DISCUSSIONS

SELECTION OF TEMPORARY DIVERSION TUNNELS AND TUNNEL

SCHEMES FOR DISCHARGE OF WATER

E. I~ Karabaev UDC 627.842

The construction of hydrostations and hydraulic-engineering projects, which involves regulating the runoff of rivers for its multipurpose use, is associated with the need to divert the water arriving at the site during the construction period. During the construc- tion period water is usually diverted through special temporary structures or through the incomplete main structures of the future hydrostation, or both. Diversion of water is affected by various factors and conditions, starting from natural ones -- the character and adequacy of the river hydrographs, volume of river discharge during the years of construction, and others -- and ending with the layout and types of planned main structures.

Diversion structures are no less important than the main structures and their cost amounts to a substantial part of the cost of the main structures of the hydrostation. This is especially true for the construction of mountain and piedmont hydrostations being con- structed on rock foundations (especially in narrow canyons), where the layouts and set of main structures are largely determined by the conditions of diverting the water and technology of construction, which is closely associated with the diversion scheme. Widely used at such hydrostations are temporary diversion tunnels, which in many cases are reconstructed later into service spillways -- for permanent use as power or discharge channels during permanent operation of the hydrostation.

In much the same way as streamflow regulation systems with discharge of water through permanent structure of the hydrostation, the water diversion system can be subjected to a technical and economic analysis for selecting its optimal parameters. The problem consists in selecting a rational scheme of use and parameters of diversion tunnels providing minimum expenditures on diverting the water under specified conditions of construction of the hydro- station. This problem is solved on the basis of technical and economic calculations (TEC), involving an examination of a number of variants of the characteristic parameters, from which should be taken those which on fulfil l ing all other requirements correspond to the condition of minimum cost. The performance of such technical and economic calculations by means of computers opens the way for obtaining a well-founded minimum cost of diverting water promoting an overall decrease in the construction cost of the hydrostation.

To solve the indicated problem a special method can be proposed for determining the ra- tional parameters of diversion tunnels, using the author's main principles and conditions af- fecting the rational parameters of temporary tunnels and also the principles of the standards for determining the cost effectiveness of capital investments and other materials.

In the available literature the analysis of constructed diversion tunnels is aimed at improving and reducing the cost of structures and their operating conditions. In the standards and works on determining the cost effectiveness of investments there are no recommendations on selecting economically substantiated parameters of temporary structures, including tunnels. The author's statistical treatment of an analysis of tunnel schemes for diverting water, in- volving an examination of 38 Soviet and 105 foreign hydrostations,* made it possible to estab- lish the main factors and initial data to be taken into account when selecting a rational

*The 105 hydrostations examined were in the following countries: Austral ia (with Tasmania), 5; England, 5; Angola, i: Argentina, I; Brazil, 3; Ghana, i; Egypt, i; India, 3; Indonesia, I; Iraq, i; Spain, i; Italy, 4; Canada, 8; China, 4; Costa Rica, i; Morocco, i; Mexico, 2; Zambia, Mozambique, Rhodesia, 3; Nicaragua, i; Norway, 3; Pakistan, 2; Rumania, 2; USA, 21; Tanzania, I; Turkey, 4; Philippines, i; Finland, i; France, 2; Switzerland, 2; Sweden, 3; Yugoslavia, 5; Japan, 13.

Translated from Gidrotekhnicheskoe Stroitel'stvo, No. 8, pp. 30-38, August, 1981.

476 0018-8220/81/1508-0476507.50 9 1982 Plenum Publishing Corporation

", ' \ \ I J I I ~'\ I I "1

' - ' .x ">k"X l \ f l \ \ \ ' ~ I /1 ~ ~'k~.~://'~;~ T / , " \\ x .x'< ~7 \ \ \ I. I I ( i i

a b c

v ...... ,

I ~.~',',~'~" o ~?>~-~

Fig. i. Most prevalent layout of hydrostations using diversion tunnels, a) Run- of-river layout I with earth dam and exposed powerhouse in river channel (Nurek and Ponysh hydrostations); b) run-of-river layout II with concrete dam and exposed powerhouse in river channel (Chirkey and Toktogul hydrostations); c) bank layout III with earth dam and concrete structures on band (Kapchagai, Charvak, and Khantaika hydrostations; d) bank layout IV with earth dam and underground powerhouse (Rogun and Kolyma bydrostations); e) run-of-river layout V with concrete dam and under- ground or exposed powerhouse on bank (Inguri and Khudoni hydrostations); i) direction of flow; 2) normal pool level; 3) earth dam; 4) concrete dam; 5) dewatering outlet in dam; 6) exposed powerhouse in channel; 7) exposed powerhouse on bank; 8) under- ground powerhouse; 9) turbine tunnels; I0) open bank spillway used when diverting the flow; ii) service tunnel spillway; 12) diversion tunnel spillway of first level; 13) diversion tunnel spillway of second level.

