# ijege-13_bs-margiotta-onorati.pdf

*Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università*

*Editrice*

*DOI: 10.4408/IJEGE.2013-06.B-54*

**THE HYDROLOGICAL CHARACTERISTICS OF THE VAJONT VALLEY**

veloped to integrate Vajont water resources with those

flowing in Piave river and in Boite as well as Maè

and Val Gallina creeks. In 1957, this plan was called

“Grande Vajont”, literally in English: big Vajont. The

plan was mainly aimed to hydropower purpose and it

included the design of the now well famous dam, with

a height of 266 m and a effective storage of 175 Mcm.

The entire water supply scheme was supposed to ex-

ploit once an a half times the amount of water with-

drawn by the plants of the entire upper Piave valley.

sibility, legal conflicts, etc., related to the disaster, but

a very little has been told about the hydrological po-

tential which has not been used because of the impos-

sibility of exploiting water stored in the reservoir.

could have been used in presence of an active res-

ervoir behind the Vajont dam.

yields were estimated based on the theory of storage-

yield curve, and then, as a comparison, the amount of

water which can be used nowadays was analyzed by a

stochastic method proposed by (C

*et alii*, 1996).

**ABSTRACT**

is dramatically known because of the disaster which

occurred in 1963, when, before the dam located on the

creek between the towns Erto and Casso started its op-

eration, a huge landslide detached from the Toc moun-

tain, falling in the reservoir during the filling stage.

Consequently, a water wave overtopped the dam. Al-

though the dam is still there, the damage caused by the

wave was so high that this disaster is remembered as

one the most dramatic in a very long time.

the dam design, the volume of water, which could

have been used if the system were realized, is here

estimated by use of a storage-yield curve theory and it

is compared to the amount of water that can really be

nowadays exploited, that has been in turn estimated

by a hydrological model proposed in 1996.

**INTRODUCTION**

ter occurred on October 9

towns as Longarone, Erto and Casso.

struction. Official documents are found since the 14th

*M.R. MARGIOTTA & B. ONORATI*

*International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013*

ly-distributed, so that parameters of the transformed

variable (D

with the same probability of failure was determined

with reference to the probability distribution of the defi-

cit in the dry season. This part of the storage-yield curve

is significant for low and medium regulations, and is

decisive for reservoirs in semi-arid regions.

that in the carryover storage-yield curve it is possible

to take into account the average deficit of the dry sea-

son preceding the critical period. This deficit is noth-

ing but the quantity

is representative of the deficit of a generic dry season.

the S months of the dry season, with d

depends on the within year diagram of the draft. It is to

say, however, that volumes required for irrigation share

about the same pattern in a given climatic region, so

that the deficit season is the same in large areas.

*et alii,*1998) substan-

is a cube-root normal, at least in the regions of South-

ern Italy. In short, the global storage-yield curve, ac-

counting for both the seasonal and the carryover ca-

pacity, is determined as

at Erto Caldaia and at Erto Bindi, two different hydro-

metric stations very close each other, which operated

in different periods. Incidentally, it may be useful to

know that the average mean annual flow provided by

both the recorded data series, is about 2.15 m

**THE STORAGE-YIELD CURVE. THEORY**

storage capacity that, when the target draft is smaller

than the mean inflow (partial regulation) is equal to

the maximum accumulated deficit of the inflow partial

sums ( M

stochastic model of the runoff process. The family of

random variables to handle in order to build carryover

storage-yield curves (r

non-exceedance probability Φ.

frequency Φ for the annual yield E is:

to ensure that the autocorrelation implied in the over-

lapping sequence of mean runoff in k years remains in-

significant. Limitations on K usually do not practically

affect the design, unless one gets very close to the full

regulation region of the storage-yield curve.

fects with some underestimation the curve in the re-

gion of the full regulation. The probabilistic method

discussed also relies on the assumption of uncor-

related annual runoff series, which is often realistic,

particularly when considering runoff data aggregated

over the water-year. Anyhow, even in presence of au-

tocorrelation it is possible to adjust the probability

distribution so that the reproduction of the observed

minima is ensured (M

k-dependent stochastic process D

**THE HYDROLOGICAL CHARACTERISTICS OF THE VAJONT VALLEY**

*Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università*

*Editrice*

suming a fifty-fifty partition between them.

is shown in Fig. 4.

in the Vajont reservoir would have been of 175 Mm

**THE STORAGE-YIELD CURVE FOR THE**

**VAJONT WATER SUPPLY SCHEME**

the dam, were used for estimation purpose.

the normal cumulative probability distribution of D

scheme was derived.

first derived, and the curves obtained by the use of Eq.1

were consequently calculated. They are shown in Fig.

2 for k varying from 1 through 10. In the figure, both E

and V are measured in millions of cubic meters.

October. Three different water uses ware considered.

