Shaft sinking cost analysis

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Authors Dowis, John Edward, 1940-

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/318302 SHAFT SINKING COST ANALYSIS

by

John Edward Dowis

A Thesis Submitted to the Faculty of the

DEPARTMENT OF MINING AND GEOLOGICAL ENGINEERING

In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE WITH A MAJOR IN MINING ENGINEERING

In the Graduate College

THE UNIVERSITY OF ARIZONA

1 9 7 2 STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable,without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

WILLARD C. flLACY Date Professor, Mining and Geological Engineering PREFACE

Upon leaving Montana School of Mines in 1963 with a

B , So degree in Mining Engineering, the author1s interest centered on the facets of property evaluation and mine development♦ Between

1963 and 1966, employment in a 300 tons-per^day uranium property and eventually the 40,000 tons-per-day operation at San Manuel, Arizona, provided experience and practical contact with the wide scope of problems and their extreme variability« At the smaller operation, practical experience in shaft sinking was the highlight of achieve­ ment. Of particular significance at San Manuel, the author was moved through each mining department in a manner allowing detailed inquiry ) into the "whys" and "what fors,! behind their development planning.

Shaft construction was recognized as one of the most coim^on "bottle­ necks" relative\ to meeting production quotas from underground mine layouts. , . .

It soon became evident that taking temporary leave from employ­ ment would allow placing this initial experience into perspective.

Entering graduate school provided an environment for combining ex­ perience with academic inquiry, and shaft sinking was chosen as the thesis subject.

In 1967, employment by the U . S . Atomic Energy Commission,

Mining Division, provided the necessary cooperation for thesis comple­ tion in conjunction with on-the-job responsibilities. Through personal contacts with industry, data accumulation began in 1968.

iii iv

Computer programming and conversion to handle data preparation,

regression analysis, and nomographic presentation was a continuing

effort since 1967•

Data contributors wish to remain anonymous« In this situation

it will have to suffice to say that only through the cooperation of

private industry and the U.S.A.E.G. Mining Division was such an in­

teresting array of data made available for analysis. The author had

an idea; gained support from Mining Division management; borrowed

' analytical procedures through suggestions by faculty advisors; imposed

his. programming inadequacies on fellow employees; and received patience

and understanding at home. Though presented under the author's name,

there are many who can accept acknowledgment and gratitude. Those on

my thesis committee are Dr. W. C. Lacy3 Dr. J . F . Abel, and J . C.

Dotson. TABLE OF CONTENTS

•Page

LIST OF TABLES ...... •...... vii

LIST OF ILLUSTRATIONS ...... x

ABSTRACT ...... xii

1. INTRODUCTION ...... 1

2. SHAFT SINKING BACKGROUND ...... 6

South African Influence on North American Shaft Sinking ...... 6 Conventional Sinking vs. Drilled Shafts ...... 10 Shaft Sinking by a C o n t r a c t o r ...... 16

3. THE.ECONOMIC FRAMEWORK OF SHAFT PLANNING ...... 19

It. MODEL ANALYSES OF CONVENTIONAL SINKING ...... 23

Total Cost Per Foot of Shaft and Stations ...... 2h Labor Distribution in the Sinking Cycle UO Detailed Labor Analysis for One District ...... It5 Detailed Labor and Materials for One Shaft ...... 6l The Models in Retrospect ...... 99

5. CONCLUSION ...... 102

APPENDIX A — NOMOGRAPH FOR BOTTOM CREW DRILL AND BLAST MAN-HOURS PER FOOT (COEUR D' ALENE DATA) ...... 108

APPENDIX B — NOMOGRAPHS FOR BOTTOM CREW MUCK MAN-HOURS PER FOOT (COEUR D' ALENE DATA) ...... 110

APPENDIX C — NOMOGRAPHS FOR TOTAL LABOR PLUS SUPERVISION (PERCENT OF TOTAL SHAFT COST) COEUR D' ALENE DATA ..... 113

APPENDIX D — NOMOGRAPHS FOR BOTTOM LABOR PLUS SUPERVISION (PERCENT OF TOTAL SHAFT COST) COEUR D* ALENE DATA ..... Il6

v TABLE OF CONTENTS — Continued

' Page

APPENDIX E -- NOMOGRAPHS FOB TOTAL MAN-HOURS PER FOOT ("X"-SHAFT DATA) ...... 119

APPENDIX F — NOMOGRAPHS FOR CUBIC YARDS OF CONCRETE PER 7-FOOT POUR ("X'-SHAFT DATA) ...... 133

SELECTED BIBLIOGRAPHY ...... lk2 LIST OF TABLES

Table Page

1. Shaft Sinking Chronology .. . . . ' . . . 4

2. Data from Shafts Accessing Sandstone Type Uranium Deposits ...... 25

3. Model Analysis — Dollars Per Foot of Shaft (including Stations and Pockets) ...... 28

k. Correlation Matrix — Dollars Per Foot of Shaft (Including Stations and Pockets) .... 39

5. Labor Distribution for the Sinking Cycle in General .... kl

6. Residuals Summary as an Indication of Model E x i s t e n c e ...... kk

7. Model Analysis Drill and Blast (Percent of Cycle Man-Hours) ...... k6

8. Correlation Matrix — Drill and Blast (Percent of Cycle Man-Hours) ...... kj

9. Model Analysis — Drill and,Blast (Man-Hours Per Foot) ...... k8

10. Correlation Matrix — Drill and Blast (Man-Hours Per Foot) ...... k9

11. Model Analysis — Mucking (Percent of Cycle Man-Hours)...... 50

12. Correlation Matrix — Mucking.(Percent of Cycle Man-Hours) ...... 51

13. Model Analysis — Mucking (Man-Hours Per Foot) ...... 52

lk„ Correlation Matrix — Mucking (Man-Hours Per Foot) .... .53

15. Model Analysis— Lining and Fittings (Percent of Cycle Man-Hours)...... 5k

vii LIST OF TABLES — Continued

Table Page

16. Correlation Matrix — Lining and Fittings (Percent of Cycle Man-Hours) . 55

17. Model Analysis — Lining and Fittings (Man-Hours Per Foot) ...... 56

18 . Correlation Matrix — Lining and Fittings (Man-Hours Per F o o t ) ...... 57

19. Coeur d* Alene Shaft D a t a ...... 58

20. Model Analysis — Bottom Crew Drill and Blast Man-Hours Per Foot ...... ^ 62

21. Correlation Matrix— Bottom Crew Drill and Blast Man-Hours Per Foot ...... 64

22. Model Analysis — Bottom Crew Mucking Man-Hours Per Foot ...... 65

23. Correlation Matrix — Bottom Crew Mucking Man-Hours Per Foot ...... 67

24. Model Analysis — Total Labor Plus Supervision (Percent of Total Shaft Cost) ...... 68

25. Correlation Matrix — Total Labor Plus Supervision (Percent of Total Shaft Cost) ...... 70

26. Model Analysis — Bottom Labor Plus Supervision (Percent of Total Shaft Cost) ...... 71

27. Correlation Matrix — Bottom Labor Plus Supervision (Percent of Total Shaft Cost) ...... 73

28. "X" Shaft Data ...... 75

29. Model Analysis — Total Excavating Man-Hours Per Foot . . . 89

30. Averages of Variables at "X" Shaft for Each Rock Type ...... 90

31. Correlation Matrix — Excavating Man-Hours Per Foot ...... 9.4 LIST OF TABLES — Continued

Table

32. Model Analysis — Cubic Yards of Concrete Per 7-Foot Pour ......

33. Correlation Matrix Cubic Yards of Concrete Per 7-Foot Pour ......

3k. General Cause-and-Effect Summary in Shaft Sinking E c o n o m i c s ...... LIST OF ILLUSTRATIONS

Figure Page

1. Plot of Percent Labor versus Percent Materials for Rectangular Shafts ...... 11

2. Labor and Materials Cost Indexes for the Construction Industry ...... 12

3. Dollars Per Foot Model Selection ...... 29

U. Dollars Per Foot Nomographs ...... 31

5. Bottom Crew Drill and Blast Man-Hours Per Foot Model Selection ...... 63

6. Bottom Crew Mucking Man-Hours Per Foot Model Selection . . . 66

7. Total Labor Plus Supervision (Percent of Total Shaft Cost) ...... 69

8. Bottom Labor Plus Supervision (Percent of Total Shaft C o s t ) ...... 72

9- Shift Report Form for Circular Concrete Shaft ...... 84

10. Shift Report Form for Rectangular Shaft ...... 85

11. Example Time Sheet Illustrating How It Is to Be Filled Out ...... 86

12. Excavating Man-Hours Per Foot Model Selection ...... 93

13. Cubic Yards of Concrete Per 7-Foot Pour Model Selection ...... 97

14. Bottom Crew Drill and Blast Man-Hours Per Foot Nomograph (Coeur d* Alene Data) ...... 109

x xi

LIST OF ILLUSTRATIONS — Continued

Figure Page

15• Bottom Crew Muck Man-Hours Per Foot Nomographs (Coeur d' Alene Data) ...... Ill

16 . Total Labor Plus Supervision (Percent of Total Shaft Cost) Nomographs (Coeur d* Alene Data) ...... llU

17. Bottom Labor Plus Supervision (Percent of Total Shaft Cost) Nomographs (Coeur d' Alene Data) ...... 117

18. Total Man-Hours Per Foot Nomographs (X-Shaft Data) ..... 120

19. Cubic Yards of Concrete Per 7-Foot Pour Nomographs (X-Shaft Data) ...... 13U ABSTRACT

The purpose of the thesis is to seek cause-and-effeet relation­ ships between shaft sinking environment (geology, labor and materials availability, management capability, etc.) and sinking costs« The nature and background of sinking by conventional means are presented through a general discussion of shaft sinking chronology; analysis of South African practices; comments on the pros and cons of drilled shafts; and emphasis on the prominence of sinking contractors*

Application of modeling techniques in pursuing the thesis of cause-and-effeet relationships is introduced by first describing the economic framework of property evaluation in which shaft planning takes place * Emphasis is placed on the models providing "shotgun" type esti­ mates of sinking cost knowing certain parameters defining; 1) conditions

. X at the shaft site; 2) production requirements of the mining company; and

3) limitations imposed on production requirements by the nature of the mineralization (depth, continuity, grade, selectivity of mining, etc.).

