account that the destruction of the head of one of a dozen or more farms supporting the gymnasium roof can lead to a peculiar chain reaction of destruction and the collapse (rapid lowering) of the roof of the building, as happened in one of the Moscow markets.

Therefore, the probability of destruction (failure) of a building element can serve as a quantitative indicator of physical wear, as it depends on changes in average strength.

If we accept the change in the probability distribution of the strength values of the building structure or the element Ν (χ), corresponding to the Gaussian law (normal distribution law), which is recognized by most researchers, then for the normal distribution Ν (χ, σ ² ) the probability density of the distribution of P (x) at x is expressed [8, p. 12-14] equation

P (x) = - == - exp (2) where σ is the standard deviation;

σ ² is the dispersion;

X; - the numerical value of the distributed value;

^x is the average value.

Then the probability of failure (destruction) of the building element Ф (и) corresponds to the value of the normal distribution function N (0,1), determined from the expression (3) where

- ^y , ~ ^x

If the distribution of the values of the required strength indicator of a building element differs significantly from the normal law (for example, it is described by the Weibull probability density distribution) and is described by a positive continuous finite function P, (x). then the probability of failure (destruction) Ф; (щ) of an element is determined from the expression where a is the lower limit of integration (the beginning of the distribution density function), which can

-3 018263 accept values from -oo to any final value, including 0;

B is the upper limit of integration (the end of the distribution density function), which can take values from any finite value, including 0, to + oo;

AND; - the value of the argument (strength indicator), for which it is necessary to determine the probability of failure (destruction) of the building element.

If the function P (x) is described in the scientific and technical literature, then the value of Φι (χ) can be determined using the corresponding tables.

For any function P (x), the value Φι (χ) can be determined graphically (the ratio of the area under the curve from a to X [to the area from a to b) or by calculation (summation with any required degree of accuracy).

The authors of the invention believe that, based on the materiality of the probabilistic nature of the failure, the average value ^{x of the} value used should be taken as an indicator of 100% wear. Then the old buildings of St. Petersburg and Moscow, which reached 30-40% wear, retain reliability of more than 80%.

The change in the probability of failure (failure) is graphically determined by the change in the area under the curve 3 in accordance with FIG. 1, where P (s) is the probability density of the distribution of strength values; Di - the relative decrease in the average value of strength during operation of the element.

As can be seen from FIG. 1, a decrease in the average strength by the value of Di leads to an increase in area 1, which is equivalent to the probability of failure of the new distribution probability density curve 3 in comparison with the area 2 of the initial curve 4.

All calculations to determine the probability of failure (failure) are even more simplified by using the theoretical symmetry of the normal curve of the probability density distribution of strength values.

In accordance with [1.2], the degree of depreciation is usually expressed as% of the total depreciation taken as 100% of depreciation. If in [1, 2] the wear assessment is presented in% of the total cost of the element being examined, then for physical wear the possible range of change (decrease) in the strength or other physical indicator is limited to the maximum allowable value with a given maximum allowable probability of failure. Therefore, the concept of 100% depreciation for physical indicators means the full maximum permissible exhaustion of the stock of the determined parameter.

Based on the described feature, each percentage of probable wear is an indicator of the growth of the probability of failure (destruction), and the percentage of wear is a hundredth of the maximum permissible interval of the probability of failure from the initial moment to the overhaul T _cr of a building element. In addition, depreciation can be characterized by an increase in the probability of failure per unit time (for example, per year), which is also of practical interest.

Thus, due to the significant curvilinearity of the dependence of changes in the probability of failure to reduce the average value of strength, the scales of possible wear are non-linear, the values of the divisions are not the same at different time periods.

It should be noted that the probability of failure or destruction of a building structure or its element with a known type of probability density distribution of strength values can be quantified for any operation period ΔΤ in accordance with the expression

14 _{/ +} | / b <Ρ-, = [ ^φ . (»Ί) - ^φ , ₊ ι (» _{ί +} ι)] / ^Δ 7 = p, (m,) bi / ar (5)

As an example, the following is a calculation of the probable wear and tear rating of a reinforced concrete beam with a service life of up to overhaul T _cr = 50 years and a maximum permissible fracture probability of 5% (0.05), which corresponds to the often accepted reliability level of 95% (0.95 ) The average initial strength of the beam T = 40.0 MPa with a standard deviation determined as a result of bench tests, σ = 6.0 MPa, which corresponds to the coefficient of variation K _in = 0.15. The probability density distribution of the beam strength values in a first approximation corresponds to the Gauss law (normal distribution law).

