ASSESSMENT OF THE STRENGTH OF THE CROSS-SECTION OF THE GROUND CANAL

ABSTRACT

In this article, the problem of assessing the strength of the cross-section of earthen canals is analyzed. The study considers the relationship between the geometry of the canal, the physical and mechanical properties of cohesive soil, and the influence of water. The use of shear force (tangential stress) methods in determining strength is substantiated.

The article analyzes the main factors influencing the stability of canal walls, including slope angle, viscosity, internal friction angle, and sediment transportation processes. The decrease in soil strength as a result of the influence of water movement is substantiated. Also, the reliability of canal slopes was assessed using the safety factor, and engineering solutions aimed at increasing it were proposed. The research results serve to develop effective and reliable solutions for the design and operation of earth canals.

АННОТАЦИЯ

В данной статье анализируется вопрос оценки устойчивости поперечного сечения каналов в земляных руслах. В исследовании рассматривается взаимосвязь геометрии канала, физико-механических свойств несвязного грунта и воздействия воды. Обосновано применение методов касательных напряжений (сдвигающей силы) при определении устойчивости.

В статье анализируются основные факторы, влияющие на устойчивость стенок канала, в том числе угол откоса, сцепление, угол внутреннего трения и процессы переноса наносов. Обосновано снижение прочности грунта в результате воздействия водного потока. Также посредством коэффициента запаса прочности оценена надёжность откосов канала и предложены инженерные решения, направленные на её повышение. Результаты исследования служат разработке эффективных и надёжных решений при проектировании и эксплуатации земляных каналов.

Keywords: earth canal, tapestry-shaped canal, water flow, sediments, strength, displacement force, dynamic strength, washing rate, bottom sediments, suspended sediments.

Ключевые слова: земляной канал, трапециевидный канал, водный поток, наносы, устойчивость, тяговое усилие, динамическая устойчивость, размывающая скорость, донные наносы, взвешенные наносы.

INTRODUCTION. Today, methods for determining the dynamic strength of the channel cross-section are divided into two groups depending on the approaches used, depending on their characteristics. The first is the method of permissible flow velocities used in the CIS countries, and the second is the method of tangential stresses (displacement force) used more in Western countries. The second method is a physical approach, on the basis of which the flow of the transporting channel fully forms the known width, depth, and longitudinal slope of the given amount of water and sediments in its channel. In many cases, this approach goes beyond the limits of its applicability when applying various empirical morphometric relationships. Therefore, this approach suggests incorporating various hydrodynamic models based on numerical methods [1-5, 7, 9,10].

The other group of methods is based on the results of the analysis of tangential stresses occurring at the bottom of deformable channels under the influence of channel flow. Initially, this approach was used only for the conditions of static strength of the channels, i.e., at flow velocities not exceeding the non-erosion velocity. However, some studies [1, 3, 8, 11] show that with certain limitations, if channel sediment transport exists in canals, it is possible to correctly draw the geometry of their bottom using this method. This circumstance expands the scope of application of the approach under consideration and allows for its wider use in the design of dynamically stable soil canals [4, 6, 11].

The problem of channel shape at boundary equilibrium was solved using the Forchheimer-Lein method, which uses the following limitation: the flow velocity decreases to zero as it approaches the bottom line, and the effect of the water displacing the particle is considered proportional to the local displacement force.

Lane and Chou [12, 13] obtained the following expressions for the permissible (critical) specific washing force (shifting force), taking into account the boundary equilibrium of the soil particle in water, internal friction forces, and its suspended state in water.:

a) at the bottom

                                           (1)

b) on the side slope

                                                       (2)

here  design diameter of the soil, m;  specific gravity of suspended soil in water (H/m³);  density of soil, taking into account its suspended state in water, kg/m³, determined as follows:

here  respectively, the density of soil particles and water, kg/м³;  soil porosity; acceleration due to gravity, м/s²;  coefficient of internal friction of soil in water.

Using the shear force method, two types of problems can be solved: determining the permissible shear stresses and permissible slopes of the water flow for given soils and the transverse profile of the channel, and constructing a stable channel profile at a given slope. The first type of problem usually arises when calculating the static equilibrium of channels with a trapezoidal profile, and the second - when calculating channels with a curvilinear cross-section.

Let us consider the second type of problem, characteristic of irrigation and land reclamation systems. The strength of trapezoidal channel beds is primarily determined by the strength of lateral slopes (hereinafter referred to as slopes), as they are more susceptible to the erosive effect of the flow compared to the canal bed. For channels with reinforced side slopes, the strength is mainly determined by the resistance of the bottom soil to erosion. Therefore, when forecasting the strength of such sections, it is necessary to consider the condition of the lateral slopes and bottom separately.

MATERIALS AND METHODS.We will take into account the influence of the maximum shear force  on the ratio of the lateral slope coefficient  and  separately. The value of  is taken to be proportional to the angle of inclination of the lateral slope , i.e., . Such a connection is studied in detail in [12], and theoretically, it is reflected in [12].  The influence of the ratio  on  can be represented by the following relationships for the base by approximating the data of the US Bureau of Land Reclamation. These relationships are expressed as coefficients  for slope and  for bottom when the water depth is equal to the maximum design depth :

дада да                                       (3)

да да                                  (4)

Then the calculated values of the maximum shear force on the slope  and at the bottom  are determined, respectively, as follows:

                                                     (5)

                                                            (6)

Taking into account the suspending forces of the soil under the action of water, the total force , moving an element located on the slope (volume , projection area ) with a lateral slope coefficient , will be as follows (Fig. 1):

                                     (7)

The holding force  is defined as the sum of the gravity of the soil suspended in water, the internal friction force , and the cohesion forces  of the soil in the water:

                                                (8)

Equalizing the displacing and holding forces, assuming , after performing algebraic transformations and adding the multiplier (for reserve)

Assuming , we get:

                                           (9)

here  is the calculated diameter of the soil, m; it is taken on homogeneous soils (coefficient of unevenness , and on uneven soils .