477

\

l -d

Stages o f periods II and III

I

1

f

i l - c

/ /

iI

Stages o f perio ds II and III

b c m .... d 9 ~level~-'-o>. ,I;ll~il~, ~ ~ . "~ !illtl', :~-----------~ i i

9 i . \ \ ~ ~- rl ?/ . 9 ~ % ,,.~,.,, ~ - / - ~ ~ E ~ \\ \

S

Fig. 2. Example of single-level and level-by-level tunnel schemes. A) Level-by-level diversion tunnel scheme with the use of tunnel spillways for layout of type II; B) single-level diversion tunnel scheme with the use of tunnel spillways for layout of the III type. Main periods of constructing the hydrostation: period I, from the start of constructing the main structures to erection of the dam to nonoverflow eleva- tions; period II, from the end of period I to the start-up of the lower station at intermediate start-up elevations of the upper pool level; period III, final construc- tion of the hydrostation to normal operating conditions of the power station; period IV, normal operation of the station. Stages of diverting the flow: l-a) Along natural channel; l-b) during low-water period after damming; l-c) during first flood after damming channel; l-d) during flood at nonoverflow elevations of the dam; in periods II and III the stages of diverting the flow depend on the specific design and natural conditions and construction conditions of the specific hydrostation. Diagrams a and d: levels of diverting the flow; diagrams b and c: cross sections through sites of hydrostations: I, II, and III, respectively, the first, second, and third levels of diverting the flow.

478

PS

5

6

Variants oflocation of ReconstJ:ue tion --" - ~ r~_k / ~ the regulating mechanica],,.--'~ofunderground 9 ,~,~-.~:i~.c.=,--~;~

/ ~ "v equipment /" \ . f componea t " PS

Fig. 3. Characteristic types of diversion tunnels, a) Tunnel spillways; b) diver- sion--service tunnels combined with the conduits of the power station, i) Uncombined nonregulated diversion tunnel spillways; 2) uncombined regulated diversion tunnel spillways; 3) diversion and diversion--service regulated tunnel spillways, reconstruc- tion of which in the last stage is carried out with transfer of the entrance portal, its sill, and mechanical equipment to higher elevations; 4) diversion and diversion-- service regulated tunnel spillways, the reconstruction of which is done without transfer of the entrance portal, its sill, and mechanical equipment; 5) diversion-- service tunnels combined with the turbine tunnels of the power station (PS), the reconstruction of which is carried out at the next stage with transfer for the entrance portal, its sill, and mechanical equipment to higher elevations; 6) diver- sion--service tunnels combined with the turbine tunnels of the PS, the reconstruc- tion of which is performed at the next stage with transfer of the entrance portal (water intake of the PS) and its sill to higher elevations, but without transfer of the regulating mechanical equipment; 7) diversion--service tunnels partially com- bined with the headrace tunnels of the PS; 8) d ivers ion~erv ice tunnels partially combined with the tailrace tunnels of the PS.

scheme and parameters of tunnels for various specific conditions of the construction of hydro- stations. Statistical treatment of the investigated schemes was performed on the basis of an introduced classification that singled out the characteristic types of solutions being used with respect to the layout of hydrostations, tunnel schemes, and temporary tunnels.

The main trends in dam construction which have occurred in the past 20 years according to the data of the International Commission on Large Dams [i, 9, ii, 12, 13] were taken into account when choosing the analyzed hydrostations-analogs with concrete and earth dams.

Analysis of Tunnel Schemes and Selection of Their Parameters. Practically, layout of hydrostations on rock foundations can be divided into run-of-river layouts with concrete dams (with various locations of the powerhouse) or with earth dams (with exposed powerhouses located in the river channel) and bank layouts with earth dams with the concrete structures and powerhouse on the bank (or with underground powerhouses).