1. The reliability of the beam is found according to

⁷ _g ? ' , -Ko / 1 L <' ² > ai = ____ | exp G 72? ’

(6) where and is the parameter of the normalized deviation characterizing the reliability of the obtained data.

2. The values from 14 ₀ (u) = 0.999 (99.9%) to the maximum allowable ^ (u) = 0.95 (95%) are taken as the initial values of the reliability of the beam. For the given extreme values of reliability, the probabilities of failures (failures) are from the initial Фо (и) - 0.001 (0.1%) to the final Ф _к (и) = 0.05 (5%), and according to the table the normal distribution functions [8, from. 188] it is easy to determine and ,, = 3.1 and and _k = 1.64. Then

-4 018263

Δυ = and ₀ - Ic = 1.46 (7) and the maximum allowable decrease in concrete strength

Δσκ = Di-σ = 1.46-6 = 8.76 MPa. (8)

The initial design strength of the beam t _to - g ₀ -n ₀ <7 = 40.0-3.1 6 = 21.4 MPa (9) and the final maximum permissible average strength t * = Г _о - Lie ₄ σ = 40.0 - 8.76 = 31.24 MPa (10)

Then the final maximum permissible design strength should be the same value

B = C = 31.24 - 1.64 - 6 = 21.4 MPa, (11) but the average value of strength decreased by 8.76 MPa or about 22% while maintaining the same distribution parameters.

3. The percentage and time scales of beam wear are determined by dividing the difference between the average values of the initial and maximum permissible strengths by 100% and the service life before overhaul. So, for the beam under consideration, the measure of wear of 1% is f _k = Yes _k / 100 = 8.76 / 100 = 0.0876 MPa /%, (12) and

Фк = а _к / бр = 21.4 / 50 = 0.1752 MPa / year. (thirteen)

The calculation results for other values of Ρ (ΐ), similar to those given above, are presented in Table. one.

Table 1

No. F (c) Ν (α) and Δσ Δτ ,. = Δινσ, MPa MPa ψκ, MPa /% Tkr. years old Fc MPa / year one 0.001 0,999 3.10 0 0 40,0 0 0 0 2 0.005 0,995 2,58 0.52 3.12 36.88 0,0369 5 0.624 3 0.01 0,990 2,32 0.78 4.68 35.32 0,0353 10 0.468 4 0.02 0.980 2.05 1.05 6.30 33.70 0,0337 twenty 0.315 5 0,03 0.970 1.88 1.22 7.32 32.68 0,0327 thirty 0.244 6 0.04 0.960 1.75 1.35 8.10 31.90 0,0319 40 0.202 7 0.05 0.950 1,64 1.46 8.76 31.24 0.0876 fifty 0.175

In FIG. Figure 2 shows the dependences and = ί (Ρ) - curve 1 and Δΐ = ί (Ρ) - curve 2, the construction of which uses the data [8, Table. one]. These graphical dependencies simplify practical calculations.

As an example of the application of the parameters of probabilistic wear to assess the condition of the beam due to the growth of the probability of its failure (destruction) when using the data in table. 1 and FIG. 2 in FIG. Figure 3 shows the dependences u = ί (ΔΤ _k1 ) and Διι = ί (ΔΤ _k1 ), which for this example turned out to be approximately linear within 30 <T <40 MPa and analytically having the following form:

u = 1.4 + 0.17 ^ -t * ₍ ) (14)

Δη = 1.7 - 0.17 (g ₀ -g *,) (15)

Next, we consider 2 options for calculating beam wear: a uniform decrease in average strength and a uniform increase in the probability of failure over the entire service life. The results of these calculations, the methodology of which is similar to the above, using tables [8] are presented in table. 2 and in FIG. 4, in which solid lines 1 and 2 depict the dependences of a uniform decrease in average strength and the probability of failure (failure) P, (T) = G _; (T). Dashed lines 3 and 4 depict the dependences of a uniform increase in the probability of failure (failure) over the service life period P _k (T) = G;, (T) and the corresponding decrease in the average strength T _k , = G | (T) in time.