Thirteen models covering the labor and materials aspects of

. i shaft sinking are presented including the total cost of the shaft and its stations. Nomographs convert each model into a readily used

"hip-pocket computer"*

The variables constituting the models are summarized in one table as a guide to answering cause-and-effeet questions* Forms for data recording during sinking are proposed to provide pertinent data for future studies. CHAPTER 1

INTRODUCTION

In addressing the 100th anniversary of the American Institute of Mining, Metallurgical and Petroleum Engineers, M r , J. B 0 Mudd

summed up the future of the shaft sinking as follows:

Despite the rapid growth in the importance of open­ cast operations, about one half of the world's minerals production is still derived from underground♦ Even if the relatively high development expenditure and working costs of underground mining strongly encourage the trend towards open pit operations there will still be those deeper deposits which could be profitably extracted given continuing progress in methods of shaft sinking, develop­ ment, and in productivity. Efficient use of labour through mechanization is of crucial importance here, not merely On cost saving grounds, but equally fundamentally, because it is becoming increasingly difficult to find men willing to do heavy manual labour in uncomfortable environments. (Spooner, 1971, p. 154).

Current emphasis in shaft sinking is on reaching deeper ore bodies with the following in mind:

1. Highest advance per day with a minimum of manpower; trend

toward drilled shafts.

2* Larger shaft cross-sections to facilitate increased pro­

duction rates of ore and greater volumes of air for

ventilation and cooling.

3. Reduced shaft maintenance and production hold ups through

stronger linings.

4 o Innovations in sinking techniques and hoisting facilities

to allow reaching greater depths in one lift.

1 As with any process of refinement directed at meeting new conditions, the shaft sinking process is becoming more involved.

The process of refinement relative to the technological developments is presented in chronological order in Table 1.

Rather than going into the detailed presentation of current techniques and equipment comparisons, this thesis is being directed at presenting a cost estimation procedure for conventionally sunk shafts with emphasis on the requirements of greater depth and spiral­ ling costs of labor and materials. Techniques and equipment will be touched upon to the extent necessary, to present the type of costs involved. Development of the estimating procedure required looking at small timbered shafts and the most complex situation, which in this thesis is taken to be the circular concrete-lined shaft. The results of this thesis can be applied in general to any shaft and specifically to shafts sunk under similar conditions to those in the data.

Emphasis on deep shaft sinking (4-4,000 feet in one lift) in

North America has only recently come into the foreground. While the

South Africans have been sinking single lift below 4,000 feet for over

20 years, it has only been in the last few years that depletion of near surface deposits in North America has necessitated this magnitude of sinking. The circular concrete shaft in North America has gained popularity only in the last 5 years with rectangular timber shafts remaining popular for deposits up to 3,000 feet in depth and par­ ticularly in the shallow shafts to 2,000 feet. The biggest competitor to rectangular shafts for these shallower developments is the drilled shaft and its associated steel lining concreted in place „ Drilling of a large diameter shaft to a depth of 7,000 feet depends primarily on the following:

1 o Sufficient, deep, ore body discoveries to establish a

demand for this type of drilling service,

2o Development of drill rigs including draw works with the

capability of handling the drill string lo&ds, torque, and

related stresses»

3• Innovations in lining design and placement to withstand

inherent stresses due to its own mass and the geologic

environment penetrated.

The problems facing shaft drilling reduce primarily to those of time and technology. - TABLE 1 — SHAFT SINKING CHRONOLOGY

1600 "Fire setting" fragmentation

1627 First recorded blackpowder blasting in an underground mine

1831 Safety fuze developed by William Bickford

1847 Nitroglycerine discovered by Ascanio Sobrerq

1861 First recorded compressed air transmission for drilling at

Mont Cenis tunnel in the Alps

1862 Shaft drilling and tubbing (Kind-Chaudron Process)

1862 Mercury fulminate blasting cap

1864 Shaft grouting by handpumping from surface

1867 Dynamite patented by Alfred Nobel

1875 Blasting gelatin developed by Alfred Nobel

NOTE: Few shafts exceed 1,000 feet in depth at this point

1885 Shaft freezing (Poetsch Process)

1893 Calyx drilling introduced to U.S. from Australia

1895 Delay action electric blasting cap patented by H. J e Smith

1896 Grouting below water table from inside shaft

1897 Hammer drill success due to J. G. Leyner

1908 Sinker version of hammer drill developed in South Africa

1920 "Loading pan" innovation to speed hand mucking

1920 "Drop shaft" technique of sinking and lining

1930 Detachable, steel drill bits

1939 Precementation in grouting

1943 Riddell mucking machine (clamshell)

1949 Tungsten carbide inserted bits 5

TABLE 1.-- Continued

NOTE: Rectangular shaft cross-section at its popularity peak

1950 Reverse circulation for large-diameter shaft drilling

1952 "Cactus grab" mucking machine

1954 Blair stage hoist developed for single-lift sinking in excess

of 7,000 feet

1954 Bain system of moveable forms for concrete lining patented

in U.S.

NOTE: South Africans commonly sink below 5,000 feet

1956 Emico 630 crawler mounted shaft mucker; cryderman shaft mucker

1957 Large-diameter drilling studies begin at Nevada Test Site of

UjS. Atomic Energy Commission

1959 South Africans break 1,000 feet per month sinking barrier

1960 Shaft sinking record of 1,106 feet per month in South Africa

1964 A 124-inch diameter shaft drilled to 1,650 feet in sedimentary

rock using one pass of drill rig

1965 A 72-inch diameter shaft drilled to 4,800 feet in hardrock

using one pass of drill rig and reverse circulation

1969 198-inch diameter shaft was drilled to 784 feet in sedimentary

rock

1969 Canadians sink first, single-lift shaft in Western Hemisphere

from surface to below 7,000 feet at International Nickel

Company's Creighton No. 9 mine. CHAPTER 2

SHAFT SINKING BACKGROUND

Before examining the details of cost estimation, it will be timely to describe the general sinking configuration for a circular con­ crete shaft, the pros and cons of drilled shafts, and the legal consid­ erations in contracting for a shaft. The literature amply documents the sinking cycle for rectangular shafts with timber or steel sets. There­ fore, little emphasis will be placed on rectangular shafts here.

Mining below 4,000 feet is not a recent development in North

America. Several districts are well below this level, but the shafts have been sunk in a series of lifts, generally a couple of thousand feet at a time. The depth problems discussed here refer to sinking in a single lift to a depth of 4,000 feet or more.

South African Influence on North American Shaft Sinking

South Africa can be singled out as the undisputed leader in shaft sinking innovation. In the last 20 to 30 years South Africans have extended their development from 4,000 to 12,000 feet vertically below the surface. Shaft development in both South Africa and North

America have faced comparable problems of high temperature, large water inflows, and rock bursts; but the greater South African shaft depths create monumental hoisting problems requiring entirely new equipment and techniques to cope with them. In his description. H. A. Longden (Longden, 1969, p. 39) noted the following improvements

since 1951 in South African sinking below 4,000 feet in one lift:

1„ Improved hoisting capacity. Besides the economic advantage

of having the permanent winding plant in commission as soon

as sinking and equipping of a shaft are completed, the per­

manent hoists, capable of sinking duties, permit the use of

large size hoppifs (buckets) (up to 15 tons) together with

high hoisting speeds. '

2„ Improved mechanical mucking at the shaft bottom by intro­

ducing the cactus-grab device.

3. Multiple-deck sinking stages. These overcome the complete

cessation of sinking while placing forms and pouring concrete.

4. Pipe-line transportation of concrete down the shaft. The

concrete pipe-line eliminates interruption of muck hoisting

when lowering concrete.

5. Improved stage hoists. The use of four-drum capstans with

provision for equal rope tensioning is adequate to about

4,000 feet depending on the rope loads (multiple-deck stage

and mechanical mucking unit). The recently developed Blair

Stage hoist will accommodate 39,000 feet of 1-1/4 inch rope

per drum and will support a stage load of 140,000 pounds

through 7,000 feet of sinking.

The sinking records for the South Africans is spectacular in

comparison to other countries. A few of the most recent achievements

are as follows: ADVANCE , PER YEAR COUNTRY MONTH

1957 S. Africa 834 Feet

1959 S„ Africa , 1,001 Feet

1961 U.S. 510 Feet

1966 Canada 641 Feet

1968 S. Africa 1,260 Feet

1969 Britain 360 Feet

Reasons behind the South African performance are 1) multiple-deck

stages allowing simultaneous concreting and mucking and 2) the use of

up to 36 individually operated rock drills on the bottom simultaneously

drilling a single round. A third item frequently referred to is

equipping the shaft on a second, separate pass after sinking is com­

pleted. The cycle consists of excavation and lining only. Items 1

and 2 above indicate the relatively large labor force (up to 100 or more men) in the shaft at one time. The third item reflects the

removal of delay time due to equipping the shaft as part of the sinking

cycle. When second-pass equipping is used, shaft equipment is suspended

from surface hoists and the sinking buckets travel on rope guides.

Second-pass equipping should not, however, be used unless it can

be clearly demonstrated that there will be an overall saving in shaft

completion time. It may allow setting sinking records, but one should

first consider economic efficiency. 9

The reasons frequently given for U.S. and Canadian sinking

performance being only about one third that of the South Africans are

the lack of young men interested and the greater labor cost per hour

for the work force available. Both of these factors combine to limit

the number of men per shift to maintain a reasonable cost per foot.

The equipment and other sinking innovations of the South Africans which allow their spectacular performance records have been watched

closely and adapted whenever suitable to the labor situation and the

sinking conditions in North America.

Turning to the sinking conditions in the United States, one

finds that capability to sink in one lift below 3,000 feet is prac­

tically nonexistent at this time. Until deeper shafts are required

in the U.S., the large South African set ups will not be required.

Even when they are needed, labor costs will restrict the amount of work that can be performed simultaneously, barring further mechan­

ization.

In summary, the significant reasons for differences in sinking

practices between the U.S. and South Africa in decreasing order of

importance would be as follows:

1 o Scarcity of skilled labor and young men willing to work

in, a shaft.

2 o High labor cost.

3. Relatively shallow, single-lift sinking requirements. 10

The reason for placing the labor scarcity as number one is in answer

to the question, "Why not use South African arrangements if the sinking

rate can be tripled?" There simply are not enough skilled or seasoned men available, at a reasonable price, who are interested in shaft sinking

to allow complementing the number of crews necessary to handle the shaft

demando »

Conventional Sinking vs. Drilled Shafts

In using the term "conventional", one refers to sinking cycles

of drilling and blasting, mucking, and placement of ground support„

Men are required to be on the bottom of the shaft, and this item of

labor has increasingly been the major cause of increased sinking costs.