Among the main tunnel schemes are: single-level or level-by-level tunnel schemes, which use for discharging water one or several levels of the diversion or diversion--service tunnel spillways; level-by-level tunnel schemes, which use the diversion--service tunnel structures combined with the headraceandta i l race tunnels of the power station.

The conditions and stages of using diversion tunnels as part of tunnel schemes, the characteristics of combining the functions performed by tunnels in the construction and operating periods, the operating conditions of the mechanical equipment of the tunnels, and the character of its subsequent reconstruction all determine the types of diversion tunnels.

479

T

" 3 ; " Z

' l ti b ~ , t

L_ J Yes ~

on parameters I

---t:,-- Stop

Lc.

Ct~ [

Fig. 4. Integrated block diagram of computer program of the economic-mathematical model for determining the required parameters of diversion tunnels, i) Input of initial data; 2) description of initial data and composi- tion of structures and formation of data; 3) compilation of mathematical models for calculating the cost of the main and auxiliary structures and structures of the convey- ance route of the diversion tunnel and costs of accompanying structures of the upper pool, flood zone, and lower pool; 4) creation of mathematical models and calculation of the hydraulic regimes in tunnel and other structures; 5 and 6) analysis and optimization of parameters: if "yes," then to block 7, if "no," then to block 5; 8) stop; 9) calculation of the cost of structures, elements, components; i0) calcula- tion of total adjusted cost; ll) calculation of the capacity AQ lacking before the design Qdes and total adjust cost of substitute structures or measures; 12) calculation of total adjusted cost of diverting the flow for characteristic stages.

All temporary and combined tunnels can be reduced to the following characteristic groups: a) uncombined diversion tunnel spillways; b) combined diversion--service tunnel spillways; c) diversion--service tunnel structures combining functions with the turbine tunnels of the power station; d) diversion-service tunnel structures partially combined with the headrace and tailrace tunnels of the power station.

The characteristic layouts of hydrostations most often using tunnel schemes for dis- charging water, the most prevalent tunnel schemes, and t~he most frequently used types of diversion and diversion--service spillway tunnels and structures are shown in Figs. I, 2, and 3.

An analysis shows that the following have the greatest effect on the parameters and types of diversion tunnels and tunnel schemes: width and shape of the river canyon at the site of the hydrostation; character of the runoff hydrograph and design discharges; type of dam and its height (or head); location and type of power station and time of starting up the units; presence of permanent service tunnel structures as part of the hydrostation; the main periods and characteristics of construction of the hydrostation, which are determined by the conditions of constructing its main structures.

480

The statistical data of the analysis show:

I. Diversion tunnels are most often used at hydrostations with earth dams.

2. Single-level tunnel schemes are primarily used; at the investigated hydrostations with earth dams they amount to 66% (in the USSR, 72%) and at hydrostations with concrete dams 83% (in the USSR, 78%).

3. In the investigated single-level and level-by-level tunnel schemes tunnel spillways are used in 80% of the cases.

4. Combined diversion--service tunnels make up the greater part (64%) of all types of tunnels used, among which 63% are represented by tunnel spillways.

5. Single-level and level-by-level schemes with spillways of types i, 2, 3, and 4 (see Fig. 3) are used more often than others in mountain a~d piedmont regions. Examples of the most prevalent tunnels and tunnel schemes are those being used in the most common layout of hydrostations of types II, III, and V (see Fig. i):

With layouts of type II -- single-level schemes of the Kurpsa hydrostation on the Naryn River with one tunnel of type 1 and the Namakhvani-i hydrostation of the Rioni River with one tunnel of type 4, or the level-by-level schemes of the Chirkey hydrostation on the Sulak River with one tunnel of type 1 and one tunnel of type 4, and also the Toktogul hydrostation on the Naryn River with two tunnels of type i;

With layouts of type III -- single, level schemes of the Kapchagai hydrostation on the Ili River with two tunnels of type 4 and Irganai hydrostation on the Avarskoe Koisu River with one tunnel of type 4, or the Perepad-i hydrostation on the Naryn River with one tunnel of type 3;

With layouts of type V -- single-level schemes of the Inguri hydrostation on the Inguri River with one tunnel of type 1 and the Khudoni hydrostation on the Inguri River (in a con- crete variant) with one tunnel of type i.