table 2

Beam operating time 7 years 5 10 fifteen twenty 25 thirty 35 40 45 fifty 1st option (uniform decrease in average strength) MPa 39,124 38,248 37,372 36,496 35.62 34,744 33,867 32,992 32,116 31.24 Ψκ.ι,% /% 0.015 0.010 0.013 0.015 0.02 0,022 0.017 0,0325 0.04 0.05 fc, MPa / year 0.1752 0.1752 0.1752 0.1752 0.1752 0.1752 0.1752 0.1752 0.1752 0.1752 P (7),% 0.15 0.2 0.4 0.65 1.0 1.35 1.9 2.6 3,5 5,0 1st option (uniform increase in probability of failure) P (7),% 0.6 1.1 1,5 2.0 2,5 3.0 3,5 4.0 4,5 5,0 Ψκ, ί,% /% 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 Phi MPa / year 0.32 0.15 0.09 0,07 0.06 0.05 0.04 0.04 0,03 0,03 t ,,, MPa 36.8 35.3 34,4 33.7 33.1 32.6 32,2 31.8 31.5 | 31,2

As can be seen from the data given in table. 2 and in FIG. 4, with a uniform decrease in the average strength of the beam over time (Fig. 4, line 1), the growth curve of the probability of failure (line 2) has an almost exponential form with a positive exponent, which is generally characteristic of the development of fracture processes. To ensure a uniform increase in the probability of failure (dashed line 3), a decrease in the average strength of a building structure or element should occur along a curve (dashed line 4) that is close in shape to an exponent with a negative exponent. It follows that in order to maintain the necessary level of reliability of the building structure for a long time, the intensity of decreasing its average strength should significantly decrease with increasing operating time or the average intensity over the entire period should not exceed _k = (T _o -Sk) / T _cr - 0.1752 MPa / year.

It should be noted that in the case of a significant difference in the actual distribution density of the individual measured strength values from the normal distribution law, the calculation of the change in the probability of failure (destruction) of a building structure is complicated, but always possible. Depending on the type of the distribution density curve, the growth rates and the values of the failure (destruction) probability of building structures achieved over time can vary.

The practical application of the proposed method is based on the use of currently known methods for assessing the strength of the structure under investigation (beams) and simple summation of the changes on an accrual basis. In this case, the average value of the residual strength of the product (beam) is determined every 10% of the service life or, in the case of an accelerated increase in the probability of failure or destruction, at shorter intervals as a result of at least 4-5 tests using current methods or other regulatory documents.

The proposed method has no negative consequences and allows the design of optimal technical solutions for repair, modernization and reconstruction of buildings and to prevent emergencies and disasters at construction sites.

Claims (1)

CLAIM A method for the probabilistic assessment of the physical deterioration of building elements, including determining the average degree of physical deterioration of a building based on a quantitative assessment of the current technical condition of its elements and the building as a whole compared to the initial state of the technical and operational properties of structures and the building as a whole, characterized in that as an indicator physical wear of the elastic element of the building take an increase in the probability of its failure or destruction for a predetermined period of time, op divide the average strength of the element at the beginning of operation and after a predetermined period of time, set the values of the initial and maximum permissible for the entire service life probability of failure or destruction of the element, according to the obtained values by dividing the difference between the average values of the initial and maximum permissible strength by 100% and the term element services form the percentage and time scales characterizing the measure of wear of the building element, on the basis of which the state of the building element is assessed due to increases the probability of its failure or destruction by constructing the dependence where φ ₁ is the intensity of the change in the probability of failure (destruction) over the period ΔΤ in fractions of 1 per unit time; and ₁ and _{1 + 1} - the value of the argument (strength indicator), for which it is necessary to determine the probability of failure (destruction) at the beginning and end of the period under consideration; P ₁ and P _{1 + 1} - probability density of distribution at the beginning and end of the period in question; B is the upper limit of the probability density of the distribution.