Figure 1 presents graphically the effect of labor cost on rectangular

shaft sinking in terms of the labor/material cost ratio« Reference to

the Engineering News Record Index in Figure 2 substantiates the greater

increase in labor cost relative to materials.

Coupled with the decreased labor supply for shaft sinking,

interest was placed on the development of full-shaft drilling tech­

niques to circumvent the need for men in the shaft. The largest shaft

drilled for a mining company to date has been a lb-foot diameter one to

a depth of about 800 feet in the Grants Uranium District of New Mexico.

An experimental shaft of about 7.5-foot diameter was drilled and lined

with steel casing to 6,000 feet on the Nevada Test Site for the U.S.

Atomic Energy Commission. These are the maximums as of 1971. For a

detailed analysis of cost estimation for drilled shafts refer to LABOR PLUS SUPPER VISION PERCENT OF TOTAL SHAFT COST 90 80 Figure 1 -- Plot of Percent Labor versus Percent Materials versusPercent Labor Percent of 1 -- Plot Figure 60 70 40 50 30 20 XXW OX X materials ratio. materials oehwcnrt lnn fet te labor/ the lining affects concrete Notehow for Rectangular Shafts. for Rectangular 30

ECN O TTL HF COST SHAFT TOTAL OF PERCENT AEIL AD SUPPLIES AND MATERIALS 40

NO. 10 12 41928 14 I15 1 0X21 1951 II 71922 17 15 13 91923 19 18 16 3 1953 4 2 9 8 5 6 B 7 A C 1957 1 50 1952 I9 60 1953 1957 1946 YEAR 1954 1952 1957 AMERICAN EAGLE 1929 1925 1956 1955 1927 999"DIAM. CONCRETE 1959 968X17 1956 1965

1 2 * D l ACO M N . C R E T E BORAS 0 X10 21 UNITED 5 VERDE# BISBEE QUEEN MAGMA COPPER*5 6.5X 1 1 16X7 8.5X12 8.5 X13 .X8 CONCRETE 6.5X18 JX MINE AJAX I XII II X74 59 8X17 8X18 8X13 8X17 60 i PER 3 T F ROUND

4 59 346 513 5 20 968 620 412 4 60 200 335 54 1 54

11

70 12

1600 Base . 1913 = 100 Construction Cost Index 1400 Labor Components Skilled 023

Common Kn N 1000 Building Cost Index

Componentj*-enais

1913 '15 '20 '25 30 '35 40 45 '60 '65 '70 YEAR

Figure 2 -- Labor and Materials Cost Indexes for the Construction Industry

Source: "Second Quarterly Cost Roundup", Engineering Hews Record, March 19, 1970 13

Selected Bibliography (Dellinger, 1965) . In an example of Dellinger1s,

a 96-inch hole cased to 72-inch inside diameter drilled to 3,400 feet would have cost about $560.00 per foot in 1965. To try to adjust this

cost to a current price by applying inflation factors would underrate

t - the drilling developments of the last 5 years. The point to be stressed

is the cost per foot relative to the size of opening created. It is

the hole diameter which dictates the size and number of hoisting com­

partments and which must be selected in view of the desired production

rate for the shaft. Thus, the major questions to consider relative

to selecting a drilled shaft or a conventionally sunk shaft are the

following:

1. Can the finished shaft, drilled to the desired depth,

be of sufficient area to accommodate the equipment

necessary to satisfy production requirements? A "no"

answer favors conventional sinking.

2. Does the profit margin of the ore body require a shorter

development period than possible by conventional tech­

niques? A "yes" answer favors drilling the shaft.

3. Is the geology at the site of such a nature to cause poor

drill cutting formation and/or flushing, loss of fluid

circulation, or hole caving? A "yes" answer favors con­

ventional sinking.

4. Are conventional sinking facilities readily available for

the job. A "no" answer favors drilling. 5. Is it necessary to air-lift equipment and supplies because

the expense of the road building precludes driving a drill

rig to the site? A "yes" answer favors conventional sinking.

6. Does the depth of occurrence of high water inflow make the

expense of pumping, grouting, or freezing a major portion

of conventional sinking cost? A "yes" answer favors

drilling.

7. Is the estimated cost of drilling; including contingencies

for drilling, lining, and station cutting difficulties;

in excess of a conventional sinking estimate? A "yes"

answer favors conventional sinking.

Regarding the contingencies that plague the drilling of shafts, one finds the following:

1. Caving of the hole. -

2. Twist-off of drill string with related "fishing" to recover

bit, collars, etc.

3. Roller bit failure and its loss in the hole.

4. "Balling up" of shales which resists penetration and

flushing of hole.

5. Lost circulation of drilling fluids in fractured formations.

6. Sticking of casing during placement requiring repeated

"jigging" (raising and lowering or bouncing) to reach the

hole bottom. 15

These are referred to as contingencies in the true sense of the word meaning something happening by chance or accident. The word chance indicates probability or the possibility of not being able to ascertain the presence of trouble from drill core analysis.

Adverse factors exist in conventional sinking. A list of the major ones is as follows:

1. Unforeseen water inflow requiring grouting and possibly

larger pump installation, all of which consume considerable

time.

2. Blasting misfires or propagations.

3. Sloughing or caving requiring placement of temporary support.

Also rock bursts.

4. High rock temperatures.

The final choice by the group or individual in charge between drilled and conventional shaft sinking will largely remain one of pref­ erence and personal knowledge. As with any new product or service, shaft drilling is in the stage of proving its worth and will undoubtedly assume a more prominent role in the face of increasing costs and a de­ creasing supply of labor willing to hire out for the conventional system. As it exists today, shaft drilling is primarily looked upon as 1) a source of quick access to an ore body, 2) economically more favorable to the small tonnage (<^1,000 TPD) operation, and 3) an economical means of developing secondary mine entrances, such as ventilation shafts, which generally can be of smaller cross-sectional ■ ■ 16 area than production openings» The two major factors to be overcome in economically adapting drilling to larger diameters and depths to

7,000 feet or more are 1) design of suitable drill rigs including draw works and 2) increased strength of casing materials and/or new casing design developmentso

Shaft Sinking by a Contractor

The secret to good, efficient shaft sinking is a trained crew.

This statement is even more relevant today with the increased mechan­ ization involved and the widely accepted use of concrete linings.

The highest pay can hold the best men, assuming favorable management, but a mining company cannot hold them at production wage scales between shaft jobs if considerable time lapses. Sinking contractors offer relatively stable employment to these men and develop expertise in sinking methods and techniques. In this time of insufficient labor interest in shaft sinking, the shaft contractor can recruit men and gradually train them to understand the sinking process and to cope with the conditions. This training time is much more easily absorbed in his operation than in that of most mining companies requiring only one or two new shafts every 10 years or so.

For these reasons and others, the shaft sinking contractor is a sign of the times. As with any contracted work, the legal aspects are important and a competent lawyer is a necessity. The person in charge of the contract and acting as representative of the company soliciting 17

the services of a contractor should at least be aware of the general

contract contents and specifications needed to be provided in the

contract.

The decision to sink is one of first deciding to drill the

shaft or use conventional methods. When the conventional approach is

selected, one must decide whether or not to put the job out on a contract bid. Equipment cost is a major factor in favor of seeking a contractor, but a major factor in favor of conventional sinking is

the contractors profit of about 20% built into his estimate. The decision of captive (owner) sinking or contractor sinking rests with an economic evaluation of the following two alternatives:

1. Estimated Cost Per Foot Of Completed Shaft By Captive

Crews

A. Availability of shaftmen

B. Competence of shaftmen

C. Availability of competent supervision

D. Capital cost of equipping the crews

E. Time involved in bringing crews and equipment together

F. Availability of sinking contractors to perform the job

2. Estimated Cost Per Foot Of Completed Shaft By Contractor

Crews

A. Availability of contractors

B. Contractor competence

C. Contractor's profit Final analysis of the decision must give consideration to the quality of the finished shaft in terms of trouble-free operation. The least expensive short-term alternative is not necessarily the most efficient long-term one. CHAPTER 3

THE ECONOMIC FRAMEWORK OF SHAFT PLANNING

Only shaft sinking by conventional methods will be considered beyond this point, and the presentation will apply to the capital investment whether the shaft be sunk by the owner or a contractor.

A distinction between owner and contractor sinking is the owner will be striving for minimum cost per foot whereas the contractor must in addition realize a profit. His profit must not make the cost per foot estimate much different from the owner's estimate because the owner would then be prone to take a second look at the alternatives.

The economic evaluation herein will be the type necessary for appropriation of funds for a new installation. Two segments of the initial evaluation are undertaken in the following order but eventu­ ally overlap and continue on relatively parallel courses:

1. Feasibility studies

2. Capital estimate

L. A. Rowe, project manager of Parsons Jurden Corp. in 1968, stated the

following relative to the importance of feasibility studies:

Project feasibility studies involve studies of ore reserves, mining methods, process, markets, plant sizes, plant locations, profitability, utilities, construction plans, transportation, labor, material and equipment costs. Over simplification or under-estimation of the importance of any one of these factors can be the beginning of serious error as far as final economic success of the project is concerned.

19 Time and money spent in preplanning a method of approach for making the capital estimate will pay divi­ dends. Engineers responsible for process data and design criteria in this area have an important responsibility not often mentioned or discussed. This can be referred to as the 1degree-of-assurance1 or 'performance factors' which should be assigned to every major process area. In almost every new plant design there are a few areas where the research and development department has provided only the bare minimum criteria for plan design. If these areas are categorized as 'low-complexity' factors, ---, then the risk taken in design is low. If the area in question happens to be one at the heart of the plant, then the degree of risk in design can be high. Now if the design engineer has been warned by the process engineer that the degree- of-assurance is low, , then the designer can make allow­ ances for this factor. Also, the estimator will allow extra capital in this area and the shock of a capital request for another hundred thousand dollars when the plant is in the construction or even the start-up phase can be eased. (Rowe, 1968, p. 154)»

In.regards to the capital estimate, he further comments:

It can be shown that a capital cost estimate for a given minerals plant can range over a wide area. The cost will be inversely proportional to the accuracy and thoroughness of the process and basic design criteria given the estimator. Sometimes the capital cost estimate developed in a feasibility study can be accepted with minor refinements, as the budget estimate for a minerals plant.

