The main elements of open pit mining, pit or trenches without securing slopes is the height N and width l ledge, its shape, steepness and angle of repose α (rice. 9.3). The collapse of a ledge occurs most often along the line Sun, located at an angle θ to the horizontal. Volume ABC called a collapse prism. Prism collapse is kept in equilibrium by frictional forces applied in the shear plane.
Violation of the stability of earth masses is often accompanied by significant destruction of bridges, roads, canals, buildings and structures located on sliding massifs. As a result of a violation of strength (stability of a natural slope or artificial slope), characteristic elements are formed landslide(rice. 9.4).
Slope stability analyzed using limit equilibrium theory or by treating a prism of collapse or sliding along a potential sliding surface as a rigid body.
Rice. 9.3. Soil slope diagram: 1 - slope; 2 - sliding line; 3 - line corresponding to the angle of internal friction; 4 - possible outline of the slope during collapse; 5 - soil mass collapse prism
Rice. 9.4. Landslide elements
1 - sliding surface; 2 - landslide body; 3 - stall wall; 4 - position of the slope before landslide displacement; 5 - bedrock of the slope
Slope stability mainly depends on its height and type of soil. To establish some concepts, consider two elementary problems:
- slope stability of ideally loose soil;
- slope stability of a perfectly cohesive soil mass.
Slope stability of ideally loose soil
Let us consider in the first case the stability of particles of an ideally free-flowing soil composing the slope. To do this, let’s create an equilibrium equation for a solid particle M, which lies on the surface of the slope ( rice. 9.5,a). Let's expand the weight of this particle F into two components: normal N to the slope surface AB and tangent T To her. At the same time, the strength T tends to move the particle M to the foot of the slope, but it will be hampered by an opposing force T", which is proportional to normal pressure.
Slope stability of a perfectly cohesive soil mass
Let's consider slope stabilityHELL height N k for cohesive soil ( rice. 9.5,6). A violation of equilibrium at a certain maximum height will occur along a flat sliding surface VD, inclined at an angle θ to the horizon, since the smallest area of such a surface between points IN And D will have a plane VD. Specific adhesion forces will act throughout this plane WITH.
Areas that limit non-working ledges are called berms. There are safety berms, mechanical cleaning berms and transport berms. Safety berms are equal to 1/3 of the height distance between adjacent berms. Mechanical cleaning berms are usually greater than or equal to 8 meters (for the entry of bulldozers to clear the fallen rock).
Transport berms are areas left on the non-working side of a quarry for the movement of vehicles. Safety berms are platforms left on the non-working side of a quarry to increase its stability and retain crumbling pieces of rock. Usually they are slightly inclined towards the overlying slope of the ledge. Berms should be left no more than 3 ledges apart. The collapse prism is an unstable part of the ledge between the slope of the ledge and the plane of natural collapse and is limited by the upper platform. The width of the base of the collapse prism (B) is called the safety berm and is determined by the formula:.
The procedure for the development of open-pit mining
The order of development of open-pit mining within the quarry field cannot be established arbitrarily. It depends on the type of deposit being developed, the surface topography, the shape of the deposit, the position of the deposit relative to the prevailing surface level, the angle of its dip, thickness, structure, distribution of the quality of minerals and types of overburden rocks. A further consequence is the choice of the type of open-pit mining: surface, deep, upland, upland-deep or submountain. Our further action is a fundamental preliminary decision about the quarry field - its possible depth, dimensions along the bottom and surface, slope angles of the sides, as well as the total reserves of the quarry mass and minerals in particular. Possible locations of consumers of minerals, dumps, tailings storage facilities and their approximate capacities are also established, which makes it possible to outline possible directions and routes for moving quarry cargo. Based on the above considerations, the possible dimensions of the quarry field, its location in connection with the surface topography, as well as the approximate contours of the mining allotment of the future enterprise are established. Only after this, taking into account the planned capacity of the quarry, do they begin to solve the problem of the order of development of mining operations within the quarry field. To accelerate the commissioning of the quarry and reduce the level of capital costs, mining operations begin where the mineral deposit is located closer to the surface. The main goal of open-pit mining is the extraction of minerals from the subsoil with the simultaneous extraction of a large volume of overburden covering and enclosing the deposit, which is achieved with a clear and highly economical organization of the leading and most expensive process of open-pit mining - the movement of rock mass from the faces to receiving points in warehouses and dumps ( up to 40%). The efficiency of moving quarry cargo is achieved by organizing sustainable flows of minerals and overburden rocks in relation to which the issues of opening the working horizons of the quarry field are resolved, as well as the capacity of the vehicles used. Technical solutions for open-pit mining and its economic results are determined by the ratio of the volumes of stripping and mining work in general and by periods of quarry activity. These relationships are quantified using the stripping ratio.
