Implementation Structural Dynamics Designing Ug Support Poem by Soumen Chattopadhyay

*Implementation of structural dynamics Engineering in designing seismic shock waves (during blasting vibration) absorber support system for hard rock underground excavation. (A Hybrid Engineering Mechanism)

——Dr. Pijush Pal Roy
Director CSIR —CMERI (Durgapur)
Outstanding scientist of CSIR — CIMFR (Dhanbad)
&
Soumen Chattopadhyay
M. Sc(physics) , B. Tech, M. Tech



1.Research objectives

In seismic excitation rock surrounding the excavation and existing support system along the periphery of the excavation vibrates in different mode as a result of which there developed a zone of differential movement which take a part to damage and crack in the static support system and there may be a permanent change of deformation of support which decrease load bearing capacity of the overlying rock mass.

During blasting underground various seismic waves produced. Apart from this when depth of mining increases phenomenon like rock burst is very common, which is not well defined. Blasting and excavation induced seismicity can not be prevented.

Blast induce seismic excitation deformed existing rock support near the zone of seismic excitation. In this particular situation we required shock absorber dynamic support system instead of static support system because such dynamic support system quickly reach in a dynamic equilibrium state to prevent any kind of deformation due to its flexibility where there is a differential movement in rock mass motion and support system.

While depth of mining increases the occurrence of seismic events due to depth of the mining and blast induce rock vibration increases.

In this paper a hybrid engineering mechanism for designing for rock support system is explained, which approaches towards development a ground support system under dynamic conditions.

The objective of such shock waves absorber support system is to increased support capacities during ground movement. Apart from the restoring its deformation during seismic excitation it also absorbed mechanical vibration and the energy released from rock burst prone zone.

2.*Introduction and assumptions*

In this paper the sub system models are chosen as simple mass system which are not intended to represent the model for an actual underground support structure in seismic excitation. However with this simple system we can understand how this selected procedure may be applied to a real problem when dynamical equilibrium is required.


Characterization of blast induce ground motion indicates that the shear strain and corresponding residual Excess Pore Pressure (EPPs) are associated with low frequency near — and far— field shear waves that are within the range of earthquake frequencies. Whereas the effect of high frequency P-wave are negligible. Various results show that rock joints have significant effects on the propagation characteristics of blast induce vibration.


In this paper rock mass is considered as elastic bodies. The explosion generated pulse in rock mass propagated parallel and perpendicular to columnar joints.


All discontinueties such as joints, faults, bedding planes and other surface of weakness exists in the surrounding of the rock excavation significantly affected by seismic excitation and it is the problem concern to the geotechnical engineering, geophysics and mining engineering.


The understanding of the interaction between rock joints and blast waves is very important as the velocities of seismic waves varies according to the geomining conditions. During rock breaking mechanism there is a outwards transmission of the strong stress wave which disturbed the existing support system. Therefore we have to think about the state of dynamic equilibrium of a single system instead of the combined system (support+ surrounding rock mass as a single one) . To solve the problem in designing shock proof support system when dynamic stress passes through an anisotropic medium such as joint plans energy scattering occurs we apply laws of classical physics or Newtonian mechanics. In sedimentary rock strata dynamic states can not propagated along a straight line. It reflects in various direction of the bedding plans. So behaviour of interaction of seismic waves in different geomining parameters is considered.

During construction shock absorbing support system we have to consider the maximum principle stress that is transactional stress which is built up in the immediate skin of the excavation and other is, stored elastic strain energy surrounding the rock mass. Maximum principle stress remains constant but the rock strength degrades over the time due to loss of confinement and a condition of potentially unstable equilibrium situation developed in the zone of excavation. Which creates dynamic disturbance.

Rock burst may release large amount of seismic energy instantaneously because there is a relaxation of elastic strain stored in a large volume in a highly stressed rock surroundings. During excavation these destructive forces acting on the support and this highly stressed conditions existing static support can not regain its original shape when both seismic waves excitation and strata movement withdrawn.


Acoustic properties of rocks relate alternating stresses of varying frequencies and elastic strain. In hard rock blasting there are longitudinal and transversal waves propagation of which is described by the simple wave equation. Propagation velocities of elastic waves in rocks decrease with increasing temperature and increase with increasing pressure.

