Chapter XXV — The Cost of Tunnel Excavation and the Time Required f… — Tunneling by Charles Prelini

Chapter XXV The Cost of Tunnel Excavation and the Time Required for the Work

Cost—The cost of a tunnel will depend upon the cost of the two principal operations required in its construction, viz., the excavation of the cross section and the lining of the excavation with masonry, metal, or timber. These two operations may in turn be subdivided, in respect to expense, into cost of labor and cost of materials. It is a comparatively simple matter to calculate the cost of the building materials required to construct a tunnel; but it is very difficult to estimate with accuracy what the cost of labor will be. The reason for this is that it is impossible to foresee exactly what the conditions will be; the character of the material may change greatly as the work proceeds, increasing or decreasing the cost of excavation; water may be encountered in quantities which will materially increase the difficulties of the work, etc. Nevertheless, while accurate preliminary estimates of cost are not practicable, it is always desirable to attempt to obtain some idea of the probable expense of the work before beginning it, and the more usual means of getting at this point will be discussed here.

Two methods of estimating the cost of tunnel work are employed. The first is to calculate the probable expense of the various items of work, based upon the available data, per unit of length, and then add to this a margin of at least 10% to allow for contingencies; the second is to apply to the new work the unit cost of some previous tunnel built under substantially the same conditions. In the first method it is usual to consider the strutting and hauling as constituting a part of the work of excavation. To estimate the cost of excavation involves the consideration of three general items, viz., the excavation proper, the strutting of the walls of the excavation, and the hauling of the excavated materials and the materials of construction.

The cost of excavating the preliminary headings or drifts is greater per unit of material removed than that of excavating the enlargement of the section. The cost of bottom drifts is also always greater than that of top headings, the material penetrated remaining the same. Mr. Rziha gives the comparative unit costs of excavating drifts, headings, and enlargement of the profile as follows:—

Bottom drifts	$9.20	per	cu.	yd.
Top headings	4.80	„	„	„
Enlargement of profile	2.84	„	„	„

The cost of hauling increases with the length of the tunnel. This fact and amount of this increase are indicated by the following actual prices for the Arlberg tunnel:—

Top heading	$6.76	per	cu.	yd.,	increasing	37	cts.	per	mile
Bottom drift	7.40	„	„	„	„	26	„	„	„
Enlargement of profile	2.70	„	„	„	„	10	„	„	„

In all the prices given above, the cost of strutting and hauling is included in the cost of excavation.

The cost of excavation is not always the same for the same character of materials in different tunnels. The following figures show the prices paid for the excavation of calcareous rock in four different German tunnels:—

Berliner Nordhausen Wetzler R.R.	$1.24	per	cu.	yd.
Ofen	1.30	„	„	„
Stafflach	2.76	„	„	„
Gries	1.92	„	„	„

The method of tunneling has little influence upon the cost of the work, as shown by the following figures from tunnels excavated through calcareous rock by different methods:—

Ofen tunnel	Austrian method	$93.19	per	lin.	ft.
Dorremberg tunnel	Belgian method	86.08	„	„	„
Stafflach tunnel	English method	91.69	„	„	„

The Martha and Merten tunnels, excavated through soft ground by the Austrian and German methods respectively, cost $87.95 and $87.55 per lin. ft. respectively. In the excavation of the various sections of the tunnel for the new Croton Aqueduct in America, the following prices were paid:—

Excavation of heading	$8	to	$10.00	per	cu.	yd.
Tunnel in soft ground	8	to	9.00	„	„	„
Tunnel in rock	7	to	8.50	„	„	„
Brick masonry	10.00			„	„	„
Timber in place	$40 per M. ft. B. M.

It is the practice in America to include the work of hauling under excavation, but not to include the strutting, which is paid for separately. In some cases only the market price of the timber is paid for separately, the cost of setting up being included in the price of excavation. The writer prefers the European practice of including the total cost of timbering under excavation, since the two operations are so closely connected, and since the contractor employs the same timber over and over again. Knowing the dimensions of the several members of the strutting, it is a simple, although somewhat tedious, process to calculate the total quantity required. An idea of the quantity of timber required for strutting in soft ground may be had from the data given on page 55. The quantity will decrease as the cohesion of the material penetrated increases, until it becomes so small in hard rock-tunnels as to cut very little figure in the total cost.