The analysis permits adopting the following basic principles and conditions for select- ing tunnel schemes and parameters of diversion tunnels in any specific cases of constructing hydrostations on rock foundations:

i. For all the difference of the initial conditions and layouts of hydrostations, the main stages of discharging the water and determining the design values of the diversion dis- charge are the same for all main diversion tunnel schemes (see those shown in Fig. 2).

2. The main stages of discharge and the values of the diversion discharges depend on the permanent set of structures under construction participating in discharging the water and on the factors and costs being taken into account, which together form a "complex" or "system" providing stage-by-stage discharge of water during construction of the hydrostation.

Although under specific conditions the composition of such a "complex" or "system" can depend on many conditions, nevertheless the permanent group of structures and cost of any diversion system should include:* the partially constructed main structures of the hydrosta- tion; structures of the tunnel proper needed at each stage of discharging the flow; auxiliary and secondary structures associated with discharging the flow (constructed to the required readiness); other structures and costs providing the necessary readiness of the upper and lower pools of the hydrostation at each stage of discharging the water.

3. Selection of the tunnel schemes and determination of the parameters of the tunnels on the basis of technicoeconomic calculations (TEC) should be carried out with consideration of the said components and specific limiting conditions of the investigated system for divert- ing water, i.e., the conditions of the hydrostation under construction. In this case in the TEC all conditions, costs, and factors being taken into account which f igure in the system are divided into known (given natural conditions and limits) and variable, which are deter- mined during the TEC.

4. It is possible to divide the parameters of diversion tunnels to be determined into necessary (or required) parameters and parameters subject to subsequent optimization. The required parameters to be optimized should include: the cross section and number of tunnels, type of tunnel structure, and hydraulic regime in it (for given limits of the initial data: slope, location of tunnel, and others).

*The power characteristics of the hydrostation under construction, which have an effect on total cost of the "complex" in a number of characteristic cases, are not indicated.

481

Depending on the problems faced during designing, the tunnel parameters to be optimized in the second stage can include: the number of tunnel segments and types of lining used on them, refinement of the length and slope of the tunnels, and a number of others(with a corre- sponding refinement of the hydraulic regime within the limits prescribed by the preceding stage of determining the parameters).

5. The data of the analysis substantiate the use of stages when determining tunnel param- eters: at first the required parameters are optimized and then those of them which must be improved with respect to the conditions of the hydrostation under consideration are optimized. This introduces clear-cut limits into the TEC.

The enumerated principles and conditions and also the principles of the standards [2-4] and an analysis of the TEC and power--economic calculations permit proposing a method of TEC for determining the parameters of diversion tunnels which uses the principles of the systems approach for a technicoeconomic analysis of the investigated diversion system of a hydro- station under construction. The principles of the method are coordinated with the system for automated design of hydroelectric stations (SAD HES) according to [5, 6].

Minimization of the Cost of Diverting the Flow and Basic Principles of the Method. Streamflow regulation by creating reservoirs calls for discharging water at the site of the dam of the hydrostation. Regulated or nonregulated discharge of the stream can be examined in the form of a system in which are united the initial natural and economic conditions of the investigated region and cost of enterprises and structures related to the creation of structures providing the achievement of the given goals of streamflow regulation.

Hydroelectric power stations as systems requiring streamflow regulation for power pur- poses [5, 6] and multipurpose hydrostations as systems intended for streamflow regulation with other economic purposes can be subjected to a technicoeconomic analysis for selecting their optical parameters.

The systems for discharging water during construction of hydroelectric power stations and multipurpose hydrostations can be regarded as a particular case of streamflow regulation systems for non-power-producing purposes.

Water is usually discharged through the structures of the hydrostation, which are directly or indirectly related to its main purpose. The investigated tunnel structures can perform both the main and secondary functions of the hydrostation. In the construction period of hydrostations in which the water is discharged through diversion tunnels these structures in the diversion systems perform the main objective function of the system: diver- sion of the design discharges Qdes makes it possible to construct the hydrostation under the given conditions and to meet other requirements.