So describing the behaviour of mode of vibration the inner friction in rocks which in turn depends on temperature, pressure, porosity and pore saturation shall be studied. Rocks possess elastic intrinsic and extrinsic anisotropies. Therefore anisotropy behaviour of elastic waves shall be considered during construction of the support system. The characteristics impedance of a rock, which is defined as a product of the sonic velocity and the density of the rock is a comprehensive physical property for an intact rock and it is closely related with strengths, fracture toughness, young modulus and poison ratio. Characteristics impedance for a given rock mass either increases markedly with increasing depth. So behaviours of geomechanical disturbances shall be considered during designing dynamic rock support. Rock quality designation (RQD) , rock mass index (RMI) , rock mass rating (RMR) and protodyakonov index and other geological parameters which are significantly variable rock to rock are needed for making such support structure. Characteristics impedance of intact rock affects the proneness of rock burst.



3. Literature Review:

In designing and development vibration and seismic shock waves (which produces during underground blasting operation) absorber proof support structure for overlying and underlying strata or rock bed is a vital aspect.

Supporting hard rock excavation in mining is important because during blasting in hard rock various seismic waves of various amplitude and strength are produced according to different geomechanical and geomining parameters which may dislodge or decrease the efficiency of the existing static support system. When natural frequency and the frequency of seismic waves co-inside the phenomenon like resonance damage the support system exponentially in day-to-day blasting. In this case, such support system do not withstand the vibration and dynamic load come in contact in the peripheral body of the support structure. The various passive energies and elastic potential energies stored in the surrounding zones of the excavation play an active role for rock collapse. Due to geothermic gradient heat developes in deep mines and thermal conductivity of the rock therein distribute heat and seismic energies.


When seismic waves propagate through a rock mass, they encounter an increasing volume of rock mass, causing decrease in energy density. Such geometrical damping diminishing energy and seismic waves simultaneously affected by numerous inelastic effects that also cause energy loss during wave propagation.

In such situations amplitude is decreased. Although generally seismic waves do not have sufficient energy much beyond the zone of disturbance due to intrinsic attenuation.
Amplitude (A) of particle displacement due to blast induce vibration is proportional to the square root of the weight of the explosive charge(Q) and inversely proportional to the distance (D) from the blast. That is:

A=KQ⁰•⁵/D
: Morris (1950) :

So during calculation of amplitude of seismic waves both should be considered, distance and weight of explosive charge.

Generally two groups of seismic waves activated by detonation of explosive charge. Body waves travel within rock mass and surface waves travel along free interfaces. At the moment of blasting rock near the hole shows a hydrodynamic behaviour.

This shock waves instantaneously moved from non-elastic state to quasi elastic zone in which the oscillatory wave motion propagated in sonic velocity and carries insufficient energy which is not destructive for surrounding rock mass.

The amount of energy transferred to a given rock mass is linear function of the product of the density and the rate of detonation, termed as characteristics impedance of explosive. Explosive which has the larger characteristics impedance or close to the characteristics impedance of rock, transfers more energy to the rock mass. So this is the most important variable. For observation of intensity and strength of seismic waves.

Body waves consist of two discrete components— compressional (P-wave) and shear (S-wave) . S-wave have two components— S-horizontal and S- vertical.

Two types of surface waves generated in mine blasting— Rayleigh (R-wave) and Love(L-wave) . P-wave are faster than S-wave. Velocity of the Love waves remains less than the shear waves velocity. R-wave propagated at a velocity less than S-wave.

But most explosive are detonated as a series of smaller explosion which are delayed by milliseconds and differences in travel paths and delay times result in overlapping arrival of both wave fronts and wave types. (Pal Roy,1995)

So we have to consider the overlapping waves phenomenon in seismic excitation.

The shock energy transmitted to the rock depends on detonation pressure of the explosive and the detonation pressure is a function of explosive density.
The most commonly used equation for the detonation pressure

P(d) (N/m²⁾ ⁼[Vₑ²(m/s) * dₑ(kg/m³) ]/3.8

P (d) = detonation pressure
Vₑ= detonation velocity of the explosive
dₑ= detonation density of the explosive.

As detonation pressure is maximum in the direction of shock waves. So velocity of shock waves depends on the above factors and taking a part during construction of seismic excitation phenomenon. All these parameters are taken to be consideration in calculating to choose the appropriate shock absorber system in support structure.


4.Operational hypothesis and application of Newtonian mechanics:

When a wave travels in a absorbing medium it losses energy as it propagates through the medium. It has been found experimentally the amplitude of the wave decays by a constant fraction of its value when the wave progresses through a certain distance. This means that the amplitude falls exponentially with distance and we can write the amplitude at a distance x which respect to the origin at x=0 as,

A(x) =A₀e⁻ᵅˣ

where Aₒ is the amplitude at x=0. The constant α is called the attenuation constant. From above equation we find that
α= - 1/A(x) dA(x) /dx


Thus α is the decrease in amplitude per unit amplitude per unit length. Therefore α is the fractional amplitude attenuation of amplitude A(x) per unit length. So during construction of shock wave absorber support system above equation must be considered.

