Reliability study of irrigation canals and pipe culvers

. The measures taken made it possible to improve the operation of the research object, the culvert capacity, it makes it possible to ensure the reliability indicators of structures at the required level, and also, according to preliminary calculations, to increase the reliability of the irrigation canal and its structures by 3-4% and increase the water supply by 5-7%. And the calculations performed confirm that the availability factor is related to the average duration of the elimination of the failure.


Introduction
The reliability of an object should be understood as its immeasurable description.However, it can be estimated based on the operating experience of this or similar object, using the methods of mathematical statistics and probability theory.
Reliability theory is a new branch of science that studies the general laws that must be observed in the design, construction, installation, testing and operation of objects or their elements in order to achieve the greatest efficiency.
Designing an arbitrary object, system requires knowledge of analysis methods according to reliability criteria and quantitative indicators.
The creation of a reliable system, structures and devices is the main task of the theory of reliability.We can say that this theory is common to all technical means.However, their specific features must be taken into account when developing measures to predict and improve the reliability of hydraulic structures.
Modern irrigation systems consist of dozens and hundreds of individual elements of an organized complex that perform very important tasks.
Reliability is understood as a property of a technical object associated with its ability to maintain the required functions over time in a given mode and operating conditions.Reliability is a complex property that is usually characterized by many conceptual indicators such as integrity, durability, maintainability and good preservation [14].

Methods
For this purpose, research was carried out on the reliability of the operation of irrigation canals during their operation in the Kasba and Mirishkor regions of the Karshi steppe, and as a result of statistical processing and analysis of the data, the relevant indicators were determined.
In the course of the research, information on the technical condition of irrigation canals was processed, information on destruction and repair and restoration work was again processed, while the observation time was 21 years.The data for the initial period of operation are based on observations and data from repair and restoration organizations, and for the last 7 years, based on the results of studies conducted by the Department of Hydraulics and Hydraulic Structures in 2014 ... 2021.The number of destructions by years of operation is presented in Table 1.As can be seen from the table, the number of destructions in the first 5 years is large.It describes the period of adaptation to the operation of the tray network during use.In subsequent years, the amount of destruction decreases and has some constant characteristic.This corresponds to the normal period of use.The distribution of types of damage, destruction and inoperability of irrigation canals and hydraulic structures on them, corresponding to the commissioning period, was determined.
Along with this, since the 9-10th year of operation, an increase in the number of destructions has been observed, among other reasons, corrosion and aging of the object can be mentioned.
The distribution of destruction of irrigation canals and their structures by months of the year was studied and it was found that they have different values by months.This situation is due to climatic factors, for example, seasonal temperature fluctuations, freezingthawing processes, installation of irrigation canals and structures for short-term storage in winter and spring after storage, re-commissioning, and during the growing season with the beginning of the crop irrigation period.It has been observed that destruction occurs less frequently in the post growing season than at any other time.Such data were also recorded in experiments carried out by some researchers on the channels of the Karshi steppe [1].