Steep trenches and half-trenches
Based on the angle of inclination, capital trenches are divided into steep ones. Steep, deep trenches usually have an internal layout. Based on their location relative to the quarry side, they are divided into transverse and diagonal. Transverse steep trenches are used in cases where the overall angle of repose of the quarry side is less. Diagonal steep trenches are commonly used to accommodate conveyor and vehicle lifts. Steep trenches are typical when transport berms (ramps) are left on the non-working side.
Temporary exits
The main difference between temporary exits and sliding ones is the following:
1. Temporary ramps do not move (do not slide) during alternate mining of the upper and lower benches within the limits of the ramps;
2. The construction of temporary ramps as a rule (in rock and semi-rocky formations) includes drilling and blasting a rock block within the ramp to the height of the ledge and driving the ramp, most often with the movement of the blasted rock to the floor slope with an excavator or bulldozer;
3. Mining of old ramps is carried out by excavating blasted rock and loading it into vehicles;
The route of temporary ramps is simple or loop; the elongation coefficient of a simple temporary route depends mainly on the width of the working area. Car ramps can be adjacent to horizons on a guide slope, a soft slope (with a gentle insert) and on a platform. An abutment on a guide slope is typical for ramps on upper, already developed horizons when vehicles move through them along these ramps.
The main types of earthworks in housing and civil construction are the development of pits, trenches, site planning, etc.
An analysis of injuries in construction shows that earthworks account for about 5.5% of all accidents, and of the total number of accidents with severe outcomes for all types of work, 10% are associated with earthworks.
Rice. 1. Slope diagram
The main cause of injuries during excavation work is soil collapse. The causes of soil collapse are mainly the development of soil without fastenings, exceeding the critical height of the vertical walls of trenches and pits, improper design of fastenings for the walls of trenches and pits, etc.
The developed soils are divided into three large groups: cohesive (clayey and similar); loose (sandy, bulk) and loess.
Excavation work can only be started if you have a work plan or technological maps for soil development.
According to safety regulations, digging pits and shallow trenches in soils of natural moisture and in the absence of groundwater can be done without fastenings. There are two ways to prevent collapse and ensure the stability of soil masses: by forming safe soil slopes or by installing fastenings. In most cases, soil collapse occurs due to a violation of the steepness of the slopes of the excavations and trenches being developed.
The main elements of open-pit development of a quarry, pit or trench without fastening are the width l and height H of the ledge, the shape of the ledge, the angle of repose α, and the steepness. The collapse of the ledge most often occurs along the line AC, located at an angle θ to the horizon. Volume ABC is called the collapse prism. The collapse prism is kept in equilibrium by trepium forces applied in the shear plane.
For cohesive soils, the concept of “angle of internal friction” φ is used. These soils, in addition to frictional forces, also have adhesive forces between particles. The adhesive forces are quite high, so the cohesive soil is quite stable. However, during mining (cutting), soils are loosened, their structure is disrupted and they lose cohesion. Friction and adhesion forces also change, decreasing with increasing humidity. Therefore, the stability of loose slopes is also unstable and remains temporary until a change in the physico-chemical properties of the soil, associated mainly with precipitation in the summer and a subsequent increase in soil moisture. Thus, the angle of repose φ for dry sand is 25...30°, wet sand 20°, dry clay 45° and wet clay 15°. Establishing a safe bench height and angle of repose is an important task. The safety of pit development depends on the correct choice of slope angle.
Based on the theory of rock stability, the critical height of the vertical wall at α=90° is determined by the formula of V.V. Sokolovsky:
Where N cr is the critical height of the vertical wall, m; C - soil adhesion force, t/m2; ρ - soil density, t/m 3 ; φ - angle of internal friction (C, ρ, φ are determined from the tables).
When determining the maximum depth of a pit or trench with a vertical wall, a safety factor is introduced, taken equal to 1.25:
The slope of a pit or trench constructed in loose soils will be stable if the angle formed by its surface with the horizon does not exceed the angle of internal friction of the soil.
In quarries developed to great depths (20...30 m or more), the greatest danger is posed by landslides that can cover the lower area of work along with machines, equipment and service personnel. The greatest number of landslides occurs in spring and autumn during periods of active flood water, rain and thawing.
The maximum permissible depth of pits and trenches with vertical walls without fastenings H pr, as well as the permissible steepness of slopes (the ratio of the height of the slope to its foundation - H:l) for various soils are given in the table. In the case where there is a layering of different soils along the height of the slope, the steepness of the slope is determined by the weakest soil.