In an elastic meterials at least two types of waves can be propagated— pressure waves and shear waves. Whereas in an acoustic meterials only pressure waves are propagating. Both shear waves and pressure waves are governed with the same equation. The elastic wave equation described the propagation of elastic disturbances produced by seismic waves in blasting. The acoustic wave equation governes the propagation of sound.

Using the stress and strain theory we can solve the seismic wave equation for elastic wave propagation. The equation of wave propagation in elastic solids are described by using Hooke's law and Newton's second law of motion. Solid bodies such as rock mass are capable of propagating forces that acting upon them.

Seismic wave velocities p-wave(Vₚ) for unconsolidated materials 1.5—2 km/s, for sedimentary rock bed it is 2—6 km/s, for igneous rocks 5.5—8.5 km/s, for steel it is 6.1 km/s.

In the aseismic approach we can prevent the support from seismic hazard by mechanism which reduces the transmission of horizontal acceleration into the support system. The fundamental concept of base isolation is to reduce frequency of a structural vibration to a minimum value then the predominant energy contain frequencies of blast hole explosion responsible for strata movement or ground motion.

During blast hole explosion isolation technique actually uncoupled the support system from the ground which is in motion.

In designing shock absorbing support system we consider the forces acting on the mass of the support system for instantaneous time period.

Here external forces P(t) . The forces due to elastic resistance fS and damping forces fD acting on the structure of the support. The elastic and damping forces at the moment of explosion work in the opposite direction because these forces resist the deformation and velocity (v, during blasting induce vibration) of the support structure and we get resultant force as

(Applied dynamic force) -(elastic resistance force) -(damping force)

e.i,
P(t) — fˢ— fᴰ (as shown in the figure.1and figure 2)
Which is equal to mass of the support and acceleration (according to Newton's second law of motion)

We know that,
force= mass*acceleration
P=m*a
Therefore, from Newton's second law of motion we get,

P(t) - fˢ -fᴰ = mÜ


As force is acting on the mass of the support for very short time therefore we consider the force as impulse.

Finally we get the equation governing dynamical equilibrium system in seismic excitation.

Mü + Cù+ Ku = p(t)

Therefore,
ᵢ∫ᶠdP = ₜᵢ∫ᵗᶠFdt
Pᶠ-Pᵢ= ₜᵢ∫ᵗᶠFdt
Pᵢ= initial momentum of the support system at time tᵢ
Pᶠ= final momentum of the support system at time tᶠ
Pᶠ-Pₜ =∇P=change in momentum of the support system during time interval tᶠ-tᵢ=∇t

The integral ₜᵢ∫ᵗᶠFdt=J is called the impulse and tᵢ it is equal to change in momentum of the support system.

Taking external forces as positive in X axis the displacement U(t) , velocity U'(t) and acceleration U'(t) are also positive in the direction of X axis and then we get the above equation as

md²V/dt² + fᴰ+ fˢ =P(t)

Displacement of the structure is governed by this equation of motion and we can reach to designing a shock proof vibration absorber support system where dynamical equilibrium is required. The region which is very prone to rock burst or sensetive to seismic waves the principal problem is induce motion of the base of the support structure Uᵍ and support movement Uˢ their relative displacement due to total ground motion U may be related at each instance of time of the disturbance by the laws of classical physics as bellows

Uˢ(t) = U(t) + Uᵍ(t)

Uₛ and Ug refer to the internal frame of reference and positive direction co-inside. Ultimately from figure we can write an equation for dynamic equilibrium in the state of seismic excitation and blasting vibration as

fᴵ + fᴰ +fˢ =0

Thus from above study it may be recommended that external blast induce vibration and seismic excitation can be minimise by introducing the elastic dampers in the support system to reduce the amplitude of vibration in support frame.

It is well known that
If vibration frequency (resonance frequency) 'f',
mass of the vibrating support system ' m',
cold/ hot movement 'mm' in ambient temperature (maximum/ minimum) and
temperature of the vibrating support system then a damping of 40% is consider necessary to provide an initial selection of elastic dampers. The formula used is as follows

Damping parameter =40% m 2π f/1000

Temperature taken in centigrade
Frequency taken in Hartz
Amplitude taken in millimetre
Mass taken in kilogram
Ambient temperature varies from (-30°C) —(+ 110°C)

As well as the most demanding mine environmental conditions.