There is no panacea for easy development and annual updating of plant capital costs. In times of a stable world and national economy the evolution of good figures for labor cost, labor productibility, material cost and availability is predictable and accurate. Preparation of good capital estimates takes time and there are no substitutes for painstaking, careful detailed study of every minute detail required to build a plant.

Length of time required to make a capital estimate will hinge heavily on the thoroughness of the data devel­ oped during the feasibility study and basic engineering phases of the project. A feature of a good estimator often overlooked is his ability to always keep in mind that optimum design is not necessarily based upon minimum capital cost. (Rowe, 1968, p. 155). 21

Assuming a vertical shaft to be the most feasible access to the deposit, it must be recognized as the "bottle neck" through which the life stream of the operation must flow. Therefore, barring major difficulties in stoping the material and moving it to the shaft, the performance of the shaft in terms of tons per day hoisted will be the key to successful (profitable) mining,

.The capital estimate portion of the evaluation must permit calculation of a rate of return on the investment. Therefore, the mineralization grade relative to the cost of producing a ton of it and the trend in market value are the major factors determining the production rate and capital investment, It becomes apparent that initial feasibility study and cost analysis must concern overall mine design, especially the manner in which the mineralization can most efficiently and completely be mined and delivered to the shaft. Before considering shaft design, then, one must concentrate first on how best to gain access to the mineralization through level development and then to methodically extract it. This initial access development, which will include the shaft, is commonly referred to as primary devel­ opment . Once the mineralized area is reached and opened up for mining to commence, it becomes general practice to refer to subsequent devel­ opment openings within the mineralized area but in the immediate vicinity of the associated primary development, as secondary development.

Primary development will be taken as a capital cost while secondary development will be a direct operating expense. Additional operating costs, direct and indirect, will also be involved in stoping, haulage, supplies, supervision, and etc. . 22

During layout of the general mining plan, several analyses, each for a different production rate need to be performed to study the costs of getting the material to the shaft. With these initial mining studies completed and appropriate costs categorized for the level development and mineralization extraction, then a "shotgun" estimate of shaft cost for a particular production rate is added to each primary development capital estimate. Testing the range of production rates relative to profit and related return on investment is the final step. Details of this testing in terms of discounted- cash-flow analysis are covered by Dowis (1970, pp. 82-87).

The term "shotgun" suggests a scattering of shaft sinking cost, which turns out to be the case in seeking an estimate. Rules of thumb abound within any one district but closer examination shows a considerable spread within it. The following chapter will present examples of how one can process an accumulation of shaft sinking data

(costs and related conditions) and produce graphic models from which the "shotgun" nature of the estimate can be given a greater degree of reliability. CHAPTER 4

MODEL ANALYSES OF CONVENTIONAL SINKING

The object of model analysis for any system or function is to seek a mathematical expression of cause-and-effect relationships intu­ itively felt to be present. The model may consist only of a 2-dimen- sional plot on graph paper. For more complicated systems the variable involved may be too numerous for their interaction to be comprehended by the human mind except in an abstract fashion. Model building for a construction item, such as a shaft, is a simplifying process from the point of view that one is seeking to predict or estimate results, not 100% correct, but within say 80%-90% of the actual. Therefore, the intention is to find only the bare minimum of variables needed to obtain this precision of estimate. To ask for precision beyond this point leads to the biggest argument against model building in the first place. This negative argument says generally that the results, even though quantifying the abstract, cannot be blindly applied to a new shaft if the new shaft conditions have not previously been incor porated from shafts in similar settings. By environment, one means variables, such as shaft dimensions, ground conditions, water inflow, crew size, number of shifts per day, etc. In other words, a point of diminishing returns can be expected relative to the purpose of the model. . 24

The purpose of the following models is to demonstrate how an accumulation of data can be turned into a "working tool" rather than a stack of reports and notes requiring shuffling through each time the question "How much will it cost under these conditions?" arises. The appeal of the models is that as new data become available, they can be added and the model updated and recomputed. In using model analyses knowledgeably, one's initial estimates can be looked upon as possessing the invaluable experience of others through this experience being built into the model.

In Chapter 3, the discussion had reached the point of requiring a "shotgun" estimate of various sized shafts to allow selection of the designed tons per day capacity for the new mine. The nomographs pre­ sented are an endeavor to illustrate their application to this rough, initial estimate.

Total Cost Per Foot of Shaft and Stations

Twenty-seven shafts scattered throughout uranium mining dis­ tricts in the Western United States were analyzed for an explanation of what variables affected the cost per foot for the finished shaft and level stations. Table 2 lists the extent of the uniform data avail­ able for each. Differences in rock type were not quantified because the geologic columns involved for each were sedimentary in origin and so interbedded with sandstones, conglomerates, shales, etc. that each shaft penetrated roughly the same types of material. To this extent, the rock type was assumed constant. In Table 3, the variables which

\ - 25

TABLE 2 -- DATA FROM SHAFTS ACCESSING SANDSTONE TYPE URANIUM DEPOSITS

Depth Shaft Shaft Shaft Shaft Sunk Number Number Area Lining Length/Width No. (feet) Levels Compartments (sq. ft.) Code — / Ratio

1 700 1 3.0 200 1 2.0 2 600 3 2.5 112 1 1.7 3 500 1 2.5 112 1 1.7 4 550 1 2.5 136 1 2.1 5 600 1 3.0 200 1 2.0 6 300 1 2.0 84 1 1.7 7 1,500 1 3.0 154 2 1.0 8 750 2 5.0 200 1 2.0 9 800 1 3.0 180 1 1.8 10 850 3 3.0 180 1 1.8 11 850 3 5.0 200 1 2.0 12 1,590 1 3 .0 144 1 2.3 13 330 1 1.5 96 1 1.5 14 396 1 3.0 119 1 2.4 15 700 3 2.5 112 1 1.7 16 960 2 2.0 154 2 1.0 17 510 1 2.5 105 1 2.1 18 623 1 3.0 126 1 2.6 19 938 1 3.0 112 2 1.7 20 650 1 3.0 112 1 1.7 21 830 2 4.0 176 1 2.8 22 848 2 4.0 176 1 2.8 23 826 2 4.0 176 1 2.8 24 848 2 5.0 190 1 1,9 25 650 1 3.0 136 1 2.1 26 400 1 2.5 136 1 2.1 27 862 3 2.0 113 2 1.0

a. Shaft Lining Code 1 = Timber Shaft Lining Code 2 = Concrete 26

TABLE 2 -- Continued

Max. Wet Water Sustained Depth Total ?haf t Inflow Year Production Months (% of Cost No. (g.p.m.) Completed (t.p.d.) To Sink Total) ($/foot)

1 0 1955 250 3 0 206 2 0 1956 200 8 0 180 3 0 1957 250 6 0 200 4 0 1955 250 4 0 262 5 0 1954 250 6 0 217 6 0 1959 150 ■ 5 0 318 7 800 1958 500 25 75 1,297 8 350 1957 600 12 40 773 9 0 1959 800 6 0 241 10 110 1956 1,000 ' 19 25 560 11 200 1958 1,500 15 45 1,176 12 0 1958 200 7 0 260 13 6 1959 200 6 15 527 14 0 1955 600 8 0 100 15 20 1959 300 5 15 857 16 25 1958 400 13 17 1,016 17 0 1957 300 7 0 211 18 4 1957 370 5 5 244 19 400 1959 400 8 30 1,009 20 85 1957 100 7 32 370 21 500 1958 600 13 45 513 22 100 1958 1,000 11 50 650 23 540 - 1957 350 8 20 887 24 120 1959 560 12 20 944 25 0 1956 350 5 0 282 26 0 1954 200 5 0 300 27 250 1960 150 13 62 700

b. Total cost includes all shaft costs below the collar plus costs for stations and pockets. 27 were felt to cause the variation in cost per foot are summarized with a brief explanation as to why each affects the model. Discussion of the correlation and other items, such as the selection of the best model from a group of data follow standard statistical procedures which the author chose not to dwell upon but suggests that the reader refer to Crow, Davis, Maxfield (i960), Draper and Smith (1966), and Abel (1967).

An important item to note in Table 3 relates to the form a variable may assume in the model. 1/3 1/2 2 3 The transformations (x , x , x , and x ) performed on the raw data of Table 2 were selected as those most likely to convert a nonlinear relationship of x to y into a linear one. Figure 3 graph­ ically depicts the tests conducted in justifying the model. The 27 observations of data are sufficient to give a standard error of resid­ ual (SEE) of 56.87 dollars per foot. Since the standard error of residual (SEE) corresponds to the standard deviation, one can use

56.87 dollars per foot to calculate the upper and lower confidence limits (C.L.) at the 99% probability level. This confidence interval can be applied to any cost estimate made by using the model, and it is a realistic appraisal of its usefulness. By using standard procedures, one finds the model answers to be within j; 22.50 dollars per foot. TABLE 3 MODEL ANALYSIS — DOLLARS PER FOOT OF SHAFT (INCLUDING STATIONS AND POCKETS)

Y Correlation T-Value No. Variable Name — / Coefficient Significance Explanation of Correlation

1 Maximum G.P.M.**(1/3) 0.8169 4.7267 Increased water inflow increases cycle time. 2 Maximum G.P,M.**1 0.6851 -4.4364 (Refer to Variable 1) 3 Maximum G.P.M.**3 0.5282 4.3524 (Refer to Variable 1) 4 Sustained T.P.D. Rate**3 0.3785 4.2431 Higher tons per day production rates generally use larger shafts requiring more total labor and materials 5 Sustained T.P.D. Rate**(l/3) 0.4179 3.8863 (Refer to Variable 4) 6 Sustained T.P.D. Rate**(l/2) 0.4175 -3.7263 (Refer to Variable 4) 7 (Length/Width Ratio)**2 -0.2580 -3.3384 Circular Concrete shafts with ratio = 1 cost more per foot. 8 % Depth Wet**(l/3) 0.8153 -3.1565 Wet part of shaft generally advances slower than the dry portion. 9 No. Compartments**! 0.3860 -3.0732 Correlated (+).with shaft area and production rate (refer to Variable 4) . 10 No. Compartments**3 0.4617 2.9702 (Refer to Variable 9) 11 Depth**3 0.3363 2.8617 Mucking portion of cycle is generally more with longer hoisting distance. 12 Months to Sink**3 0.5724 -2.3701 Correlated (+) with depth. Slower ad­ vance rate increases man-hours per foot. 13 7. Depth Wet**l 0.7438 1.6094 (Refer to Variable 8) 14 Months to Sink**(l/3) 0.6888 -0.8771 (Refer to Variable 12) 15 (Length/Width Ratio)**(1/3) -0.3803 -0.1878 (Refer to Variable 7)

a . Computer language (FORTRAN) nomenclature is used for representing the power of a variable, Maximum G.P.M.**(1/3) represents the cube root of Maximum G.P.M. STANDARD ERROR OF ESTIMATE (Syx) DOLLARS PER FOOT 200 250 150 100 50 o C£ 0. iue3 --3Figure Dollars Selection ModelFoot Per 400 200 300 100 II (A) (B) Adequacy ofData.(B) Adequacy UBR F OBSERVATIONS OF NUMBER lto and of Plot 15 REGRESSION 15 '0.97 (A) (B) 923 19 STEP 20 y . SyX 25 27 035 30 0.6 0.2 0.4 0.8 i.o 29