A technicoeconomic analysis of the diversion system is carried out for selecting those parameters of it for which the cost of diverting the water would be minimum. In this case the TEC of the diversion systems are performed on the basis of those optimality criteria which are use for analyzing the parameters of the hydrostation as a whole and its main struc- tures analogous to the recommendations [5, 6].*

Representation of the discharge of water during construction of a hydrostation in the form of a system subjected to a technicoeconomic analysis for the purpose of cost minimiza- tion makes it possible to solve a number of diversion-related problems arising during construc- tion. In particular, with the use of the principle of minimization of the cost of diverting water under the initial conditions of a hydrostation it is possible: to determine the rational parameters of temporary tunnels and other structures for discharging water during construc- tion; to optimize the organization and technology of construction works related to discharg- ing the water; to take into account the effect of power factors of the power station under construction (time of starting up the units and electric power production, etc.) on the cost of diverting the water, etc.

With consideration of the aforesaid, for determining the parameters of diversion tunnels the following basic principles of minimization of the cost of diversion are used: a) stage- by-stage examination of diversion of water at the site of the investigated hydrostation; b) determination of the permanent set of components of the cost and structures of the system

*With consideration of the power characteristics of the power station under construction the use of these same optimality criteria in the TEC of the investigated diversion system is all the more valid.

482

h Input of data d Descripnon, formation - - 1v t tModel$ of c~e, el,, ~| j l 1 __ i __

~(if ........ Yq~ Calr Ci 1

[ I

[ ~] block I ] ~ _.__j [ _ i _~. ~r~ ..il [ l [

Yes ~__

on parameters

t

Fig. 5. Integrated block diagram of computer program of the economic-mathematical model for determining the optimal parameters of diversion tunnels, i) input of initial data; 2) description of the initial data and composition of elements and structures and formation of data; 3) compilation of mathematical models for calculat- ing the cost of elements of tunnels and accompanying structures providing operation of the tunnels; 4) compil- ation of mathematical models and calculation of the hy- draulic regime in the tunnel and, if necessary, in other structures conveying the diverted flow; 5 and 6) analysis and optimization of parameters; analysis (Ctot.tr + min Ctot.tr); if "yes," then to block 7, if "no," then to block 5; 8) stop; 9) calculation of the cost of elements of the tunnels and accompanying structures; i0) calculav tion of total adjusted cost; Ii) calculation of the capa- city AG lacking before Qdes.div. tun and total adjusted cost of substitute structures or measures; 12) calculation of total adjusted cost of divertin~ water throuRh the diversion tunnels for characteristic stages.

providing diversion at each stage under the specific conditions of the hydrostation; c) cal- culation of the cost related to diversion under the given conditions of the investigated stage; d) performance of comparative TEC of the diversion system for each investigated variant of the tunnel parameters. As mentioned above, the tunnel parameters to be optimized in the TEC are divided into those required and those to be optimized additionally.

The optimality criteria used by us in the TEC for determining the parameters of tunnel structures diverting the flow differ from the optimality criteria usually used for such struc- tures in streamflow regulating systems for power purposes [5, 6], where they do not perform the main functions of the system.

In conformity with the systems approach [5, 7], for the main structures of the investi- gated system the optimality criterion has a direct relation and is determined by the optimal- ity criterion of the system itself. Taking into account this and the principles [2, 3]~ as the cost effectiveness criterion for the TEC of diversion tunnels and other structures of

the diversion system we will take the minimum total adjusted cost analogous to [3-6]

~tOt.--~ min~to t or Cto t --~ minCto~, (1)

483

The use of the method of comparative cost effectiveness when determining the parameters of diversion tunnels is uniquely determined in the same way by this criterion in the TEC.

For the investigated variants of the tunnel parameters the total adjusted cost of facil- ities figuring in the investigated system are calculated by equations analogous to those given in [3, 4]. In a general form they are written

Ctot = E s Kt (1 q- ~a) "-t +~, '~Ot (1 Jr Esa~-t , /----I 1 t=t 0

(2)

where n is the number of facilities figuring in the investigated system; E s and Esa , respect- ively, standard coefficients of effectiveness of capital investments and adjustment of costs at different times; K t and AOt, respectively, capital investments in the facilities of the investigated variant in year t and changes in annual outlays in year t compared with the preceding year ( t - i); T, year of adjusting the costs (base year); to, year of the start of operation of the diversion tunnel; T, year of completion of the investigated stage.

For the facilities figuring in the system, the capital investments in which are carried out during the year and the annual outlays are the s~me in the investigated stage of diversion, the adjusted total cost in the investigated variant of the parameters are determined by the equat ion

Ctot =- EsK q -~ 0 , (3) i=1 t----~

where Ctot and K are, respectively, the total adjusted cost and total investments with respect to the facilities of the system; O, the annual outlay for the facilities of the system at the investigated stage.