5.Stress and strain behaviour and wave equation of velocity propagation(file attached)




6.Research Design and Methodology:



High strength steel support covered by Fibre Reinforced Polymers(FRPs) significantly enhanced the toughness and ductility provide an increased resistance to seismic forces and it offers excellent corrosion resistance for a large life.

Seperation or a little isolation from the surrounding rocks by introducing polymer matrix and Led Rubber bearing or by incorporating flexible materials such as visco elastic dampers effectively reduced damage during vibration as such support system enhancing their seismic resilience.

Energy generated by seismic forces absorbed by such support system and may exhibits durability and resistance to cracking.


The design of the isolated (through visco elastic dampers) structure consume target displacement from its mean position.

Because vibrational amplitude demands to regain its shape and dimension which is self adjusted according to the geomechanical and geomining condition after absorbing seismic excitation.

The vibration and friction occuring along the surface of the periphery of the excavation support system enables the structure to stay in the elastic range without having any structural damage. Also it supplies a significant amounts of damping to the structure due to incorporation of
1. polymer matrix,
2.led rubber bearing,
3.visco elastic dampers etc as shown in the figure 3(a, b, c, d, e) inbetween support and rock that is interface of support and surrounding rock mass.

Introduction of such dampers give a model of dynamic behaviour of the structure.


And then Oscillatory motion of the support structure dissipate energy for (for internal momentary deformation) , friction, rubbing, cracking, permanent deformation etc.

Because of the larger the energy dissipation capacity the smaller the amplitude of vibration.

In such support structure passive energy control devices impart forces that are developed in response to the motion of the structure. Because the energy is passively controlled as system itself is of dynamic character. In state of dynamic equilibrium through transformation of the kinetic energy (which produced during blasting) to heat energy when it is in vibrating mode.

Energy input during explosion to the support structure can't reached intensely in metallic body as it is covered by Fibre Reinforced Polymer Matrix (FRPM) and protect it from permanent inelastic deformation.

Such fibre polymer matrix shows stable hysteretic behaviour, low cycle fatigue property, long term reliability and relative insensitivity to a temperature and heat produced in mines.

Such support system shall be consist of Passive energy dissipation device.

Passive energy dissipation device when installed to the support system then it actually works as a seismic isolation as a means of protecting both support structure and underground excavation during blast hole explosion.

The basic function of passive energy dissipation (PED) device in a support is to absorb or consume a portion of the blast induce input energy. The means by which the energy dissipation is adopted by following methods—

1. Metallic Yield Dampers
2. Friction Dampers
3. Visco elastic dampers
4. Viscous Fluid dampers
5. Tuned liquid dampers
6. Tuned mass dampers
7. Base isolation
8. Laminated Rubber bearing
9. Fibre reinforced polymer matrix


We can achieve a design of vibration proof and shock absorber underground support system.

Property of tuned spring and damping elements providing a frequency dependent hysteresis that increases required oscillations in the support. The first and foremost factor during installation of such dampers we have to consider the amount of rock mass in overlying rock bed.

Laminated Rubber bearing (LRB) : LRB exhibits high damping capacity both in horizontal and vertical direction. The high damping rubber bearing is made from natural rubber.

As absorption coefficient hardness factors of rock are frequency dependent therefore during incorporation of shock absorbing meterials in the support system this frequency dependent parameter to be considered.



7.Science and Mechanism of Dampers



By combining Newton's second law, the acceleration of Simple Harmonic Motion (SHM) , and Hooke's Law, we can derive the equation relating the angular frequency (ω) to the mass(m) and the spring constant (k) . We shall the convention of using 'a' for acceleration:

Newton's second law: F=m*a
Simple Harmonic Motion: α=-ω²ˣ
Hooke's Law: F=-kx
F=-mω²x=-kx
k=mω²
ω=√(k/m)

We can then find the period (T) associated with this oscillating mass-spring (as shown in figure 1.b) by the definitions of period and angular frequency. We shall use 'f' to indicate the frequency (not the angular frequency, they're different)

T=1/f
ω=2πf
so T=2π/ω= 2π√(m/k)

Simple Harmonic Motion is periodic motion, motion that repeats itself over consistent intervals, that is *assumed to ignore* *damping.*

The spring constant (k) is a quality of the spring that describes how 'strong' the spring is.

Spring with a higher spring constant are more difficult to compress and extend than springs with a lower spring constant.