The cost of hoisting excavated materials through shafts depends upon the depth from which it is hoisted, and upon the character of hoisting apparatus employed. The following table, showing the cost of hoisting for different lifts and by different methods, is given by Rziha, the cost being in francs per cubic meter:—

Height in Metres.	Windlass.	Horse Gins.		Steam Hoists.
Height in Metres.	Francs per Cu. M.	One Horse. Francs per Cu. M.	Two Horses. Francs per Cu. M.	Francs per Cu. M.
15	0.172	0.077	0.062	0.035
30	0.212	0.087	0.070	0.045
45	0.257	0.100	0.080	0.050
60	0.305	0.112	0.092	0.082
90	0.410	0.152	0.110	0.087
120	0.535	0.195	0.135	0.092
150	0.722	0.240	0.157	0.112

Mr. Séjourné, a French engineer, who has been connected with the construction of numerous tunnels by the Belgian method where he was in position to secure comparative figures, has given the following rules for calculating the cost of tunnels. Assuming A to represent the cost of excavating a cu. yd. in the open air, the cost of excavating the same quantity underground in driving headings will be from 9 A to 11 A, and in enlarging the profile it will be about 5 A. The cost of constructing single-track tunnels varies with the thickness of the lining, and may be calculated by the following formulas:

Without lining,	C = 5.5 A.
With roof arch only,	C = 6.4 + 6.4 A.
With lining 18 in. thick,	C = 9.4 + 7 A.
With lining 2 ft. thick,	C = 11 + 8 A.

In these formulas C is the cost per cu. yd. of excavation, including the masonry. For double-track tunnels the amounts given by the above formulas may be used by reducing them about 7¹⁄₂% or 8%.

The second method of estimating the cost of tunnel work consists in assuming as a unit the unit cost of tunnels previously excavated under similar conditions. Mr. La Dame gives the following unit prices for a number of tunnels driven through different materials:

Nature of Soil.	Tunnels, No. of	Excav. per Cu. Yd.			Cost per Lin. Ft.	Max. and Min. per Lin. Ft.
Granite-gneiss	56	$3.07	@	$3.85	$100.	$61.46	@	$190.40
Schist	39	1.38	@	1.53	75.42	43.11	@	70.68
Triassic	3	...			90.85	84.75	@	93.33
Jurassic	69	1.23	@	1.38	77.86	35.24	@	157.2
Cretaceous	34	0.61	@	0.77	59.60	27.37	@	92.25
Tertiary and modern	39	0.33	@	0.61	105.80	51.52	@	188.36

In the following table is given a list of tunnels excavated through different soils, from the most compact to very loose materials, and driven according to the various methods which have been illustrated.

DOUBLE-TRACK TUNNELS.

Name of Tunnels.	Quality of Soil.	Cost per Lin. Ft.	Method of Tunneling.
Mt. Cenis	Granitic,	$273.73	Drift.
St. Gothard	...	193.63	Heading.
Stammerich	Granitic,	157.90	English.
Stalle	Broken schist,	290.58	Austrian.
Bothenfels	Dolomite,	115.64	English.
Dorremberg	Calcareous,	86.08	Belgian.
Stafflach	Calcareous,	91.69	English.
Ofen	Calcareous,	93.19	Austrian.
Wartha	Grewack,	87.95	Austrian.
Mertin	Grewack,	87.55	German.
Schloss Matrei	Clay schist,	94.25	English.
Trietbitte	Clay and sand,	229.0	German.
Canaan	Clay-slate,	69.50	Wide heading.
Church-Hill	Clay with shells,	178.0	...
Bergen No. 1	Trap rock,	182.31	...

SINGLE-TRACK TUNNELS.

Name of Tunnels.	Quality of Soil.	Cost per Lin. Ft.		Method of Tunneling.
Mt. Cenis	Gneiss,	$82.27		Heading.
Stalletti	Granite and quartz,	62.75		Austrian.
Marein	Clay schist,	64.36		English.
Welsberg	Gravel,	165.07		Austrian.
Sancina	Clay of 1st variety,	129.40		Belgian.
Starre	Clay of 2d variety,	191.61		Belgian.
Cristina	Clay of 3d variety,	307.42		Italian.
Burk	...	83.90		Wide heading.
Brafford Ridge	...	85.33		Wide heading.
Dunbeithe	Limestone,	70.47		Wide heading.
Fergusson	Sandstone,	37.46	16	Wide heading.
Port Henry	Limestone,	80.00	17	Wide heading.
Points	Granite,	72.00	16	Wide heading.

The Habas tunnel through quicksand, between Dax and Ramoux, France, cost $118.50 per lin. ft. The cost of the Boston subway was $342.40 per lin. ft. The Severn and Mersey tunnels, constructed through rock under water, cost respectively $208.38 and $263 per lin. ft. The First Thames Tunnel, driven by Brunel’s shield, cost $1661.66 per lin. ft. The Hudson River and St. Clair River tunnels, excavated through soft ground by means of shields and compressed air, cost respectively $305 and $315 per lin. ft. The Blackwall double-track tunnel under the River Thames, which is the largest tunnel ever built by the shield system, cost $600 per lin. ft.