When developing pits and trenches as preventive measures to combat landslides and collapses, the following work is carried out with a calculation justification: construction of retaining walls; deliberate collapse of overhanging canopies; reducing the slope angle by cleaning with draglines or dividing the slope into ledges with the installation of intermediate berms.
The vertical walls of trenches and pits are secured using both inventory and non-inventory devices.
Table 1. Acceptable parameters of slopes made without fastenings
| Soils | N pr, m | Excavation depth, m | |||||
| up to 1.5 | until 3 | up to 5 | |||||
| α, deg | H:l | α, deg | H:l | α, deg | H:l | ||
| Bulk uncompacted Sand and gravel Sandy loam Loam Clay |
1 1 |
56 63 |
1:0,25 1:0,5 |
45 45 |
1:1 1:1 |
39 45 |
1:1,25 1:1 |
Types of fastenings may be different. Their designs depend on the type of soil, excavation depth and design loads. In cohesive soils of natural moisture, panel fastenings are installed (with a gap of one board, and in wet loose soils - continuous. The spacers of such fastenings are made sliding.
The fastenings are designed for active soil pressure. Active pressure in sandy soils, where the adhesion forces between particles are insignificant, Pa,
Where H is the depth of the trench, m; ρ - soil density, t/m3; φ - angle of repose (angle of internal friction for cohesive soils), degrees.
For cohesive soils, active soil pressure
Where C is soil cohesion.
When calculating fastenings in cohesive soils, it should be taken into account that when calculating pits and trenches, the soil on the surface loosens and loses cohesion, so the second part of the formula in some cases can be ignored.
The diagram of active soil pressure is a triangle, the vertex of which is located along the edge of the trench, and the maximum value of pressure p max is at the level of the bottom of the trench.
Rice. 2. Panel mounting diagram:
1 - spacers; 2 - racks; 3 - shields; 4 - pressure diagram 
Rice. 3. Anchoring of trenches:
1 - anchor; 2 - guy; 3 - collapse prism; 4 - shields; 5 - stand
In spacer-type fastenings, fastening boards, racks and spacers are subject to calculation. Spacers are designed for strength and stability.
The distance between the racks of the panel inventory fastening depends on the width of the boards used h:
In cases where spacers in trench fastenings make it difficult to carry out construction and installation work in them, for example, laying pipelines or other communications, guy lines and anchors are used instead of spacers.
It should be noted that the installation and disassembly of the non-inventory fastenings used, consisting of individual boards, racks and spacers, is associated with labor-intensive and dangerous work. The work of dismantling such fasteners is especially dangerous. In addition, non-inventory fasteners require high material consumption and have a low turnover of fastening material, which increases their cost.
External additional load when developing excavations (dumping earth, installing construction machines at the edge of a slope, etc.) can cause the collapse of soil masses if their location is not taken into account.
Taking into account additional loads when determining the active soil pressure is carried out by bringing the additional load to be uniformly distributed on the collapse prism with a density equal to the density of dense soil.
Rice. 4. Scheme of formation of the “visor” a 
Rice. 5. Installation of an excavator when developing a pit or trench
The height of the additional load thus obtained is added to the depth of the trench. When developing deep pits with an excavator equipped with a straight shovel and installed at the bottom of the excavation, a “peak” is formed.
Table 2. Allowable distances L
This occurs due to the fact that with this installation, the excavator forms slopes equal to 1/3 of the boom height. The danger of the “canopy” collapse leads to the need to install excavators equipped with a backhoe at the top of the excavation being developed. When construction machines are located near an excavation with unreinforced slopes, it is necessary to determine the distance L from the machine support closest to the excavation to the edge of the slope (Fig. 1). This distance depends on the height of the excavation H, the type and condition of the soil and is determined from the table. 1 and according to the formula
When constructing buildings and structures from ready-made structures and parts using a large number of construction machines and mechanisms, the construction site turns into an assembly site.
Installation of structures consists of mutually interconnected preparatory and main processes. Preparatory processes include the construction of crane tracks, delivery of structures, large-scale assembly of parts, arrangement of scaffolding for the work of installers; the main processes include slinging of structures, lifting, installation of structures on supports, temporary fastening, alignment and final fastening of mounted elements. Most accidents during the installation of building structures occur due to errors in the design of buildings and structures; in the manufacture of structures in factories, in work projects, etc.
The main issues of safe organization of work, in addition to choosing the most rational installation method and the appropriate sequence of installation of individual elements, are: determining the necessary devices for the production of all types of installation processes and work operations (types of conductors or other fixing devices, rigging equipment, etc.); installation methods that prevent the possibility of dangerous stresses arising during the lifting of structural elements; methods of temporary fastening of mounted elements, ensuring spatial rigidity of the mounted part of the building and the stability of each individual structural element; the sequence of final fastening of elements and removal of temporary devices.
