The forecast of a temperature regime of soils containing the pile foundation of a pithead on diamond-mining mines of cryolithic zone

Urii A.Khokholov，Dmitrii E.Solovev，Alexander S.Kurilko，Alexander V.Drozdov

(Mining Institute of the North SB RAS，Yakutsk 677980，Russia)

0 Introduction

In accordance with Construction Norms and Regulations 2.02.04-88[1]when constructing on the permafrost soils depending on design and technological features of buildings and constructions，engineering and geocryologic conditionsand possibility oftargeted change of properties of bottom site two principles of use the permafrost soils as the footing of constructions are applied:

The principle I–permafrost soils of footing are used in the frozen state to be saved during construction and throughout the period of operation of the construction;

The principle II–permafrost soils of footing are used in the thawed or thawing state(with their preliminary thawing on calculated depth prior to construction of a building or with an assumption of their thawing during operation of the facility).

Construction and operation of mine technical objects on all facilities of the diamond-mining company“ALROSA”are carried out by the principle I as in their basis are the rocks which completely lose strength during thawing.

It is especially important for construction of the surface complexes of mines and pit shaft equipped with hoisting plants，which piles foundations and collar parts are exposed to technogenic thawing in the process of tunneling and construction works，as well as during operation.The permafrost soils are the reasons of thawing:

-ventilating air delivery in mine with a year-round positive temperature;

-thermal influence of warmed buildings;

-influence of atmospheric heat during the summer;

It is known that the surface complex of underground mine with the lifting which is carried out on vertical pit shafts，includes the tower-type pit-head which pile fields are located round a pit shafts.This construction creates large load on the pile field which stability is guaranteed only at the particular temperature of soils providing their year-round stay in a frozen state suggesting that they required artificial strengthening in any way.As it is known from practice，the most prime and efficient way of strengthening of soils in cryolithic zones conditions is their artificial cooling by dint of freezing system.

With the beginning of the freezing system there emerges a gradual cooling，and then freezing of rock mass surrounding a vertical pit shaft and a pile foundation of pit-head.At the same time，available experience testifies that for the aims of prevention of deformation and destruction of shaft timbering by shear stresses，arising in the process of freezing of surrounding rocks，existence a damping thawed ring-shaped zone round a pit shaft is necessary.According to some researchers[2-5]，the necessary minimum size of such zone fluctuates from 0.5 to 1 m.It is necessary to organize a work of freezing station，so that not to allow a deep freezing of rocks of a damping zone and at the same time to support a frozen state of rocks of the pile foundation of pit-head，providing thus its design carrying capacity.

1 Mathematical model

To forecast and to manage a temperature regime of rocks foundation of tower pit-heads and providing its stability the three-dimensional mathematical model is developed.It describes processes of heat exchange taking into account temperature of freezing liquid，length of freezing holes，their quantities and their location，an annual course of temperature of free air，air temperature in a pit shaft，lamination and degree of salinity containing a shaft and the foundation of pit-head of rocks.

To forecast thermal conditions in collar part of vertical shaft we will allocate calculated area(which is presented in Fig.1.

Fig.1 Three-dimensional area for calculation of a temperature regime of rocks in the foundation of tower pitheads

For the solution of a problem of heat conductivity we used the natural method of smoothing considering a function of non-frozen water.

where C—is the volume heat content of rocks，J/(m3·℃);t—temperature of rocks，℃;Llh—latent heat of phase changes of water，J/kg;Wnfw—amount of not frozen water，decimal fraction;ρ—density of rocks，kg/m3;τ—time，s;λ—thermal conductivity of rocks，W/(m·℃).

On bottom and side borders of area a lack of heat streams(a boundary condition of the II sort)is set

where through ?/?n the external normal to bottom and to side borders of area is designated.

On a day surface we set the following regional condition taking into account the temperature of free air

where α1—is a coefficient of heat exchange of a surface of the earth with atmospheric air，W/(m2℃);t1—temperature of a free air，℃.

On an internal surface of a shaft the boundary condition of the III sort is set

where through ?/?nGthe external normal to border is designated;t2—air temperature in a shaft，℃;α—coefficient of heat transfer through walls of a pit shaft，W/(m2·℃);Rc，х0，у0—radius and coordinates of the center of a shaft，m;Rk，z2，у2—radius and coordinates of the center of the ventilating channel，m.

In an initial instant distribution of temperature of rocks and air temperature in wells is set

Existence of freezing devices is considered by a cooling temperature task in the corresponding coordinates.

For approximation of a curve of non-frozen water the following formula is used

where W—is a cooperative humidity，decimal fraction;Wah—adsorbed humidity，decimal fraction;tb—temperature of the beginning of freezing of moisture in rock，℃;te—temperature of the complete freezing of moisture in breed，℃;n—empirical parameter.

For the solution of an one-dimensional problem of a freezing-thawing directed in a form(1)，numerical methods of the through account are used.

The carrying capacity of piles is defined according to formulas and dependences which are given in Construction Norms and Regulations 2.02.04-88[1].

