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.
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), sloughs 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 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 compose 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 tgα=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 – specific gravity 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 holding moments M s,l and shearing moments M s,a forces. 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 the calculation of 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 stress 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 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 Ф /(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
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 the platform. An abutment on a guide slope is typical for ramps on upper, already developed horizons when vehicles move through them along these ramps.
When solving practical problems, the determination of the forces transmitted by the soil to the vertical or inclined faces of a structure is usually separated into a separate task from the general stressed state of a soil mass. Typical structures for which the assessment of soil pressure E is essential are various kinds of retaining walls (Fig. 6.1, a), basement walls (Fig. 6.1, b), bridge abutments (Fig. 6.1, c), hydraulic structures (Fig. 6.1, d), pit fencing, lintels, etc.
Rice. 6.1. Ground pressure on various structures.
1 - area (“prism”) of soil collapse;
2 - area (“prism”) of soil uplift.
As experiments and field observations have convincingly shown, the soil pressure E on a structure depends significantly on the direction, magnitude and nature of the displacements of the vertical or inclined contact faces of the structure along which interaction with the soil mass occurs.
Let's consider the effect of displacements using the example of a simple retaining wall (Fig. 6.2). In the case of a confidently motionless wall (Fig. 6.2, c), soil deformations occur without lateral expansion and therefore, under the action of only the soil’s own weight, one can take σ x = ξσ z = ξγ gr z, where ξ is the coefficient of lateral soil pressure (see Section 3.3 , formula 3.23). In this case, the total lateral pressure per unit length of the wall (in the direction perpendicular to the xz plane) will be determined as E 0 = ξγ gr h 2 /2. Pressure E 0 is usually called resting pressure, since the value of the coefficient ξ in E 0 corresponds to the case of the absence of lateral displacements of the soil.
Rice. 6.2. Dependence of soil pressure on magnitude and direction
horizontal displacement of a wall or structure.
Under the influence of soil pressure, displacements U of the structure may occur away from the backfill soil (in Fig. 6.2 they are taken with a minus sign, i.e. U< 0). При этом в массиве грунта образуются поверхности скольжения, и постепенно формируется область обрушения, которую называют collapse prism (wedge)(1 in Fig. 6.2, b). The shear resistance forces arising in the shifting soil lead to a decrease in soil pressure, which, with the displacement value U a of the structure, determined by the formation of the collapse prism, reaches a limiting (minimum) value called active pressure or with a thrust E a (Fig. 6.2, a). As experiments have shown, to achieve E a, very insignificant values of displacement of the wall from the ground are required (U a ≥ (0.0002 ... 0.002)h, where h is the height of the wall in m).
Often, as a result of the action of external forces, structures move towards the ground. This can manifest itself in structures that perceive large horizontal loads, for example, in the case of the abutment of an arched bridge (Fig. 6.1, c), hydraulic structures (Fig. 6.1, d) as a result of upstream water pressure.
When moving the U wall onto the ground (Fig. 6.2, d), a soil uplift prism(2 in Fig. 6.2, d) and shear resistance forces arise, preventing uplift. As a result, an ever-increasing soil reaction occurs along the edge of the wall, which at the moment of formation of the uplift prism reaches a maximum value called passive pressure or resistance from the ground E p (Fig. 6.2, a). To develop and create passive soil pressure, a large displacement U p of the wall onto the ground is required, significantly (by 1 ... 2 orders of magnitude) exceeding U a. This is caused, in particular, by compaction of the soil behind the wall. Under the action of an external load that forcibly displaces the wall onto the ground, the soil first becomes compacted and only then does a sliding surface begin to form - soil uplift.
Thus, under active pressure refers to the maximum pressure of the soil of the backfill on the wall (structure) under conditions when the wall is displaced from the backfill (due to deformation of the base from the pressure of the backfill) and the soil behind the wall has entered a state of limiting equilibrium. Passive pressure- this is the limiting value of the reaction (reactive pressure) during forced displacement of the wall onto the ground under conditions when the soil behind the wall goes into a state of limit equilibrium (within the uplift prism). We emphasize that in relation to the structure, active pressure is active, and passive pressure is reactive force. Active soil pressure can be one of the reasons for loss of stability of a structure or wall (shear, tilt and overturning).
To determine the active and passive pressures on massive structures of great rigidity in design practice, approximate solutions are usually used, based on the concepts of the theory of limit equilibrium (LTE - see Section 3.1), discussed below.