The required tunnel parameters and those being optimized are determined in a variant-by- variant performance of TEC for finding the minimum total adjusted cost min Ctot.re and Ctot.tr, respectively, of diverting water at the site of the hydrostation and through the tunnel route of the diversion spillway at each examined stage with consideration of the order, conditions, and criteria indicated above.

For the investigated variant of the required tunnel parameters the costs Ctot.re of diversion (for o elements of the "complex" providing discharge of the water) can be calculated by the equation

Ctot.tr ---- ~(Cma.req'~tr.re. q-~au.tr q-C-r) q-~ub.tr~min~-tot.tr. (4) /=.1

For each investigated variant of the tunnel parameters being optimized the total adjusted cost Ctot.tr of diverting the flow through the tunnel routes (for t elements of them and ac- companying structures) are determined by the equation

t

C--mt.tr = s (C l +~-~au.tr) q- ~sub.tr ~ min-Ctot.tr. i----1

(5)

In Eqs. (4) and (5) the component elements are determined by the equations

C--marne = ~J~'i,ma.tr ; i----1

i=1 n

Cau.r e = ~. Ci, au.re; i=1

m

i=I

(6)

484

subor~ E C r i= I J

(6)

]

Cz = ~.jE ~ =C-up.s t +~-head.can+....+ Cup.port-6 i= l

"~gate -~ "'" +Ctai l ,can + Cdown, st ; l

8

ECsub.nY = ~ C i, sub.tr " i= l

When determining the tunnel parameters being optimized the entire route of the diversion tunnels and the structure accompanying it have t elements forming the system diverting the

J flow through the tunnel route; in it ~C] is the total adjusted cost of j elements of the

t=1

diversion tunnel proper. In the investigated objective function (Ctot.tr + min Ctot.tr) this cost of t elements of the investigated variant is variable, changing depending on the change in the elements or parameters being optimized. Accordingly, Cup.st, Chead.can, etc., are the adjusted cost of the upstream stretch of the tunnel, headrace canal, and other elements of it. When_ choosing the optimal tunnel parameters the adjusted cost Ctot.tr should be no more than Ctot.re determined in the preceding stage. The cost Ctot.tr includes the cost Cau.tr of ~ accompanying structures being constructed to a state corresponding to the investi- gated stage of diversion of the flow; Ci,au.tr is the cost of the i-th accompanying structure.

ZCsub.tr is the total adjusted cost of s additional elements of the tunnel and accompany- ing and other structures which could compensate the lacking capacity of the tunnel AQ before the design discharge Qdes.div. tun in the investigated variant of the tunnel parameters being optimized; Ci, sub.tr is accordingly the adjusted cost of the i-th substitute structure, ele- ment, or measure.

In many cases it is necessary to take into account in the total cost in (4) and (5) the effect of the costs caused by electric power production and start-up of the capacities of the hydrostation during construction: when their final construction to the design parameters coincides in time with diversion of the flow; when the functions of the diversion tunnels are combined with the tunnels of the hydrostation, etc. They are arbitrarily omitted in Eqs. (4) and (5).

In individual cases of optimizing the parameters of diversion tunnels in the second stage, when diversion of the flow through the tunnel route proper without a substantial effect of accompanying structures and of the other indicated factors is investigated, the total adjusted capital investments can be taken as the optimality criterion in Eqs. (5) and (7).

The adjusted cost with respect to the elements figuring in Eqs. (6) and (7) can be cal- culated in a general form by Eqs. (2) and (3). In this case the depreciation deductions for temporary structures should take into account their relatively short service life.

During practical TEC for determining the parameters of diversion tunnels at each stage of diverting the flow the given initial data permit taking into account the characteristics of the stages of the tunnel scheme and periods of constructing the hydrostation, the conditions in the upper and lower pools corresponding to them, the component elements of the "systems" providing diversion at the investigated stages, etc. For the investigated variant of the tunnel parameters being optimized appropriate hydraulic and other calculations are performed, which correspond to the investigated stage of diversion. On the basis of them the component elements figuring in the system at the investigated stage and additional measures to provide the design discharge Qdes.div.tun are refined.