The most important factor for eliminating injuries during the installation of building structures is the correct calculation of structures during transportation, storage and installation.
During transportation, large-sized structures should be installed on two supports and calculated according to the single-span beam scheme. The accepted design scheme for transportation, as a rule, does not coincide with the design scheme adopted when calculating the structure for the main impact. The wooden supports on which the structure rests should be checked for bending.
Rice. 6. Scheme for securing the truss during transportation:
1 - spacer; 2 - cable; 3 - bracket; 4 - farm; 5 - lanyard; 6 - traction; 7 - loop
When transporting long columns on spreads, the support on the trailer must be movable, allowing free rotation, in order to eliminate transverse bending moment. The number of stacked rows in height is up to 5.
Rice. 7. Raising the truss with a traverse:
1 - traverse; 2 - farm
Wall panels and partitions are transported in a vertical or inclined position. In this case, dangerous lateral shocks are possible in the plane of least rigidity of the panel. To localize them, special shock absorbers are used, installed in the supporting parts. When transporting large-sized through trusses, special panel carriers are used, and the sections are checked according to the most dangerous sections of the truss elements. Determination of forces in braces and truss nodes is carried out using structural mechanics methods, taking into account the dynamic coefficient and the adopted system of supporting the truss during transportation. On panel carriers, trusses are secured using stops and guy wires (Fig. 1).
The safety of work during the installation of structures is ensured primarily by correctly designed traverses and slings. When lifting and installing trusses (Fig. 5.2), the forces in individual elements can be significantly greater than those calculated for operating loads. It is also possible for them to change the sign of the stresses - stretched elements may be compressed and vice versa. Therefore, as a rule, when lifting, the traverse is secured to the middle nodes of the truss.
Columns are not additionally calculated for the load arising during lifting. The working drawings of the columns provide for the possibility of safely lifting them from a horizontal to a vertical position (Fig. 3).
Rice. 8. Lifting the column:
1 - column; 2 - cable; 3 - frame grip; 4 - wooden linings
When installing a column in a foundation shell, before embedding its base, the column must be secured with braces or wedges (Fig. 4). In both cases, the column is calculated for the action of wind load. If the support is not sufficiently secured, the columns may topple or tilt. In general, the stability equation has the form
Where K is a safety factor equal to 1.4; M 0 - overturning moment due to wind, Nm; M y - holding moment created by the mass of the column, N m; M closed - the same, with fastening, Nm.
In cases where, according to the calculations made, stability is not ensured, inventory wedge inserts and steel conductors are used.
Rice. 9. Temporary fastening of columns during installation:
1 - brace; 2 - clamp; 3 - column; 4 - wedges; 5 - foundation 
Rice. 10. Temporary fastening of structures:
a - extreme truss; b - medium farms; 1 - column; 2 - farm; 3 - stretching; 4 - spacer
The assembled individual elements of the structure (columns, trusses, beams) must form stable systems until the full range of installation work is completed. To do this, individual parts of the mounted elements are connected into spatially rigid systems using permanent connections, purlins or temporary braces.
When lifting structures, slings, steel and hemp ropes, traverses and various grips are used.
The method of slinging and the design of the sling depends on the dimensions and weight of the element being mounted, the location of the slinging points on the element being lifted, the lifting equipment used, the lifting conditions and the position of the element at various stages of installation. Slings are divided into flexible ones with one, two, four and six branches and rigid ones such as traverses or grips.
Force in each branch of the sling
Where α is the angle between the vertical and the sling; G - weight of the lifted load, N; n - number of slings; k - coefficient.
As the angle of inclination of the sling branches increases, the compressive forces in them increase. Take α = 45... 50°, and the angle between the branches of the slings is no more than 90°.
Sling branch length
where h is the height of the sling; b - distance between slings diagonally. 
Rice. 11. Scheme of forces in the branches of the sling 
Rice. 12. Dependence of forces in the branches of the sling on the angle between the slings
Sometimes chains are used instead of ropes for slinging. The choice of ropes or chains is based on the highest tension of the rope branch S: 
where P is the breaking load, which is taken according to the breaking force of the rope given in the manufacturer’s passport or according to the diameter of the chain link, N; K - safety factor (3...8), depending on the type of slings and lifting mechanisms.
To increase the service life of slings, prevent crushing and abrasion against each other or against sharp corners of the edges of structures, twisting, and impacts, inventory metal pads are used.