MULTIPLE CORRELATION COEFFICIENT SQUARED (Rz) 30

The nomographs for this model (see Figures 4A through 4H) allow rapid solution, using a straight edge, of the mathematical relationship as follows:

Y = -2858.52 + 0.000000074 DEPTH3 - 459.91 CMPRT

+ 9.08 CMPRT3 - 226.19 L/W1/3 - 20.29 L/W2

- 6.68 GPM +557.08 GPM1/3 + 0.0000068 GPM3

+ 1960.29 TPD1^3 - 478.37 TPD1/2 + 0.00000045 TPD3

- 162.58 MOTHS1/3 - 0.070 MNTHS3 + 7.33 WET

- 440.71 WET1/3

Definitions of the variable abreviations are given in Table 4 which summarizes the extent to which each variable, including the dependent one, relates to every other variable. Table 4 is very important to the user of the nomographs because blindly plunging into them will produce ridiculous answers, such as negative dollars per foot. As an example of careless use one should not be seeking an estimate for a 6 compartment shaft to produce 50 tons per day for the following reasons:

1 o Both the number of compartments and the tons per day rate

are outside the range of data from which the model was

derived.

2. Looking at the relationship of CMPT (number of compart­

ments) and TPD (tons per day) in Table 4, one finds them

to have a positive correlation with one another. Thus as I- one increases, the other does likewise. DEPTH SUNK

FEET 1300 1500 1100 500 900 300 700 Figure 4 -- Dollars Per Foot Nomographs FootPer --Dollars 4 Figure 2.0 (A) Depth Sunk Versus Number of Compartments of Number Versus Sunk Depth (A) UBR F COMPARTMENTS OF NUMBER . 4.0 3.0 5.0 31 - 3900'

- 4000*

- 4200- SECOND CUMULATION DOLLARS PER FOOT -4200 -4400 -4000 -4500 -3800 -3700 -3600 -4300 -3900 -4100 -3500 LU LU LU LU iue4 -DlasPrFo Nmgah, continued. Nomographs, FootPer -- Dollars 4 Figure 100 (C) Second Cumulation Versus Maximum Water Maximum Versus Cumulation Second (C) 200 AIU WTR INFLOW WATER MAXIMUM Inflow (100 to 800 Gallons Per Minute)Per to 800 (100 Gallons Inflow ALN PR MINUTE PER GALLONS 300 0 500 400

0 700 600

800 33 SECOND CUMULATION DOLLARS PER FOOT -4000 -4400 -4200 -3800 -3600 0 Figure 4 — Dollar Per Foot Nomographs ,FootPer continued. Dollar — 4Figure 20 (D) Second Cumulation Versus Maximum Water Maximum Versus Cumulation Second (D) o o DTI FR -0 G PM) 0-100 FOR (DETAIL AIU WTR INFLOW WATER MAXIMUM ALN PR MINUTE PER GALLONS Inflow (0 to 100 Gallons Per Minute)Per to100 (0 Gallons Inflow 40 C o. l "o 60

80

34 100 THIRD CUMULATION DOLLARS PER FOOT -3400 -2600 -3000 -2200 -4200 -3800 -1800 -1000 4600 -600 1400 200 100 iue4 Dlas e otNmgah> continued. Nomographs> Foot Per Dollars — 4 Figure 300 E TidCmlto ess Sustained Versus Cumulation Third (E) UTIE POUTO RATE PRODUCTION SUSTAINED Production Rate (Tons Per Day) (Tons Per Rate Production OS E DAY PER TONS 700500 ■3600 '2000 0 0 0 4 -3200 800 400 2800 (200 1600 4400 ' 900 1100

1300

1500 35 MONTHS TO SINK 20

O; — Dollars P e r Foot Nomographs , cont-

Fourth Cumulation Versus Months to 'nUed

Sink 5000

3000

2000

iOOO

-1000

40

P E R « ”TT = " PTt o t a l 50 r *gure 4 — Dollars Per Foot Nomographs, continued (c) Fifth Cumulation Versus Wet Depth (10 to 75 Percent of Total) o W E T DEPTH 8 PERCENT OF TOTAL (DETAIL FOR O-IO PERCENT)

- Dollars Per Foot Nomographs

Fifth Cumulation Versus W e t • Con« n u e d (0 to 10 Percent of Total) Depth TABLE 4 -- CORRELATION MATRIX — DOLLARS PER FOOT OF SHAFT (INCLUDING STATIONS AND POCKETS)

CMPRT CMPRT3 L/W1/3 L/W2 GPM GPM1/3 GPM3 TPD1/3 TPD1/2 TPD3 MNTHS1/3 MNTHS3 WET WET1/3 Y

DEPTH3 +0.09 +0.03 -0.20 -0.10 +0.42 +0.28 +0.56 +0.06 +0.05 +0.01 +0.43 +0.56 +0.34 +0.20 +0.34

CMPRT +0.96 +0.48 +0.47 +0.40 +0.51 +0.13 +0.65 +0.6-5 +0.51 +0.38 +0.13 +0.36 +0.39 +0.39

CMPRT3 +0.35 +0.33 +0.35 +0.51 +0.07 +0.62 +0.62 +0.55 +0.40 +0.11 +0.38 +0.44 +0.46

L/W1/3 +0.96 -0.11 -0.13 -0.26 +0.25 +0.25 +0.13 -0.33 -0.44 -0.30 -0.23 -0.38

L/W2 +0.05 +0.03 -0.11 +0.28 +0.27 +0.11 -0.19 -0.32 -0.13 -0.07 -0.26

GPM +0.89 +0.85 +0.26 +0.25 +0.08 +0 .66 +0.67 +0.77 +0.69 +0.69

GPM1/3 +0.61 +0.38 +0.38 +0.25 +0.74 +0.56 +0.38 +0.92 +0.82

GPM3 95% Confidence +0.12 +0.11 -0.06 +0.56 +0.83 +0.60 +0.43 +0.53 N - 27 TPD1/3 /r/ i 0.381 +0.99 +0.76 +0.56 +0.35 +0.36 +0.38 +0.42

TPD1/2 +0.79 +0.56 +0.35 +0.38 +0.39 +0.42

TPD3 +0.41 +0.21 +0.33 +0.33 +0.38

MNTHS1/3 +0.80 +0.79 +0.73 +0.69

MNTHS3 +0.67 +0.51 +0.57

WET +0.91 +0 .74

WET1/3 +0.82

DEPTH ■ Depth Sunk

CMPRT m Number of Compartments

L/W ■ Length/width Ratio

GPM - Max. Water Inflow

TPD - Sustained Production Rate

MNTHS ■ Months To Sink

WET ■ Wet Depth (% of Total)

Y - Dollars Per Foot W VO 40

Reference to Table 4 becomes a necessity in developing a "feel" for which direction (increase or decrease) to vary one variable relative to a change in another. Note that in moving from the first to the last nomograph for a model that the answer is being accumulated„ Upon fin­ ishing on the last nomograph, one has the estimated cost per foot for the shaft and level stations,

Labor Distribution in the Sinking Cycle

In Table 5, a uniform suite of data is presented for 9 shafts scattered throughout a variety of districts in the Western United States,

Five of these are uranium mines in sedimentary host rocks, one represents access to a water tunnel construction project, and the remaining two are from base metal operations» The shaft involving steel sets and con­ creting was started with steel sets alone but bad ground conditions required pouring a full concrete lining through 60% of the shaft depth.

Six models were investigated from these data as follows:

1, Drill and blast labor as a percent of total cycle

man-hours,

2, Drill and blast man-hours per foot,

3, Mucking labor as a percent of total cycle man-hours,

4 o Mucking man-hours per foot,

5, Lining and fittings (sets, guides, etc.) as a percent

of total cycle man-hours,

6 o Lining and fittings man-hours per foot,

i TABLE 5 — LABOR DISTRIBUTION FOR. THE SINKING CYCLE IN GENERAL 1/

Drill and Excavation Area Blast Muck t o . Shaft Type Dimension (ft2) <7„) (mp/ft) (mh/ft^) (%) (mh/ft) (mh/f t-

1 Circular Concrete 9 ' Diam. 64 20.8 1.49 0.023 22.0 1.57 0.025

2 16' Diam. 201 21.1 2.12 0.011 34.9 3.49 0.017

3 17' Diam. 227 30.2 8.65 0.038 48.6 13.90 0.061

4 . Steel Sets W/Conc. 17' x 6.5' 110 26.6 2.92 0.027 24.4 2.68 0.024

5 Steel Sets 12' x 11' 132 21.0 3.08 0.023 41.3 6.04 0 .046

6 16' x 6.5' 104 29.0 4.89 0.047 34.6 5.67 0.055

7 Timber Sets 12' x 7' 84 21.1 2.23 0.027 26.0 2.74 0,033

8 11' x 8' 88 25.0 2.01 0.023 42.9 3.45 0.039

9 11' x 11' 121 33.2 13.23 0.109 41.2 19.84 0.164

1/ The data represent shafts sunk between 1957 and 1969 using mechanical mucking methods, mh/ft^ as Man-Hours Per Cubic Foot . mh/ft = Man-Hours Per Foot % w Breakdown of cycle time including only the men in the shaft directly related to excavation, support placement, and shaft equipping. TABLE 5 — Continued