The seismic behaviour of support structure with added visco elastic dampers is studied experimentally. The experimental results show that significant improvement of structural performance under seismic conditions. It has been seen that effectiveness of dampers is strongly dependent upon mine temperature and highly stressed conditions.

The visco elastic damper is a well known passive control device in mitigating peripheral vibration of the support structure induced by long period seismic excitation also it is actively effective during strong air blast when wind stressed try to deformed the support system. Since its dynamic properties are dependent on several factors such as— overlying load of rock mass, loading frequency and temperature, the increases of its temperature from dissipating kinetic energy significantly affects its behaviour, perticularly for long duration loading.

Analysis models incorporating such effect is being proposed by focusing on heat generation and trasfer.

In nonlinear hysteresis models based on visco elastic (EV) constitutive rule using fractional time derivatives of shear stress and strain. While in other systems there dimensional finite element method is applied. These models are not extensively implemented for arbitrary loading. Moreover their accuracy are inherently limited to the appropriate estimation of convective heat transfer parameters. However in practice, a certain degree of deviation due to some uncertainties can be tolerable. This paper proposes an evaluation Methodology for practical application to the shock absorber support system for a dynamic equilibrium.

Visco elastic meterials (VEM) that can resist deformation that is regain its shape, size and dimension as soon as external forces attenuated is practically useful in the underground mine support structure technology. By sandwiching thins slabs of VEM between steel plates, a visco elastic dampers is made and is used as a passive control device to mitigate vibrations of the support structure. VEM dampers effectively reduced the induced stress and strain while strong wind due to heavy air blast passing through it. Also it capable to absorb seismic excitation during blasting and earthquake which deformed the rock texture when installed properly.

Commonly VE damper properties are evaluated by considering its steady states response to harmonic loading and the hysteretic relationship between the force and the deformation or between the shear stress and shear strain.

Fluid viscous dampers work based on the principle of dissipation of energy due to fluid flowing through orifices.

The damper consist of a stainless steel piston, a steel cylinder divided into two champers by the piston head— a compressible hydraulic fluid (silicone oil) and an accumulator for smooth fluid circulation. In fluid viscous dampers as the piston moves(left to right or right to left) , fluid flows from one chamber to another chember through the orifice. This movement of fluid from a large area (cylinder chamber) to a smaller area orifice and from a smaller orifice to a larger area (cylinder chamber) results in the dissipation of energy because of head loss. Fluid viscous dampers can operate in an ambient temperature ranging from -40°C to 70°C(as shown in the figure 3.a) .

The damping force of the damper is proportional to the pressure difference across the piston head and is expressed as a function of velocity of piston.

Polymer matrix: polymer matrix composites (PMCs) are comprised of a variety of short or continuous fibres bound together by an organic polymer matrix. Reinforcement in a polymer matrix composites (PMCs) provides high strength and stiffness. The PMCs designed so that the mechanical load, seismic excitation, air blast wind pressure to which the support structure is subjected in service are supported by the reinforcement. The function of the matrix is to bond the fibres together and to transfer loads between them.

Polymer matrix composites (PMCs) devided into two categories — reinforced plastic and advanced composites. The distinction is based on the level of mechanical properties (usually strength and stiffness) .

High damping rubber bearing is similar with LED rubber bearing, belongs to seismic isolation bearing. It is composed of special rubber with excellent damping attribute, sandwich together with layer of steel of the support structure. Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. Thus high damping rubber has excellent vibration reduction ability. Due to excellent flexibility and high restoring ability (HDR) can absorb some input energy of the seismic excitation before the energy is transmitted to the support structure. High damping rubber bearing features highly vartical loading capacity, recovery ability. Full of hysteretic behaviour HDRB can produced seismic isolation effect due to blast induce vibration. HDRB itself producing the seismic isolation function, doesn't need install other devices. Thus the cost of maintenance and repair is reduced.

Temperature influences on the flexibility and damping performance of the high damping rubber bearing HDRB is extremely small. Thus HDRB has a wide range of applied field. High damping rubber bearing are commonly used in base isolation system which can protect the support structure from heavy seismic excitation due to heavy blasting in metal mines by elongating natural vibration period of the support structure and improving the energy dissipation capacity of the system.


8.Limitation and applicability of the study:


1. Such support system shall not be installed near the blasting face underground.

2. In the mine permanent roadway it shall be effective.

3. In the four way junction of the underground mine it is very effective rather than the temporary road way.

4. Displacement of such support system from one place to another is a factor of time consuming.

5. As it is permanent nature of support so it shall be installed where permanent roadways are necessary both in traveling and haulage road.

6. It is not cost effective so it shall be installed in some strategic places.






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