The total adjusted capital investments and outlays on elements of the system in the investigated stages figuring in Eqs. (4) and (6) are determined on this basis for the in- vestigated variant of the tunnel parameters being optimized.

When comparing variants of the required tunnel parameters the minimum cost Ctot.re of the diversion system at the investigated stage determines the selected parameters of the tunnels. Analogous calculations are performed for the next stages of diversion, which permit final refinement of the required tunnel parameters and also taking into account their effect on the main structures of the hydrostation, designs, and costs established in the project.

If it is necessary to optimize individual parameters of the diversion tunnels in the second stage practically the same sequence of calculations is retained in the TEC, but in this case a diversion system is investigated which includes the tunnel route proper and the structures accompanying it, see Eqs. (5) and (7).*

*The sequence of TEC is presented in the "Methodological Instructions for Determining the Parameters of Diversion Tunnels" (first edition) compiled by the author under the supervision of Doctor of Technical Sciences V. M. Mostov at the Experimental Design Office, Research Department, Gidroproekt, and examined at the Central Asian Branch of Gidroproekt, M. I. Kalinin Leningrad Polytechnic Institute, etc.

486

It should be noted that the selected parameters of diversion tunnels, naturally, should not make the designs, construction cost, and other indices established in the hydrostation project worse or more costly.

Unlike the earlier performed TEC,* the proposed method of determining tunnel parameters has a unified methodology and cost effectiveness criteria, substantiates the components and factors to be taken into account, determines the stages of diversion and stages of performing the TEC to be investigated, etc.

Experience shows that determination of the parameters of temporary tunnel structures involves alarge amount of various calculations and design works. In connection with this there is an urgent need to replace the mass of calculations for determining tunnel parameters by a stage-by-stage computer analysis of economic-mathematical models (EMM's) of the relation between costs and parameters of diversion tunnels. The preceding equations (4) and (5) for each stage of diversion (with given conditions and limitations) in essence represents RiM's of the relation between costs and parameters of diversion tunnels, which, however, are dif- ficult to realize on the basis of the mathematical apparatus. Future EMM~s for determining the parameters of tunnels should be based on principles of systems analysis of the said diver- sion systems on the basis of Eqs. (4)-(7). Under specific conditions of EMM's will be non- linear at each stage of determining the tunnel parameters. Taking into account the need to adjust cost at different times to a base year, it is advisable to use a static EMM for con- venience. Figures 4 and 5 show the basic EMM's in the form of integrated block diagrams of programs for determining the required and optimal parameters of diversion tunnels. It is natural that the proposed EMM's need further elaboration with the realization of specific examples of determining tunnel parameters for hydrostations under construction.

CONCLUSIONS

i. The presented principles of minimization of the cost of diverting water during con- struction based on an analysis of hydrostations under construction represented in the form of diversion systems make it possible to reduce the total cost of diverting water during construction of hydrostations and to solve a number of optimization problems. In particular, they permit determining the rational parameters of diversion tunnels and tunnel schemes; and this in turn reduces the cost of constructing hydrostations in mountain regions.

2. To refine individual principles of the method of TEC for determining the parameters of diversion systems it is expedient to use it for determining the parameters of diversion tunnels when designing hydrostations planned for construction on rock foundations.

3. Detailed elaboration of the EMM's of the relation between costs and parameters of diversion tunnels on the basis of the presented principles of TEC makes possible to subsequent conversion to systems of automated determination of the parameters of tunnel schemes and diversion tunnels in coordination with the development of systems for automated designing of hydropower facilities.

LITERATURE CITED

I. World Dams Today, Japan Dams Association, Tokyo (1970). 2. Standard Method of Determining the Cost Effectiveness of Capital Investments [in Russian],

Gosplan SSSR, Gosstroi SSSR, Akad. Nauk SSSR, Moscow (1969). 3. Instructions on Determining the Cost Effectiveness of Capital Investments in the Develop-

ment of Power Facilities [in Russian], Energiya, Moscow (1973). 4. Basic Principles of the Determination of Cost Effectiveness of Hydropower Facilities

[in Russian], Gidroproekt, Moscow (1972). 5. Yu. S. Vasil'ev, "Principles and methods of calculating the optimal parameters of water

conveyance structures of hydroelectric stations," Authors's Abstract of Doctoral Dis- sertation, Leningrad Polytechnic Inst. (1973).