Lining Avg. Max. and Rock Advance Shaftmen Shifts Water Dpeth Fittings Type Per Bay Per Per Lining Inflow Sunk lo. Shaft Type (%) (mh/ft) (mh/ft3) Cods (ft.) Shift Day Code (gpm/100) (feet/100)

1 Circular Concrete 57.0 4.07 0.064 1 6.7 2 3 3.0 2.00 1.75

2 43.9 4.39 0.022 1 6.5 4 3 3.0 15.00 11.50

3 21.3 6,10 0.027 3 4.9 7 3 3.0 0.10 8.96

4 Steel Sets W/Conc. 48.8 5.34 0.049 3 5.6 3 3 2.5 2.50 10.03

5 Steel Sets 37.6 5.48 0.042 1 5.3 4 3 2.0 0.20 5.15

6 36.6 5.52 0.053 3 2.1 4 1 2.0 0.10 2.09

7 Timber Sets 53.0 5.59 0.067 1 9.0 3 3 1.0 0.10 5.84

8 32.2 2.60 0.030 1 4.4 2 2 1.0 0.05 2.88

9 25.6 12.28 0.102 2 2.4 3 3 1.0 4.50 11.27

Rock Type Code: 1 = Interbedded sandstones and shales 2 = Dolomite 3 = Igneous and metamorphic

Lining Code: 1.0 = Timber sets 2.0 = Steel sets 2.5 = Steel and concrete 3 . 0 = Concrete - 43

Inclusion of these models in this thesis was decided when analysis of

the residuals for each showed a very close comparison of predicted Y

versus measured Y. In other words, a very strong indication exists in

favor of believing a meaningful, general relationship can be derived if

enough data are made available. These residuals are summarized in

Table 6, Considering the broad source of the data in Table 5, nomo­

graphs were not developed because insufficient observations were

included for each type of shaft to place statistical significance on

the results,

Mathematical expressions of these models and regression quality measures (R and Syx) for each are as follows with the variable

abbreviations defined in Tables 8, 10, 12, 14, 16, and 18:

1. Drill and blast (%); (R2 = 0.94, Syx = 1.6%)

Y = -230.88+646.89RT1/3-384.7 2RT1/2-5.32ADV1^-H) .0088 MEN3

2. Drill and blast (mh/ft): (R2 = 0.95, Syx = 1.3mh/ft)

Y = 36.53 - 25.33ADV1/3 + 0.012ADV3 + 0.012MEN3 + 1.04SHIFT2

3. Mucking (%): (R2 = 0.90, Syx = 4.27=)

Y = -6.68+34.7 2AREA1/3-0.01ADV3-6.9 3LING-11.51DEPTH1^

4. Mucking (mb/ft): (R2 = 0 .95, SyX = 1 .9mh/ft)

Y = 29.45-21.72ADV1/2+0.021ADV3+0.021MEN3+7.48SHIFT

5. Lining and fittings (%): (R2 = 0.99, SyX = 1.9)

Y = -6.04^0.032AREA2+0.32ADV2-0.045MEN3+35.95LING1/3

6. Lining and fittings (mh/ft): (R2 = 0.90, SyX = 1.2)

Y = -6.87+7,78MEN1/3+0.66GPM2-0.044GPM3-0.016DEPTH2 TABLE 6 — RESIDUALS SUMMARY AS AN INDICATION OF MODEL EXISTENCE

• Models From Labor Distribution For The Sinking Cycle In General Drill And Blast Mucking Lining And Fittings (mh/ft) (mh/ft) Obs No, Item (7.) (%) (%) -T——"(mh/ft)

Predicted Y 21.9 2.55 37.4 3.54 43.4 4.39 1 Measured Y 21.1 2.12 34.9 3.49 43.9 4.39 Residual + 0.8 + 0.43 + 2.5 + 0.05 - 0.5 0 Predicted Y 29.6 8.25 45.4 13.56 . 21.5 6.76 2 Measured Y 30.2 8.65 48.6 13.90 21.3 6.10 Residual - 0.6 - 0.40 - 3.2 - 0.34 + 0.2 + 0.66 Predicted Y 21.3 1.71 19.2 2.03 58.3 5.16 3 Measured Y 20.8 1.49 22.0 1.57 57.0 4.07 Residual + 0.5 + 0.22 f 2.8 + 0.46 + 1.3 + 1.09 Predicted Y 26.5 3.27 26.1 4.68 47.6 6.19 4 Measured Y 26.6 2.92 24.4 2.68 48.8 5.34 Residual - 0.1 0.35 + 1.7 + 2.00 - 1.2 + 0.85 Predicted Y ’ 22.6 4.21 39.7 6.32 39.7 5.09 5 Measured Y 21.0 3.08 41.3 6.04 37.6 5.48 Residual . 4- 1.6 1.13 f 1.6 + 0.28 + 2.1 - 0.39 Predicted Y 29.5 5.99 40.4 7 .01 34.3 5 .42 6 Measured Y 29.0 4.89 34.6 5.67 36.6 5.52 Residual + 0.5 1.10 5.8 1.34 - 2.3 - 0.10 Predicted Y 22.7 0.26 40.6 0.77 33.2 2.80 7 Measured Y 25.0 2.01 42.9 3.45 32.2 . 2.60 Residual - 2.3 - 1.75 - 2.3 - 2.68 + 1.0 + 0.20 Predicted Y 20.5 1.94 26.8 2.35 52.1 3.82 8 Measured Y 21.1 ; 2.23 26.0 2.74 53.0 5.59 Residual - 0.6 - 0.29 + 0.8 - 0.39 - 0.9 - 1.18 Predicted Y 33.2 12.47 38.5 19 .10 25.9 11.69 9 Measured Y 33.2 13.23 41.2 19.84 25.6 12.28 Residual 0 - 0.76 - 2.7 - 0.74 + 0.3 - 0.59 45

The unusually high values of the multiple regression coefficient (R^)

and low values of the standard error of the estimate (SyX) , considering

only four variable terms in each model, makes these models appear very

promisingo The data come from published reports and company files rep­

resenting a random sampling when realized that the shafts are scattered

throughout the Western United States„ By collecting additional obser­ vations for these data, a very useful tool in cost estimation appears

to be available, Tables 7, 9, 11, 13, 15, and 17 summarize the inter­

relationships between variables within each model and briefly explain

their significance.

Detailed Labor Analysis for One District

The example models presented so far have been of a general

nature independent of location. Another approach to securing data is

to analyze the cost and conditions within each district. This may be a more reasonable approach to allow greater precision in estimation by

limiting the variables to those affecting a particular district. In

the U e So Bureau of Mines Information Circular 7961 (Olds and Parsons,

1957), data including that in Table 19 were found. Four aspects of

these data were analyzed using 10 shafts for which uniform data were

given with the following models resulting:

1 o Bottom crew drill and blast man-hours per foot

Y = 590.65+5.18 YEAR -229.61 YEAR1/3+0 .050 CMPRT3

2 o Bottom crew muck man-hours per foot

Y = 21.56+0.00000050 AREA3 -0.61 HOIST1/3-7.74 LNGRD1/3 TABLE 7 — MODEL ANALYSIS DRILL AND BLAST (PERCENT OF CYCLE MAN-HOURS)

Correlation T-Value No, Variable Name —a/ Coefficient Significance Explanation of Correlation______

1 Rock Type Code**(l/3) 0.7858 3.0815 Lower penetration rate of drilling in harder rock types.

2 Rock Type Code**(l/2) 0.7780 -3.0405 (Refer to Variable 1)

3 (Avg. Advance/Day)**(1/3) -0.7926 -1.6643 It takes more mucking time than drilling time to increase the length of a round by one foot.

(Shaftmen/Shift)**3 0.3686 1.3809 An additional shaftman affects drilling man-hours more than mucking when using mechanical muckers.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable. Rock Type Code**(l/3) represents the cube root of Rock Type Code.

■p- CT\ 47

TABLE 8 -- CORRELATION MATRIX — DRILL AND BLAST (PERCENT OF CYCLE MAN-HOURS)

RT*/2 APyl/3 MEN3 Y r T1/3 +0.99 -0.56 +0.48 +0.79

RT1/2 -0.55 +0.49 +0.78

ADV1/3 -0.05 -0.79

MEN3 +0.37

RT = Rock Type Code

ADV = Avg o Advance Per Day

MEN = Shaftmen Per Shift TABLE 9 — MODEL ANALYSIS — DRILL AND BLAST (MAN-HOURS PER FOOT)

Correlation T-Value No, Variable Name —a/ Coefficient Significance Explanation of Correlation __

I (Avg. Advance/Day)**(1/3) -0.6405 -6.4101 Drill set up and tear down time is smaller portion of drilling time for longer rounds; longer rounds allow greater overall penetration rate per round.

(Shifts/ D a ^ 5'1* 2 0.1018 5.1549 On one shift basis, responsibility rests with one crew which functions more efficiently.

3 (Avg. Advance/Day)**3 -0.4784 2.8069 (Refer to Variable 1)

4 (Shaftmen/Shift)**3 0.3889 2.5389 Additional men often do not contribute proportionately in increasing produc­ tivity.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable, (Avg. Advance/Day)**(1/3) represents the cube root of (Avg. Advance/Day).

OO 49

TABLE 10 -- CORRELATION MATRIX -- DRILL AND BLAST (MAN-HOURS PER FOOT)

ADV3 . IffiN3 SHIFT2 Y 1/3 ADV +0.85 -0.05 +0.61 -0.64

ADV3 -0.19 +0.42 -0.48

MEN3 +0.15 +0.39

SHIFT2 * +0.10

ADV = Avg„ Advance Per Day

MEN '= Shaftmen Per Shift

SHIFT = Shifts Per Day TABLE 11 -- MODEL ANALYSIS — MUCKING (PERCENT OF CYCLE MAN-HOURS)

Correlation T-Value No. Variable Name a/ Coefficient Significance Explanation of Correlation____

1 (Shaft Area/10)**(l/3) 0.6268 -4.2766 Increased shaft area increases the mucking portion of the cycle while reducing the percentage of the re­ maining cycle.

Lining Code**l -0.1521 -3 .4705 Mucking is a smaller portion of a concrete shaft cycle than mucking in a timber shaft.