Results and discussion
The destructive runoff parameter, which is one of the most important indicators in the theory of reliability, is determined as follows for an irrigation canal and its elements (per 1 km of canal length).When determining this indicator, it is necessary to take into account the fact that the canal network will be operational during the season, as well as the possibility of stopping idle sections of the channel.Based on this, we accept the coefficient of use of the irrigation network during the growing season =0.We determine the laws of distribution of the probability of failure of the irrigation canal and its pipeline distribution structures and, based on the calculations, establish the statistical and theoretical functions of the probability of operation without failure (Fig. 1).
In practice, the experience of operating the system shows that many sudden failures occur during the operation of the irrigation canal.It has been determined that failures that usually look like this obey the law of exponential distribution [2]. ( where λ is the parameter of the exponential distribution.When the breakdown flow parameter obeys this law, the time changes are negligible, i.e. (3) When establishing the theoretical function of the probability of non-failure of the irrigation canal system and structures on it, according to its form, the statistical function also obeys an exponential law.
We check the compatibility of the above theoretical and statistical distributions using the Kolmogorov criterion.In this case, the maximum value of the modulus of the difference between the statistical and theoretical functions was taken as a measure of difference [2]. (4) In our case, we got D = 0.172.Then we proceed to determine the parameter of this exponential distribution: (5) For these calculations, we use the table given in the literature [32, p.279], and by the value of λ we determine P(λ) = 0.857.As a result, this means that the value of the maximum difference between the statistical and theoretical functions is not less than the actual one [3].
Hence, for our case, the conditions of the Kolmogorov matching criterion are satisfied.The mean time of failure for a kilometer section of an irrigation canal is: To obtain the value of the mean time of failure-free operation, the probability of failure and the probability of failure-free operation of the studied irrigation canal per one kilometer were respectively determined: Based on the calculations, the following conclusions can be drawn: During the commissioning of the irrigation canal and the pipe culvert in it (in our country this period is five to seven years), it was observed that the flow failure parameter is much higher than during the normal operation period, and this situation is explained by the uneven failure of the canal.However, it should be noted here that during normal operation, the flow failure parameter tends to a constant increased value, and this proves the correctness of the accepted law for distributing the operating time of the irrigation canal and its structures without failure.
----ο-----static; ------------theoretical.Based on the theory of reliability, irrigation canals and their hydraulic structures, in particular pipe culverts, are part of the system of objects to be restored; channel.Here, the complex coefficient of index readiness [3] is taken as a reliability indicator: Here, as a reliability indicator, a complex coefficient of index readiness is adopted [3]: where T av is the average recovery time; T 0 is the mean time not to fail, determined by: (10) where f(t) is the non-failure probability distribution density.According to the results of calculations, the time distribution density and the function for determining the failure of irrigation canals are shown in Fig.According to calculations implemented in practice, the availability factor of the entire network is K t = 0.86 and it is confirmed that it is lower than the value recommended by Academician S.E.Mirshulava [2].As a result, on the basis of the calculations performed in the original project, the introduction of reserves was not planned.Proposals for the implementation of additional measures in the pipe culverts of the Kamashi-Mirishkor concrete irrigation canal served as the basis for the construction of additional equipment and devices.[14,15]

Conclusions
The measures taken made it possible to improve the work of the research object, the culvert capacity, made it possible to ensure the demanded level of the reliability indicator of structures, as well as to increase the reliability of the irrigation canal and its structures by 3-4% according to preliminary calculations, and increase the water supply by 5-7%.The calculations performed confirm that the availability factor is related to the average duration of the elimination of the outage.[16,17,18] Having drawn conclusions, we can say that the results obtained allow us to determine the elements that do not meet the requirements during the operation period, or make it possible to determine the frequency of restoration and repair work.[19,20,21]

8 .
It has been established that for the first five years in the irrigation canal, the average values of the destructive flow parameters are within 0,59• ...0,44• 1/(h• km).In the subsequent decade of operation, this value significantly decreased, and the average destruction flow parameter was within 0,29• ...0,48• 1/(h0km).According to the results, the arithmetic mean values were 0,34• 1/(h•km), standard deviations (S = 0,22• ).The upper and lower values of the destruction flow parameter were respectively equal to 0,25• 1/(h km) and 0,36• 1/(h km).These values confirm the results obtained by the researcher R. Khodzhakulov for the flume channels of the region with similar conditions.

Fig. 1 .
Fig.1.Probability function of non-failure of the irrigation canal

2 .
It is established that finding the outage time and the delivery time of information about the outage obey the lognormal distribution law.The calculation work and the distribution law are determined on the basis of the methodology and program developed at the National University of Water Management and Natural Resources of Ukraine [1]. 1 -empirical distribution line; 2 -theoretical density of lognormal distribution; 3empirical distribution function; 4 -theoretical density of the lognormal distribution at the parameters μ = 5.6 h.

Fig. 2 .
Fig. 2. Theoretical density and log-normal distribution function of the time to determine the failure of the irrigation canal.

Fig. 3 .
Fig. 3. Distribution density of the restoration time of a concrete irrigation canal. 1 -empirical distribution density; 2 -theoretical distribution density.

Fig. 4 .
Fig. 4. Restoration time distribution function of a concrete irrigation canal.

Table 1 .
The number of destructions by years