Rigid slings are used when the lifting height of the assembly crane is insufficient or when the structure being lifted does not allow the use of flexible slings. As a rule, a rigid sling is used in the form of a traverse. Crossbeams are most widely used during the installation of prefabricated reinforced concrete trusses and beams, especially prestressed ones, as well as long-span metal structures. Traverses are used in two types: bending and compression.
Recently, a progressive method of installing large-block structures has been increasingly used, which makes it possible to reduce their labor intensity, increase work safety and construction time. The dimensions and weight of steel structures shipped from factories are limited by the carrying capacity of vehicles and the dimensions of production premises. Typically, the length of the elements sent is 12... 18 m. Sometimes, at the request of customers, roof trusses are supplied up to 24 m long.
When carrying out various construction and installation works, scaffolding and scaffolding made of metal tubular elements are used, in the operation of which there are defects, often leading to collapse. Scaffolding and scaffolding are temporary but reusable building structures.
Sometimes severe group accidents may occur due to scaffolding collapses. An analysis of a number of emergency cases showed that their collapse occurs for a number of reasons, which are divided into three groups.
The first group is a complex of reasons caused by unsatisfactory design of scaffolds without taking into account the actual operating conditions of the structure. For example, fastening scaffolding to the vertical surface of a construction site is carried out using anchor plugs of various designs, staggered across two tiers in height and through two spans along the length of the building. However, fastening in this way is not always possible due to the various features of the structures to which these scaffolds must be attached. When changing the scheme of fastening scaffolding to a building, the operating conditions of the scaffolding for different types of loads change, the design of the structure changes, which can cause an accident of the latter.
The second group is the reasons discovered at the stage of manufacturing and installation of scaffolding. Inventory scaffolding must be manufactured using industrial methods. However, in practice this is not always possible. Often scaffolding is made directly on the construction site without a corresponding design or with sharp deviations from the design values and dimensions. Often, when installing scaffolding, builders replace missing elements with others without calculation and theoretical justification for such replacement. Before installing the scaffolding structure, it is necessary to carefully prepare the foundations for their further installation, since the stability of the entire structure depends on the condition of the support. When installing scaffolding, it is necessary to ensure the necessary drainage of surface and groundwater, failure to do so could result in damage to the foundation under the scaffolding.
The third group - the causes of forest collapse relate to the stage of their exploitation. They are often the result of insufficient technical guidance or lack of supervision during the installation and operation of scaffolding.
According to statistics, a significant number of forest accidents occur due to overload. Violation or change in the loading pattern of scaffolding, which is usually designed for a certain type of load according to a predetermined layout, can lead to their collapse.
The scaffolding consists of racks arranged in two rows with a step between the racks in two mutually perpendicular directions equal to 2 m in the axes, as well as longitudinal and transverse crossbars installed every 2 m in height. To ensure that the nodes do not move, horizontal diagonal connections are installed in each tier through 4...5 panels.
According to the method of connecting scaffolding elements to each other, the most common in construction practice are two types of metal tubular scaffolding.
Scaffolding with boltless connections has an unchangeable frame design for both masonry and finishing work. Branch pipes are welded to the racks, and round steel hooks bent at right angles are welded to the crossbars. With this method of fastening, the installation of each horizontal element of the scaffolding is reduced to inserting hooks into the corresponding branch pipes of the racks until they stop.
Scaffolding of another type - on connections in the form of hinged clamps. In this case, different distances between the posts are accepted in relation to the loads during masonry and finishing work.
The spatial rigidity of the entire scaffolding frame is additionally ensured by placing diagonal connections in the vertical plane along the outer row of posts in the three outer panels at both ends of the scaffolding sections.
Rice. 13. Scaffolding with boltless connections:
a - installation diagram of scaffolding; b - detail of supporting the tubular stand; c - coupling of horizontal elements with the stand; g - node, fastening scaffolding to the wall
Based on their design characteristics, scaffolding is divided into frame, ladder, rack, and suspended. Forests are divided according to their purpose: for the production of stone and reinforced concrete, finishing and repair work; installation of structures; construction of shell vaults. 
Rice. 14. Scaffolding with hinged clamps:
a - installation diagram (dimensions in brackets - for finishing work); b - hinge element
Scaffolding used for masonry is installed (increased) as the work progresses. Scaffolding for finishing and repair work is erected to the entire height of the facility before work begins. Lefts for installation work are used as temporary supports for mounted structures. They must match the weight of the structures being installed. Scaffolding for the construction of prefabricated and monolithic reinforced concrete shells has a complex rigid spatial frame. Such scaffolding is made according to individual projects, depending on the shell designs, taking into account the shell construction technology.