(Depth/l00)**(l/3) 0.2329 -2.1299 Increased hoisting distance slows down the mucking portion of the cycle,

(Avg. Advance/Day)**3 -0.5653 -1.7693 High advance rates imply faster and more efficient mucking set ups.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable, (Shaft Area/10)**(l/3) represents the cube root of (Shaft Area/10).

in O 51

TABLE 12 — CORRELATION MATRIX — MOCKING (PERCENT OF CYCLE MAN-HOURS)

ADV3 LING' DEPTH1/3 Y

AREA 1/3 -0.27 +0.44 +0.68 +0.63

ADV3 -0.10 +0.01 -0.57

LING1 +0.09 -0.15

DEPTH1/3 +0.23

AREA = Shaft Area/10

ADV = Avg. Advance Per Day

LING = Lining Code

DEPTH = Depth/100 TABLE 13 — MODEL ANALYSIS — MUCKING (MAN-HOURS PER FOOT)

Correlation T-Value No, Variable Name a/ Coefficient Significance Explanation of Correlation

I (Avg. Advance/Day)**(1/2) -0.5896 -6.6275 Increased mucking rate increases advance rate.

(Shifts/Day)**1 0.1433 5.9328 On a one shift per day basis responsibility rests with one crew which tends to function more efficiently.

(Shaftmen/Shift)**3 0.4430 3.2220 An additional man may not provide a proportional increase in produc­ tivity.

(Avg. Advance/Day)**3 -0.4757 3.1975 (Refer to Variable 1)

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable. (Avg. Advance/Day)**(l/2) represents the square root of (Avg. Advance/Day).

in ro 53

TABLE 14 — CORRELATION MATRIX MUCKING (MAN-HOURS PER FOOT)

ADV3 MEN3 SHIFT1 Y

ADV1^2 +0.87 -0.06 +0.61 -0.59

ADV3 -0.19 +0.41 -0 .48

MEN3 +0.13 +0.44

SHIFT1 +0.14

ADV = Avg. Advance Per Day

MEN -■ Shaftmen Per Shift

SHIFT = Shifts Per Day TABLE 15 — MODEL ANALYSIS — LINING AND FITTINGS (PERCENT OF CYCLE MAN-HOURS)

Correlation T-Value No. Variable Name — ^ Coefficient Significance ______Explanation of Correlation

1 (Avg. Advance/Day)**2 ■ 0.7118 10.5753 Faster advance/day requires more time to keep up lining and fittings.

2 Lining Code**(l/3) 0.1873 8.7423 Concrete requires the greatest time for lining.

3 Shaft Area**2 -0.5115 - 3.9445 The lowering and placement of support members and material does not increase linearly as shaft size increases.

4 (Shaftmen/Shift)**3 ■0.5864 3.7874 Handling and placement is enhanced by having more hands available.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable, (Avg. Advance/Day)**2 represents the square of (Avg. Advance/Day).

i n 55

TABLE 16 -- CORRELATION MATRIX — LINING AND FITTINGS (PERCENT OF CYCLE MAN-HOURS)

ADV2 MEN2 LING1/3 Y

AREA2 -0.11 +0.83 +0.53 -0.51

ADV2 -0.15 0 +0,71

MEN3 +0.43 -0.59

LING1^3 +0.19

AREA = Shaft Area/10

ADV = Avg, Advance Per Day

MEN = Shaftmen Per Shift

LING = Lining Code TABLE 17 -- MODEL ANALYSIS — LINING AND FITTINGS (MAN-HOURS PER FOOT)

Correlation T-Value No. Variable Name — / Coefficient Significance Explanation of Correlation______

1 Max. Water Inflow -0.1607 -3.5764 High water inflow tends to wash cement (GPM/100)**3 out of concrete before it sets up.

2 Max. Water Inflow -0.1084 3.4517 (Refer to Variable 1) (GPM/100)**2

3 (Shaftmen/Shift)**(l/3) 0.1862 2.3853 (No explanation. Inconsistant with Variable 4 of Table 15).

(Depth Sunk/100)**2 0.5383 -0,7745 Lowering of material requires more time with greater depth.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable, Max. Water Inflow (GPM/100)**3 represents the cube of Max. Water Inflow (GPM/100).

VI 57

TABLE 18 — CORRELATION MATRIX — LINING AND FITTINGS (MAN-HOURS PER FOOT)

GPM2 GPM3 DEPTH2 Y

MEN1/3 +0.14 +0.16 +0.33 +0.19

GPM2 +0.99 +0.58 -0.11

GPM3 +0.55 -0.16

DEPTH2 •fO. 54

MEN = Shaftmen Per Shift

GPM = MaXe Water Inflow/100

DEPTH = Depth Sunk/100 58

TABLE 19 -- COEUR d'ALENE SHAFT DATA

Depth Shaft Skip Starting Sunk Area Number Mucking Capacity No. Year (feet) (sq. ft.) Compartments Methods SJ- (cu. ft.)

1 52 1,661 165.6 3 1 24

2 53. 2,000 132.6 3 1 21

3 53 313 169.8 3 2 16

4 57 354 110.5 2 2 13

5 54 600 165.6 3 1 36

6 56 2,051 165.6 3 1 30

7 46 522 245.3 4 2 24

8 51 965 245.3 4 1 24

9 57 159 102.0 2 1 10

10 52 287 128.3 2 2 16

a. Mucking method 1 = Mechanical mucking Mucking method 2 = Hand mucking 59

TABLE 19 -- Continued

Bottom Crew % Of Total Cost Maximum Man-Hours/Ft, Labor 4- Supervision Number Hoisting Drill &, Bottom No. Skips Distance k' Blast Mucking Crew Total

1 2 1,744 4.72 3 .62 37.7 70.0

2 2 750 4.00 2.86 37.9 71.1

3 2 33:2 3.64 5.82 41.2 72.0

4 1 211 2.92 6.88 35.0 78.2

5 1 450 4.71 4.71 35.3 68.4

6 2 1,060 3.12 3.01 40.9 61.0

7 2 622 9.45 11.76 49.3 74.3

8 2 1,447 6.38 7.05 44.3 62.8

9 1 83 2.50 5.83 48.0 71.5

10 2 200 3.01 4.21 31.1 68.8

be Maximum hoisting distance less than depth sunk indicates skip dumping facilities being installed at some interval as the shaft advances to keep the cycle time to a minimum. 60

TABLE 19 Continued

Avg„ Length No. Holes Of Round Lbs. Explosives No. Per Round (feet) Per Foot____

1 27 . 5.6 37.0

2 30 6.2 32.3

3 30 6.0 37.2

4 18 3.6 32.5

5 36 5.6 41.2

6 27 6.6 23.8

7 22 4.6 35.6

8 34 6.1 31.8

9 24 6.8 12.3

10 21 5.2 19.2 61

3. Total labor plus supervision (% of total shaft cost)

Surface labor, such as hoistman, toplanders, and mechanics,

are assumed to be included.

Y = 131.29 -11.23 SKIP1/3 -19.73 LNGRD1/3 +0.00012 EXPLV3

4« Bottom labor plus supervision (% of total shaft cost)

Y = 307.87 -61.89 YEAR1/3 +0.00000033 AREA3 -5.12 LNGRD2

+0.67 LNGRD3

Tables 20, 22, 24, and 26 explain the significance of the variables.

Figures 5, 6,7, and 8 present the tests made in selecting the models.

Analyzing the residuals of each model, one finds the following confidence limits:

Standard Error Confidence Model No. Of Residuals (SER) Limits (lb)

1 0.42 mh/ft 0.30 mh/ft

2 0.82 mh/ft 0.59 mh/ft

3 2.05% 1.47%

4 2.21% 1.58%

Tables 21, 23, 25, and 27 define the abbreviations in the mathematical expressions and summarize the intercorrelations of all variables in

their respective model. Nomographs for models 1, 2, 3, and 4 are included in Appendices A, B, C, and D respectively,

- " ■ - , Detailed Labor and Materials for One Shaft

To reach the ultimate in precision of estimation, the author

investigated the sinking performance for a uranium mine referred to her,e as the "X" Shaft. This was the first analysis performed even TABLE 20 — MODEL ANALYSIS — BOTTOM CREW DRILL AND BLAST MAN-HOURS PER FOOT

Correlation T-Value No«, Variable Name Coefficient Significance Explanation of Correlation

1 No. Compartments**3 0.9019 3.8010 No. Compartments reflects shaft area; more man-hours for larger shafts.

2 Year of Sinking**(1/3) -0.8987 -2.7904 Reflects increased efficiency as shaft sinking experience increases

3 Year of Sinking**! -0.8921 2.6304 (Refer to Variable 2)

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable. No. Compar tment s **3 represents the cube of No. Compartments.

O' ro STANDARD ERROR OF ESTIMATE (Syx) MAN HOURS PER FOOT 0.2 iue - 5 Figure 0.4 0.6 0.6 1.0 O V) k- K $ 2 m 3 < _i to o a: LU O O u t K 3 o: K k CL

- Bottom Crew Drill and Blast Man-Hours Per Foot andPer Man-Hours Blast DrillCrew - Bottom 2 oe Selection Model 0.5 2.0 (A) i.o (B) Adequacy of Dataof(B) Adequacy 5 lto 2 andS ofR2 Plot 4 3 0.96 UBR F OBSERVATIONS OF NUMBER 1.51 6 REGRESSION 7 (A) (B) yx 8 STEP 7 5 Syx 9 6 10

8 0.2 0.6 0.8 0.4 1.0 63

MULTIPLE CORRELATION COEFFICIENT SQUARED (Rz) 64

TABLE 21 -- CORRELATION MATRIX — BOTTOM CREW DRILL AND BLAST MAN-HOURS PER FOOT

YEAR1/3 CMPRT3 Y

YEAR1 +0.99 -0.77 -0.89

YEAR1/3 -0.77 -0.90

CMPRT3 +0.90

95% Confidence

N = 10 > /r/ 0.627

YEAR = Starting Year

CMPRT = Number of Compartments

Y = Bottom Crew Drill & Blast Man-Hours Per Foot TABLE 22 -- MODEL ANALYSIS — BOTTOM CREW MUCKING MAN-HOURS PER FOOT

Correlation T-Value Of No. Variable Name —a/ Coefficient Significance Explanation Of Correlation

1 Shaft Area**3 0.6838 6.4322 Shaft area directly related to volume of broken round to be mucked,

Hoist Distance**(l/3) -0.1497 -3.7825 Deeper shafts generally have larger skips and faster hoisting speeds.