2 Definition of work regimes of freezing system

The developed mathematical model was applied when determining of work regimes an of the freezing system providing a frozen condition of soils in a subfoundation of pit-head foundation and collar part of shafts on diamond mines of stock company ALROSA.

In this article，calculations are given as an example for conditions of the vertical cage shaft(VCS)of“Aykhal”mine.

Calculations were carried out for a period of up to 4 years.Time of the beginning of calculations corresponded to the beginning of November.Two values of cooling temperature of a freezing liquid－15℃and－20℃，and also 3 parameters of temperature of air in a shaft were considered:+5℃，+10℃ and+15℃.It was considered，while calculating of periodic switching on and off of the freezing system.We can see that it is the main operating parameter when choosing its optimum work regime.

Let's consider it in more details an option of calculation at which the freezing system works 6 months in a year，and in remained time(within 6 months)it is disconnected(regime I).Temperature of a freezing liquid in freezing columns of－20℃，air temperature in a shaft pit+5℃.In figure 2 temperature isolines on the horizontal plane are given in depths of 10 m，and in figures 3 and 4-temperature isolines on the vertical plane parallel to and perpendicular to an axis of the ventilating channel.As we can see from the figures，on the depth of 10 m round the shaft after 4 years the frozen core could be formed with temperature of－7～－9℃，and on the depth of 14 m-the frozen core wit temperature of－6～－8℃is formed

Fig.3 Temperature field round VCS to the end of the 4th year of operating of freezing system.Section through an axis of a shaft parallelly to an axis of the ventilating channel

Fig.4 Temperature field round VCS to the end of the fourth year of operation of freezing system.Section through a shaft axis perpendicular to an axis of ventilating channel

In Fig.5 the dynamics of change of carrying capacities of several piles of a pit-head for the calculated period of 4 years is shown.From schedules we can see that changes of carrying capacities of piles have cyclic character，at inclusion of freezing station there is an increase of a carrying capacity of piles，and at shutdown，on the contrary，their decrease.Thus according to the project design load on a pile of 16 m long，makes 100 ton，and on a pile of 10 m long and 80 ton.The close arrangement of freezing columns at piles of a shaft leads to intensive cooling of containing rocks，thereby providing a necessary carrying capacity of piles with a large supply.Also the tendency to gradual increase of carrying capacities of piles is observed that in the long term will demand correction of a duty of system of freezing.

Fig.5 Dynamics of carrying capacities of piles of a shaft

In Fig.6 dynamics of development of zones a thawing soils round a pit shaft at different depths from a surface is shown at various parameters and work regimes of freezing system.This figure shows us that the size value of zones a thawing depends on a work regime of freezing system:at its inclusion there is a decrease in the sizes of zones a thawing，and at shutdown –their increase.For the given option of calculation(regime I)the decrease tendency the sizes of zones a thawing round VKS clearly is traced.It is clear，that in this case through a particular instant there will be a freezing of surrounding breeds that is inadmissible.

At change of regime work of freezing system(the regimeⅡ-works 3 months，and then for 3 months it is disconnected)at constancy of other parameters，minimum necessary thawed zone round a trunk(see Fig.6)also is not provided.

As further calculations showed the change of work regimes of freezing system(regimeⅢ-works 6 months，on the 6 month it is disconnected)in total with temperature increase of a freezing liquid from －20℃ to－15℃，allows to provide the necessary sizes of zones of a thawing and their stabilization in long-term prospect(see Fig.6).This regime work of freezing system of soils provides a necessary carrying capacity of the pile bases of a pit shaft.

Fig.6 Dynamics of zones of a thawing round VCS at various duties of freezing system

Thus when cooling temperature increase to－15℃it is possible to operate a thermal condition of rocks round a shaft providing safety of its concrete lining.As rocks possess big heat inertance，it gives the chance of management of a temperature condition of surrounding rocks of a pit shaft with the appropriate organization of works for temperature monitoring.The received values of system of thermomonitoring of rocks around an arrangement of piles of foundation of pit-head piles and surrounding rocks of shaft have to be verified with results of model operation，and if necessary to correct the operation of freezing devices for providing demanded heating environments of soils.

3 Conclusions

We developed the three-dimensional mathematical model of heat exchange of ventilating air with environmental rocks in collar part of vertical shafts of cryolithic zone mines considering existence of coolers，temperature of freezing liquid，length of freezing holes，their quantity and their location，temperature of atmospheric and miner air，inhomogeneity and degree of salinity of containing rocks.This model allows to calculate and predict change of carrying capacities of piles of pithead piles taking into account work of freezing system.

With use ofthe developed three-dimensional mathematical model the rational regime work of freezing system，for conditions of the vertical cage pit shaft(VCT)of“Aykhal”mine was defined.The chosen regime allows to provide a carrying capacity of piles a pit-head and existence of a damping thawed ring round a shaft not less than 0，5 m in size for protection concrete lining a pit shaft from freezing and possible deformations.

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