From equation (9), the strength of the lateral slope  along the cross-section of the channel is expressed as follows:

                                   (10)

Accordingly, the maximum slope of the channel flow, allowing for slope erosion, is determined from this expression

                                        (11)

Including for unbound soils

                                          (12)

                                        (13)

In practical calculations, in formulas (10) - (13), it can be assumed that . Here  is the hydraulic radius.

RESULTS AND DISCUSSION. The dependencies given in (10) - (13) give a more accurate result in determining the strength of trapezoidal channels, since they more fully take into account the properties of the soil and the acting forces and can be applied for a wide range of coefficients  (practically any ). Considering the limiting equilibrium of the soil element at the bottom of the channel, respectively, the strength criterion  of the channel bottom (longitudinal profile of the channel) is taken as follows, and the maximum permissible slope  of the channel-forming flow to erode the bottom is determined as follows.

                                                   (14)

 .                                                (15)

Formulas (14) - (15) for determining the strength criteria were verified using experimental data obtained in the work [14]. Based on the generalization of these data, the values of the strength criteria for the calculated stages of the sediment flow were determined.

These experiments were conducted on a rectangular hydraulic tray with a variable slope. When analyzing the experimental results, we consider the influence of the ratio  on the magnitude of tangential stresses through the coefficient . The values of this coefficient were determined based on the data presented for the rectangular channel in Fig. 2 (b).

Comparison showed that due to the influence of the b/h ratio and taking into account the strength properties of the soil, the proposed criterion (14) is equal to

                                                                  (16)

is a much more stable quantity than the criterion. In the sample of 113 experiments - for the case of soil particle sizes from 0.185 mm to 4.5 mm (as well as gravel and crushed stone fractions), the relative root mean square deviation of τ, obtained using criterion (14) for the beginning of erosion, is as follows: for sediments, the obtained value was σ= 28.2%, and without taking into account gravel fractions (for 82 experiments) - 20%. The average value of the fundamental strength criterion for this stage was found to be  and, accordingly, the mobility criterion: . Similar deviations (according to experiments) are also observed in the values of the strength criterion, calculated not by the flow depth , but by the hydraulic radius. When using the hydraulic radius, it is not required to introduce the coefficient  for the effect of the ratio , since this effect is mainly felt in cases where  is present.

The strength criterion , expressed by the hydraulic radius , is written as:

 .                                                 (17)

Similarly, calculations for the strength criterion of the bed bottom were carried out based on experimental data for two more characteristic stages of sediment movement - the beginning of ridge formation and the beginning of suspended movement of the soil.

The average values of the strength criterion obtained for these stages according to formula  (14) are:

5.18 - for the beginning of gria formation,

1.08 - for the beginning of soil movement in the water.

Accordingly, the fundamental mobility criterion received the following values:  and .

The beginning of intensive erosion of granular sand sediments is approximately characterized by the following relationship: , where  is the coefficient of internal friction of the soil in water.

The beginning of suspended motion of the soil is characterized by approximately

Initial data show that the permissible strength criterion for the calculated stages of sediment formation on slopes can be taken as close to the critical values obtained for the bottom.

The design phase of sediment movement is selected depending on the type and function of the water flow. For canals with a water discharge of , the strength is determined by the stage at which individual soil particles begin to erode. Such canals are usually water intakes for a closed drainage network and are used in drying and humidification systems.

Such canals serve to regulate the level regime of reclaimed lands. More stringent requirements will be imposed on them to ensure the design parameters of the cross-section and the connection of the land reclamation network in the vertical plane during operation.

In channels with , the strength criteria corresponding to the initial stage of grain formation are adopted. Because the mobility of granular bottom sediments prevents their growth.

For the largest canals, when the maximum water discharge is , the calculation stage is taken as the beginning of the movement of the soil in the water. In this case, only design discharges during the flood period are taken into account, since their duration of influence on the channel is not long. In regulated river-water intake (water intake) channels of the land reclamation network with a water discharge greater than , the channel process develops more intensively. Therefore, it is advisable to calculate such channels based on the dynamic equilibrium condition using morphometric relationships that take into account the laws of channel process development.

When calculating the strengthening of the bottom and slopes with a protective fill made of coarse-grained materials, the beginning of the washing of individual soil particles is taken as the calculation stage.

CONCLUSION. Consequently, the issue of assessing the strength of the cross-section of earth canals is currently one of the most pressing problems. The obtained experimental data were analyzed, and the study established the relationship between the geometry of the canal, the physical and mechanical properties of the unbound soil, and the influence of water. The use of shear force (tangential stress) methods in determining strength is substantiated.

Based on the obtained data, the main factors influencing the stability of canal walls were analyzed, including the angle of inclination, viscosity, angle of internal friction, and sediment transportation processes. As a result of the influence of water movement, the decrease in soil strength was substantiated. Also, the reliability of canal slopes was assessed using the safety factor, and engineering solutions aimed at increasing it were proposed. The research results serve to develop effective and reliable solutions for the design and operation of earth canals.

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