In making estimates of the cost of projected tunnel work based on the cost of tunnels previously constructed through similar materials, it is important to keep in mind the date and location of the work used as the basis for calculations. For example, a tunnel excavated in Italy, where labor is very cheap, will cost less than one excavated in America, where labor is dear, all other conditions being the same. Other reasons for variation in cost due to difference of date and location of construction will suggest themselves, and should be taken into full consideration in estimating the cost of the new work.

Time—The time required to excavate a tunnel depends upon the character of the material penetrated and upon the method of work adopted. Tunnels driven through soft ground by hand require about the same time to construct as tunnels driven through hard rock by the aid of machinery. Tunnels can be driven through hard rock at about as great a speed as through soft or fissured rock, chiefly because the work of blasting is more efficient in hard rock, and because no time is required in timbering. The following table shows the average rate of progress in different parts of the tunnel excavation through both hard and soft materials in feet per month:—

Quality of Soil.	Heading.						Excavation of Shafts.						Enlargement of Profile.
Quality of Soil.	By hand.			By machine.			By hand.			By machine.			By hand.
Very loose soil	16.7	-	26.8	...			6.6	-	16.7	...			6.6	-	16.7
Loose soil	33.4	-	100	...			16.7	-	33.4	...			16.7	-	33.4
Soft rock	66.8			233.8	-	334	33.4	-	66.8	66.8	-	132.6	33.4	-	50
Hard rock	50	-	66.8	233.8	-	334	33.4	-	50	66.8	-	132.6	66.8	-	100
Very hard rock	33.4			233.8	-	334	16.7	-	33.4	66.8	-	132.6	66.8	-	100

The following tables showing the average rate of progress have been compiled from the actual records made in the tunnels named:

Name of Tunnel.	Dimensions in Feet.	Monthly Progress in Feet.	Character of Material.	Observations.
Excavation of headings by hand:
Mount Cenis	10 × 10	65.8	Schist,	Bottom drift.
Sutro	6.7 × 5.7	70.14	Quartzose,	...
St. Gothard	8.4 × 8.7	70.14	Granite,	Top heading.
Excavation of headings by machine:
Mount Cenis	10 × 10	188.7	Calcareous schist,	Bottom drift.
Sutro	8.15 × 10	227.45	Quartzose,	...
St. Gothard	8.4 × 8.7	339.45	Granite,	Top heading.
Trari	8 × 9.35	167	Gneiss,	Top heading.
Arlberg	8.35 × 9.35	474.2	Mica schist,	Bottom drift.
Palisades	16 × 7	160	Trap rock,	Top heading.
Busk	15 × 7	126	Granite,	Top heading.
Cascade	16 × 8	180	Basaltic rock,	Top heading.
Franklin	15 × 7	240	...	Top heading.

The following table shows the monthly progress of completed tunnel in feet excavated through rock:

Name of Tunnel.	Progress in Feet.	Material.	Method.
Cascade	207	Basalt,	Top heading.
Palisades	186	Trap rock,	Top heading.
Busk	190	Granite,	Top heading.
Tennessee Pass	169.5	Granite,	Top heading.

The average monthly progress in feet of excavating tunnels through treacherous ground may be quite generally assumed to be for: (1) clay of the first variety from 43.4 ft. to 60 ft.; for clay of the second variety from 33.4 ft. to 43.4 ft.; for clay of the third variety from 23.3 ft. to 33.4 ft., and for quicksand from 30 ft. to 50 ft. The monthly progress in feet made in sinking the shafts of the Hoosac and Musconetcong tunnels in America was as follows:—

Name of Tunnel.	Dimensions in Feet.	Depth in Feet.	Progress in Feet.	Character of Material.
Hoosac:
East shaft	15.4 × 27.7	1035	21.7	Mica schist.
West shaft	8 × 16	267	16.7	Gneiss.
Musconetcong:
Vertical shaft	8.35 × 16.7	113.5	100	Loose rock.
Inclined shaft	8.35 × 26	304.	32	Loose rock.

The average monthly progress of sinking shafts in treacherous soils may be assumed to be as follows: clay of first variety, 50 ft. to 75 ft; clay of second variety, 36.75 to 50 ft; clay of third variety, 23.4 ft. to 36.75 ft; quicksand, 16.7 ft. to 33.4 ft.

For the reason that the details change with the various conditions encountered in every work, all the tunnel operations have been treated in a general way, purposely avoiding to give any detail. Also the rate of progress and items of cost of tunnels have been given in a broad manner because they greatly vary in the different works. This information, however, can be easily obtained by consulting the Engineering Magazines, where are reported all the tunnel works of America and Europe, and where are given so many details which are very valuable to expert engineers in charge of similar works, but not to students and people who are looking only for general knowledge.

Notes

16 Are unlined.

17 Lined with timber.

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