According to the nature of support, scaffolding is divided into stationary (fixed), mobile, suspended and lifting.
The forests described above are stationary. The maximum height of such scaffolding is determined by calculation and reaches 40 m for masonry, 60 m for finishing work. When the height of the object exceeds 60 m, suspended scaffolding is used. Such scaffolding is suspended from consoles mounted on top of the object. Mobile and lifting scaffolding is used for repair work on the facades of buildings with a height of 10... 15 m. They are designed for their own stability, and therefore their lower support frames are widened to 2.5 m.
The stability of a scaffolding section depends both on the applied vertical loads and on the system of fastening the section and scaffolding to the object.
To organize workplaces in small areas of the front of construction, installation and repair work, scaffolding is installed indoors. According to their design characteristics, they are divided into: collapsible, block, mounted, suspended, telescopic.
Prefabricated scaffolds consist of individual elements and are labor-intensive during installation, dismantling and transportation, which limits their use.
Block scaffolding is a three-dimensional element moved from floor to floor by a tower crane. Some types of block scaffolds have wheels to move them around the floor. From a set of block scaffolds, a strip paving is arranged along the wall with fencing of the free edge, and, if necessary, paving is done over the entire area of the room.
Hanging scaffolds are designed for working at heights. These also include hanging cradles. Cradles are used for repair work on building facades. Self-lifting cradles have winches at the ends, which can be manual or electric (in the latter case, electric motors can operate synchronously and separately to eliminate distortions).
Suspended scaffolding is used for the installation of beams or trusses. They are strengthened together with the stairs on columns, even before the columns are raised.
Scaffolding on telescopic towers is used both inside high buildings and for outdoor work. They consist of a working platform with fences and a supporting part. The working platform can be raised and lowered. The supporting part can be a car.
In cases where it is impossible or impractical to install scaffolding, scaffolding and fences during construction and installation work, workers must be provided with safety belts.
Rice. 15. Column installation:
1 - suspended scaffolding; 2 - hanging staircase
The shock-absorbing element is a tape stitched with a special seam, which absorbs the dynamic load when falling due to breaking the stitching.
In addition to the belt, safety belts of the VM (spinner-mounter) and BP (top worker) brands have shoulder-hip straps and chest straps. When a person falls from a height, such a belt evenly distributes the load over the entire body, which eliminates the possibility of a spinal fracture. Belts and carabiners are tested twice a year for strength with a static load of 2 kN.
The calculation of settlement is that the settlements are equated, on the one hand, of a stamp (flexible or rigid) located on an elastic homogeneous linearly deformable half-space, and, on the other hand, to the surface of a boundless linearly deformable layer at the same values of the external load acting the same along the entire boundary of this layer, and the deformation modulus. As a result of this equation, the thickness of such a layer h eq, called equivalent, is found. Figure 5.6.1 shows the diagram of the method:
Calculation of settlement using the equivalent layer method
♯ Types of slope violations
A slope is an artificially created surface that borders a natural soil mass, excavation or embankment.
Slopes are often subject to deformation in the form of collapses (Fig. 5.7.1,a), landslides (see Fig. 5.7.1 b,c,d), sloughing and sloughing (see Fig. 5.7.1,e).
Collapses occur when the soil mass loses support at the foot of the slope. Landslides and landslides are characterized by the movement of a certain volume of soil. Collapse occurs when shear forces exceed the resistance of non-cohesive soil on an unsupported surface. Floating is the gradual deformation of the lower part of a flooded slope or slope without the formation of clear sliding surfaces.
The main reasons for loss of slope stability are:
– construction of an unacceptably steep slope;
– elimination of the natural support of the soil mass due to the development of trenches, pits, erosion of slopes, etc.;
– an increase in external load on the slope, for example, the construction of structures or storage of materials on or near the slope;
– reduction of adhesion and friction of the soil when it is moistened, which is possible when the groundwater level rises;
– incorrect assignment of calculated characteristics of soil strength;
– the influence of the suspended action of water on soils at the base;
– dynamic impacts (traffic traffic, pile driving, etc.), manifestation of hydrodynamic pressure and seismic forces.
Violation of the stability of slopes is often the result of several reasons, therefore, during surveys and design, it is necessary to assess the likely changes in the conditions of existence of soils in the slopes during the entire period of their operation.
Figure 5.7.1. Typical types of slope deformations:
a - collapse; b - sliding; c - landslide; d - landslide with uplift; d - swimming;
1 - collapse plane; 2 - sliding plane; 3 - tensile crack; 4 - soil uplift;
5 - weak layer; b, 7 - steady and initial water levels;
8 - melting surface; 9 - depression curves.