In particular, one case was referred to agricultural pur-

poses, for which water demand is entirely concentrat-

ed in the dry season; another one was considered for

civil purpose, where the water consumption is taken

as homogenously distributed within the year, and the

*Fig . 1 - Cube – i9root normal distribution of annual runoff*

*Fig. 2 - Annual Curve E-V*

*k,Φ*

*Fig. 3 - Dry Seasons Curve E-V*

*S,Φ*

*Fig. 4 - Totally STORAGE-YIELD Curve E-V*

*Φ*

*M.R. MARGIOTTA & B. ONORATI*

*International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013*

in which coefficients of variation of daily flows

are significantly greater than 1. The reason is that

for lower C

upper-bounded. Nevertheless, this procedure has

been applied to the Vajont case in order to provide a

first approximation result.

the Vajont at Erto Caldaia in the periods 1941-1946

and 1948-1953 and at Erto Bindi between 1954 and

1958 were used.

spectively, qrd values have been calculated for rd rang-

ing from 0.5 to 5. They are summarized in Tab. 2.

respectively.

the mean annual flow, that is about 2.15 m

be used. Whereas, this last percentage increases to

about 70% if the design discharge is doubled. On

the other hand, no further significant advantage is

achieved even if the maximum derivable discharge

is consistently increased. Therefore, in absence of

water storage in the reservoir, the amount of water

which can be used is nearly 40-50 million of cubic

meters, much less than 350 Mm

withdrawal for civil purposes.

**CONCLUSIONS**

estimate the amount of water which has not been used

because of the fact that the reservoir ended its opera-

tion after the well known disaster occurred in 1963.

160 Mm

“grande Vajont” plan, the reservoir was supposed to

collect runoff from the Piave river and from the Boite,

Maè and Val Gallina creeks, so increasing significantly

the amount of water to use.

**THE DIVERSION CHANNEL DESIGN**

**METHOD BY CLAPS**

*ET ALII*(1996)the annual yield which can be achieved by simple wa-

ter withdrawal at its site.

version channel are based on the use of flow duration

curves, that involve a deterministic approach to the

design task. In an effort to overcome the deterministic

connotation in this approach, they suggested a specific

methodology for the selection of the design discharge

in such channels, based on the estimation of volumes

transferred annually with assigned non-exceedance

probability (C

*et alii*, 1996).

Qrd transferred with a 'diversion ratio' rd , which is the

ratio between the channel design discharge Dq and the

river average discharge q.

series of 11 different rivers in southern Italy, with co-

efficient of variation C

scale the variable qrd is Gaussian, regardless of the

values of rd and of the river considered.

tributions of qrd and rd itself. The relations found were

shown to depend uniquely on the coefficient of variation

of the daily data, as reported in the following formulas:

**THE HYDROLOGICAL CHARACTERISTICS OF THE VAJONT VALLEY**

*Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università*

*Editrice*

withdrawn. To this aim, a method proposed by C

*et alii*(1996) was used. As a result, we demonstrated

that, in this case, no more than about 60 Mm

tween 160 and 320 Mm

case of a water supply scheme including the Vajont

creek only, and excluding the other creeks which

should have been connected to the reservoir.

*Fig. 5 - Curves of qrd vs. rd for the Vajont river at Erto*

*Caldaia with different non exceedance probabilities*

*Fig .6 - Curves of qrd vs. rd for the Vajont river at Erto*

*Bindi with different non exceedance proba*

*bilities*

**REFERENCES**

*The use of Gamma distribution in estimating regulated output from storages.*Civil Engineering

*Curve probabilistiche di possibilità di derivazione dei deflussi.*Proc. XXV Conv.

*Studio per la valorizzazione e la salvaguardia delle risorse idriche in Basilicata.*

*Vajont La storia idraulica.*Libreria Internazionale Cortina, Padova. ISBN 88-7784-2385.

*Impianti Idroelettrici,*Vol. I., II edizione, Patron, Bologna.

*Discussion of paper by Alexander, 1962.*Water Resources Use and Management. Melbourne Univ. Press.

*Hydrologic budget of continents and estimate of the balance of global fresh water resources.*Soviet

**4**: 349-360.

*Tab. 1 - Statistical parameters of daily flow data series*

*Tab. 2 - qrd-rd values as estimated from equation (7) by daily flow data recorded at Erto Caldaia and Erto Bindi*

*M.R. MARGIOTTA & B. ONORATI*

*International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013*

*iver and Reservoir Yield.*Water Resources Publication, Littleton Co.

*Deficit analysis by extreme value theory.*Proc. 3

*Possibilità di regolazione dei deflussi con il metodo dei periodi critici.*Proc. XIX Conv. di

*Bacino del Piave. Note idrologiche con particolare riguardo all’impianto idroelettrico Piave-Boite-Maè-*

*Vajont*. L’Energia Elettrica: 773-782