6. L. P. Mikhailov, "Selection of the parameters of the unit blocks of hydroelectric sta- tions," Gidrotekh. Stroit., No. 8 (1977).

l

7. B. L. Erlikhman (ed.), Transactions of Gidroproekt, Collection Noo 29 [in Russian], Moscow (1973).

*According to the data published in the journal Gidrotechnicheskoe Stroitel'stvo in 1965-1975.

487

8. F. F. Gubin and V. L. Kuperman, Economics of Water Management and Hydrotechnical Con- struction [in Russian], Stroiizdat, Moscow (19Z3).

9. V. L. Kuperman, V. M. Mostkov, V. F. Ilyushin, V. V. Semenkov, et al., "Improvement of diversion tunnel designs," Gidrotekh. Stroit., No. 8 (1975).

I0. Y~. G. Nikolaev and A. G> Yakobson, River Diversion during Construction of Hydrostations [in Russian], Ser. BGG, Energiya, Moscow (1969).

iio S. N. Moiseev, "Diversion of floods during construction past earth--rock dams," Gidrotekh. Stroit., No. i (1975).

12. Reference Materials "World Hydroelectric Stations," Nos. i, 2, 5, 6, and 7 [in Russian], Gidroproekt, Moscow (1971-1975).

13~ Proceedings of the International Congresses on Large Dams with Respect to Problems: No. 12, Vol. 2, New Delhi (1951); No. 20, Vol. i, New York (1959); Nos. 25 and 26, Volso I and III, Rome (1961); No. 31, Vol. 3, Edinburgh (1965); No. 33, Vol. II, Istanbul (1967); No. 36, Vol. I, Montreal (1970); No. 41, Vol. II, Madrid (1973); General Reviews, Vol. IV, Mexico City (1976).

14. E. I. Karavaev, "Comments on the revision of the standards for hydraulic tunnels," Gidrotekh. Stroit., No. 1 (1971).

BEARING CAPACITY OF SAND BASES (DISCUSSION OF CONSTRUCTION

SPECIFICATIONS)

V. N. Dombrovskii UDC 624.153.522.046

As is known, the bases of retaining structures (dams, retaining walls, ramps) are sub- jected to the effect of inclined loads and are calculated with respect to the first group of limit states -- bearing capcity. An analysis of recent experimental and theoretical works [1-15] devoted to a study of the stability of sand bases under inclined static loads revealed substantial differences in a quantitative estimation of the bearing capacity of these bases. These estimates in various methods of calculation differed by a factor of 8-10, which forces one to doubt the reliability of their theoretical basis. Figures 1 and 2 give a graphic com- parison of the values of the bearing capacity of a sand base with an angle of internal fric- tion of the soil of 29 ~ for various methods of calculation as a function of the shape of the lower surface of the footing (strip, square), relative angle of slope of the load, and depth of the lower surface of rectangular plates with a width of 0.40 m.

The cause of such considerable differences lines in the difference in interpretation of the most important parameters figuring in the traditional canonical Prandtl--Terzaghi equation, which, in particular, is used in Construction Norms and Regulations (SNIP) 11-15-74 [7], SNiP II-16-76 [8], and other standards [9, 15]. For instance, the scatter of the values of the bearing capacity factors reaches tenfold, the slope of the load sevenfold, and the shape of the lower surface fivefold. It is paradoxical that according to [9, i0] the coefficient of slope of the load depends on the angle of slope of the load, and according to [6], SNiP II-15-74 [7], and SNiP II-16-76 [8] on the angle of slope of the load and angle of internal friction of the soil, but in this case it is necessary to bear in mind that for a fixed slope of the load a smaller value of the slope coefficient on relative bearing capacity of the base corre- sponds to a larger angle of friction of the soil.

To resolve the contradictions between theory and experiment and to establish the actual ultimate loads causing loss of bearing capacity of a sand base, experimental investigations (58 experiments) were carried out on large-scale models (b = 0.40 m) to study the influence on soil stability of the shape of the lower surface of the footing (l~b~4, where b is the width and l is the length of the plate), angle of slope of the central load (0~61~h5, where

Translated from Gidrotekhnicheskoe Stroitel'stvo, No. 8, pp. 38-42, August, 1981.

488 0018-8220/81/1508-0488507.50 9 1982 Plenum Publishing Corporation