There are three types of slope failure:
– destruction of the front part of the slope. Steep slopes (a > 60°) are characterized by sliding with destruction of the front part of the slope. Such destruction most often occurs in viscous soils that have adhesive ability and an angle of internal friction;
– destruction of the lower part of the slope. On relatively flat slopes, destruction occurs in this way: the sliding surface comes into contact with a deep-lying hard layer. This type of destruction most often occurs in weak clay soils, when the hard layer is located deep;
– destruction of the internal section of the slope. The failure occurs in such a way that the edge of the sliding surface passes above the front of the slope. Such destruction also occurs in clay soils when the hard layer is relatively shallow
♯ Methods for calculating slope stability
The main elements of open-pit mining, pit or trenches without securing slopes are the height H and width l of the ledge, its shape, steepness and angle of repose α (Fig. 5.8.1). The collapse of the ledge occurs most often along the line BC, located at an angle θ to the horizon. Volume ABC is called the collapse prism. The collapse prism is kept in equilibrium by frictional forces applied in the shear plane.
Soil slope diagram:
1 - slope; 2 - sliding line; 3 - line corresponding to the angle of internal friction;
4 - possible outline of the slope during collapse; 5 - prism of soil mass collapse.
Slope stability is analyzed using limit equilibrium theory or by treating the collapse prism or sliding along a potential sliding surface as a rigid body.
The stability of a slope mainly depends on its height and type of soil. To establish some concepts, consider two elementary problems:
– slope stability of ideally loose soil;
– slope stability of an ideally cohesive soil mass.
In the first case, let us consider the stability of particles of ideally friable soil composing the slope (Figure 5.8.2.a). To do this, we will compile an equilibrium equation for a solid particle M, which lies on the surface of the slope. Let us decompose the weight of this particle F into two components: normal N to the surface of the slope AB and tangent T to it. In this case, the force T tends to move the particle M to the foot of the slope, but it will be hampered by the opposing force T ", which is proportional to the normal pressure.
Diagram of forces acting on a slope particle: a - loose soil; b - cohesive soil
where f is the coefficient of friction of a soil particle on the ground, equal to the tangent of the internal friction angle.
Equation for the projection of all forces onto the inclined face of a slope under conditions of limit equilibrium
where tanα=tgφ, from here α=φ.
Thus, the limiting angle of repose of bulk soil is equal to the angle of internal friction. This angle is called the angle of repose.
Let us consider the stability of a slope AD with height H k for cohesive soil (Fig. 5.8.2b). A violation of equilibrium at a certain maximum height will occur along a flat sliding surface of the VD, inclined at an angle θ to the horizon, since the VD plane will have the smallest area of such a surface between points B and D. Specific adhesion forces C will act along this entire plane.
Equilibrium equation for all forces acting on the landslide prism of the AED.
According to Fig. 5.8.2b side of the collapse prism AB = N to ctg θ, we obtain
where γ is the specific gravity of the soil.
The forces resisting sliding will be only the forces of specific adhesion, which are distributed along the sliding plane
At the top point B of the ABP prism the pressure will be zero, and at the bottom point D it will be maximum, then in the middle it will be half the specific adhesion.
Let's create an equation for the projection of all forces onto the slip plane and equate it to zero:
where 
Assuming sin2θ=1 at θ = 45°, we obtain
From the last expression it is clear that when the height of the pit (slope) H k > 2s/γ, the soil mass will collapse along a certain sliding plane at an angle θ to the horizon.
Soils have not only adhesion, but also friction. In this regard, the problem of slope stability becomes much more complicated than in the cases considered.
Therefore, in practice, to solve problems in a strict formulation, the method of circular cylindrical sliding surfaces has become widespread.
♯ Method of circular cylindrical sliding surfaces
The method of circular cylindrical sliding surfaces has become widespread in practice. The essence of this method is to find a circular cylindrical sliding surface with a center at a certain point O, passing through the bottom of the slope, for which the stability coefficient will be minimal (Fig.).
Rice. 5.9.1. Scheme for calculating slope stability using the round-cylindrical sliding surface method
The calculation is carried out for the compartment, for which the sliding wedge ABC is divided into n vertical compartments. The assumption is made that the normal and tangential stresses acting on the sliding surface within each of the compartments of the sliding wedge are determined by the weight of this compartment Q t and are equal, respectively:
where A i is the sliding surface area within the 1st vertical compartment, A i = 1l i ;
l is the length of the sliding arc in the drawing plane (see Fig. 5.6.1).
The shear resistance along the surface under consideration in the limit state, which prevents the slope from sliding, is τ u =σ·tgφ+c
The stability of the slope can be assessed by the ratio of the moments of holding forces M s,l and shearing forces M s,a. Accordingly, we determine the stability safety factor using the formula
The moment of the holding forces relative to O is the moment of forces Q i .
Moment of shear forces relative to point O
♯ Soil pressure on the enclosing surface
Soil pressure on the enclosing surface depends on many factors: the method and sequence of backfilling; natural and artificial compaction; physical and mechanical properties of soil; random or systematic ground shaking; settlement and movement of the wall under the influence of its own weight, soil pressure; type of associated structures. All this significantly complicates the task of determining soil pressure. There are theories for determining soil pressure that use premises that allow solving the problem with varying degrees of accuracy. Note that the solution to this problem is carried out in a flat formulation.
The following types of lateral soil pressure are distinguished:
Resting pressure (E 0), also called natural (natural), acting in the case when the wall (enclosing surface) is motionless or the relative movements of the soil and the structure are small (Fig.;
Resting pressure diagram
Active pressure (E a), which occurs during significant movements of the structure in the direction of pressure and the formation of slip planes in the soil corresponding to its limiting equilibrium (Fig. 5.10.2). ABC - base of the collapse prism, prism height 1 m;
Rice. 5.10.2 Active pressure diagram
Passive pressure (E p), which appears during significant movements of the structure in the direction opposite to the direction of pressure and is accompanied by the beginning of “soil uplift” (Fig. 5.10.3). ABC - base of the bulging prism, prism height 1 m;
Passive pressure circuit
Additional reactive pressure (E r), which is formed when the structure moves towards the ground (in the direction opposite to the pressure), but does not cause “soil uplift”.
The largest of these loads (for the same structure) is passive pressure, the smallest is active. The relationship between the forces considered looks like this: E a<Е о <Е r <Е Р
44 Algorithm for calculating foundation settlement
The task of calculating foundation settlement is reduced to calculating the integral.
SNiP provides for calculating the integral by a numerical method by dividing the soil layer of the base into separate elementary layers of thickness h i and the following assumptions are introduced:
1. Each elementary layer has constants E 0 and μ 0
2. The stress in the elementary layer is constant in depth and is equal to half the sum of the upper and lower stresses
3. There is a boundary of the compressible thickness at a depth where σ zp =0.2σ zq (where σ zq is the stress from the soil’s own weight)
Algorithm for calculating foundation settlement
1. The base is divided into elementary layers of thickness; where h i<0.4b, b- ширина подошвы фундамента.
2. Construct a diagram of stresses from the soil’s own weight σ zq
3. Construct a diagram of stresses from external load σ zp
4. The boundary of the compressible thickness is established.
5. The voltage in each elementary layer is determined: σ zpi = (σ zp top + σ zp bottom)/2
6. The settlement of each elementary layer is calculated: S i =βσ zpi h i /E i
7. The final settlement of the foundation base is calculated as the sum of settlements
all elementary layers included in the boundary of the compressible thickness.
45. The concept of calculating precipitation over time
By monitoring the settlements of foundation foundations, a graph of the development of settlements over time was obtained.
The concept of degree of consolidation is introduced: U=S t /S KOH
The final settlement is calculated using the SNiP method.
The degree of consolidation is determined by solving the differential equation of one-dimensional filtration:
U=1-16(1-2/π)e - N /π 2 +(1+2/(3π))e -9 N /9+…
The physical meaning of the degree of consolidation is expressed by the value of the indicator N:
N=π 2 k Ф t/(4m 0 h 2 γ ω)
Where, k Ф ~ filtration coefficient, [cm/year]
m 0 – coefficient of relative compressibility of the layer; [cm 2 /kg]
h is the thickness of the compressible layer; [cm]
t - time; [year]
γ ω - specific gravity of water
Determine the settlement of the foundation base after 1, 2 and 5 years. Pressure under the base of the foundation p = 2 kgf/cm2; soil - loam; thickness of the compressible layer 5m; filtration coefficient k Ф = 10 - 8 cm/sec; Coefficient of relative compressibility of loam m 0 =0.01 cm 2 /kg.
1. Determine the value of the consolidation coefficient: ^Ne conversion from seconds to year
C V =k F /(m 0 γ ω)=(10 -8 *3*10 7)(cm/year)/(0.01(cm2/kg)*0.001)=3*10 4 cm2/year
2. Determine the value of N:
N= π 2 C V t/(4h 2)=0.3t
3. Determine the degree of consolidation:
U 1 =1-16(1-2/π)e -0.3 t /π 2
4. Calculate the final settlement:
S=hm 0 p=500*0.01*2=10 cm
5. We calculate precipitation over time as:
S t =S k U i