Length of Round**(1/3) •0.4901 -2.4148 Setup time is smaller part of total muck time for longer round.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable, Shaft Area**3 represents the cube of Shaft, Area. iue Bto rwMcigMnHusPrFo oe Selection Model PerFoot Man-Hours Mucking Crew Bottom 6— Figure STANDARD ERROR OF ESTIMATE (Syx) MAN HOURS PER FOOT 0.5 2.0 2.5 1.0 1.5 0 L_ tlJ

MULTIPLE CORRELATION COEFFICIENT SQUARED (R%) 67

TABLE 23 -- CORRELATION MATRIX — BOTTOM CREW MUCKING MAN-HOURS PER FOOT

HOIST1/3 LNGRD1/3 Y

AREA3 +0.52 -0.05 +0.68

HOIST1/3 +0.21 -0.15

LNGRD1/3 -0.49

95% Confidence

N = 1 0

/r/ - 0.627

AREA = Shaft Area

HOIST = Maximum Hoisting Distance

LNGRD = Avg. Length of Round TABLE 24 — MODEL ANALYSIS — TOTAL LABOR PLUS SUPERVISION (PERCENT OF TOTAL SHAFT COST)

Correlation T-Value No. Variable Name a/ Coefficient Significance Explanation of Correlation

1 Skip Capacity**(l/3) -0.5557 -3 .6610 Less idle time per round with larger skips, less man-hours per round.

(Pounds Explosives/Ft.)**3 -0.2139 2.4417 Better fragmentation with more pounds/ ft., more efficient mucking.

Length of Round**(1/3) -0.6842 -2.2980 Setup time for drilling and mucking represents less of total cycle time.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable, Skip Capacity**(1/3) represents the cube root of Skip Capacity.

O' 00 Figure 7 Figure

STANDARD ERROR OF ESTIMATE (Syx) PERCENT 0 4 2 3 I oa LbrPu uevso (ecn of ShaftCost) (PercentTotal Supervision Plus Labor Total (B) Adequacy of Dataof(B) Adequacy (A)R.2of Plot ^ S and O H 2

2 6 4 5 2 3 0.84 6 8 10 9 8 7 6 5 3 2.51 UBR F OBSERVATIONS OF NUMBER REGRESSION 4 (A) Syx (B) STEP 5 6 7 8 0.6 0.2 0.8 0.4 i.o 69

MULTIPLE CORRELATION COEFFICIENT SQUARED (Rz) 70

TABLE 25 — CORRELATION MATRIX — TOTAL LABOR PLUS SUPERVISION (PERCENT OF TOTAL SHAFT COST)

LNGRD1^3 EXPLV3 Y

SKIP1/3 +0.16 +0.55 -0.56

LNGRD1/3 -0.26 -0.68

EXPLV3 +0.21

95% Confidence

N = 1 0

/r/ - 0.627

SKIP = Skip Capacity

LNGRD = Avg. Length of Round

EXPLV = Lbs. Explosives Per Foot

Y = Total Labor & Supervision

(% of Total Shaft Cost) TABLE 26 — MODEL ANALYSIS — BOTTOM LABOR PLUS SUPERVISION (PERCENT OF TOTAL SHAFT COST)

Correlation T-Value No. Variable Name — Coefficient Significance Explanation of Correlation

1 Length of Round**3 0.3608 3.5501 Cycle time increases with longer found, and bottom costs are in­ creased proportionately.

2 Length of Round**2 0.3391 -3.3958 (Refer to Variable 1)

3 Year of Sinking**(l/3) -0.3193 -2.1066 Shaft sinking efficiency increases with time resulting in lower costs,

4 Area**3 0.5722 0.9364 Shafts of larger area require more drill holes and more mucking per foot of advance.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable. Length of Round**3 represents the cube of Length of Round. iue8 --8 Figure

STANDARD ERROR OF ESTIMATE (Syx) PERCENT 0 3 2 4 5 otmLbrPu uevso (ecn o£ShaftCost) (PercentTotal Supervision PlusLabor Bottom A Po o andSyX of(A) Plot (B) Adequacy ofData (B) Adequacy o t- 2 4 2 3 6 5 6 8 10 9 8 7 6 5 3 UBR F OBSERVATIONS OF NUMBER 2.96 ERSIN STEP REGRESSION 4 0.86 (A) 5yx (B) 5 6 7 8 0.6 0.2 0.8 0.4 i.o 72

MULTIPLE CORRELATION COEFFICIENT SQUARED ( R2) 73

TABLE 27 -- CORRELATION MATRIX- BOTTOM LABOR PLUS SUPERVISION (PERCENT OF TOTAL SHAFT COST)

AREA- LNGRD' LNGRD'

YEAR1/3 -0.78 +0.29 +0.35 -0.32

AREAS - 0.11 -0.14 +0.57

LNGRD2 +0.99 +0.34

LNGRD3 +0.36

95% Confidence

N = 1 0

/r/ ^ 0.627

YEAR = Starting Year

AREA = Shaft Area

LNGRD = Avg. Length of Round

Y = Bottom Labor & Supervision

(% of Total Shaft Cost) ' ' • 74

though it is the last to be considered here» It was the proof of the

thesis that cause-and-effect relationships exist in mine development

and that these can be related mathematically and graphically to become

a "hip-pocket computer", so to speak, for rapid reference.

Because of the success of this model, the other models pre­

sented were pursued« Detail, such as included in this analysis, is

fundamental to development of a precision estimating tool. Here one

seeks the variables affecting round-by-round sinking performance. The

data can, in addition, be the base for developing more general models

as previously described. The secret to success lies in establishing a

format for data retrieval. The data in Table 28 contain very little

operating data except that obtained from time cards and a daily fore­ man's report which was sketchy and inconsistent in reporting cycle

details.

At the outset of data gathering, two forms similar to Figures

9 and 10 were developed in hopes that their use, rather than the daily

foreman's report, would, give extensive cycle data at little additional

time. Generally the shiftboss would be given the responsibility since

he also fills out the foreman's time sheet. The biggest problems found

in trying to distribute, labor within a cycle was determination from

the time sheet and foreman's report when one cycle ended and the next

began. Marking the approximate time of day beside each portion of the

cycle as requested in Figures 9 and 10 alleviates this problem. Figure

11 depicts the detail proposed for the foreman's time sheet to properly 75

TABLE 28 — "X" SHAFT DATA

Electric Logs General Sample Depth Specific Self Pot. Resistance Rock Type No. No. (feet) Gravity (m.a.) (ohms)

Very Fine Grain 1 29 292 2.116 15 36 Sandstone 2 32 321 2.039 33 64 3 35 436 2.039 34 57 4 36 460 2.219 28 41 5 41 616 2.063 23 37 6 71 1,472 2.312 39 43 Fine Grain 7 26 243 2.482 30 61 Sandstone 8 34 364 1.895 32 41 9 43 654 1.995 30 43 10 44 664 1.716 24 38 11 70 1,460 2.333 30 13 12 75 1,520 2.080 42 38 13 76 1,540 1.886 40 41 Medium To 14 33 354 2.034 60 58 Coarse Grain 15 65 1,360 2.371 29 23 Sandstone 16 ■ 69 1,398 2.137 ‘ 37 42 Clays tone 17 28 276 2.233 22 50 18 31 306 2.242 19 31 19 38 577 2.330 32 33 20 39 595 2.276 20 45 21 40 610 2.292 24 46 22 45 832 2.229 29 22 23 63 1,320 2.381 32 50 24 66 1,372 2.426 28 50 25 67 1,376 2.169 34 28 26 68 ■ 1,386 2.449 28 18 Siltstone 27 27 260 2.027 40 74 28 37 492 2.321 27 36 29 42 634 2.307 30 45 30 54 950 2.125 19 23 31 55 960 2.197 23 30 32 61 1,278 2.391 28 15 33 64 1,350 2.341 31 23 34 72 1,480 2.248 37 53 35 74 1,496 2.331 42 43 Micrite 36 46 1,050 2.283 17 23 37 56 1,089 2.303 23 17 38 57 1,102 2.286 23 20 39 58 1,120 2.381' 25 18 40 59 1,174 2.275 26 20 76

TABLE 28 — "X" SHAFT DATA, continued

Sample Cementation (%/100) No. No. Clay Quartz Carbon Calcite Total

1 29 0.11 0.17 0 .07 0.00 0.35 2 32 0.04 0.18 0.00 0.00 0.22 3 35 0.11 0.00 0.00 0.00 0.11 4 . 36 0.15 0.00 0 .00 0.00 0.15 5 41 0.31 0.00 0.00 0.01 0 .32 6 71 0.49 0.00 0.02 0.00 0.51 7 26 0.07 O.O0 0.00 0.33 0.40 8 34 0.17 0.00 0.00 0.00 0.17 9 43 0.16 0.00 0.00 0.00 0.16 10 44 0.20 0 .00 0.00 0.00 0.20 11 70 0.39 0.00 0.00 0.00 0.39 12 75 0.07 0.14 0 .00 0.00 0.21 13 76 0.03 0.21 0.03 0 .00 0.27 14 33 0.09 0.00 0.00 0.00 0.09 15 65 0.56 0.00 0.00 0.00 0.56 16 69 0.40 0.00 0.00 0.00 0.40 17 28 0.92 0.00 0.00 0.00 0.92 18 31 0.69 0.00 0.19 0.00 0 . 88 19 38 0.49 0.00 0.05 0.00 0.54 20 39 0.62 0.00 0.11 0.00 0.73 21 40 0.70 0.00 0.06 0.11 0.87 22 45 0.81 0.00 0 .06 0.04 0.91 23 63 0.48 0.00 0.07 0.05 0.60 24 66 0.82 0.00 0 .00 0 .00 0.82 25 67 0.95 0.00 0.00 0.00 0.95 26 ' 68 0.90 0.00 0.00 0.00 0.90 27 27 0.22 0.00 0.05 0.00 0.27 28 37 0.14 0.00 0.00 0.27 0.41 29 42 0.30 0.00 0 .14 0.00 0.44 30 54 0.42 0.00 0.06 0.06 0.54 31 55 0.53 0.00 0.09 0.18 0.80 32 61 0.37 0.00 0.02 0.00 0.39 33 64 0.37 0.00 0.05 0.00 0.42 34 72 0.78 0.00 0.03 0.00 0.81 35 74 0.49 0.00 0.03 0.00 0.52 36 46 .. 0.15 0.00 0.05 0.65 0.85 37 56 0.31 0.00 0.09 0.50 0.90 38 57 0.18 0.00 0.04 0.62 0.84 39 58 0.16 0 .00 0.00 0.49 0.65 40 59 0.18 0.00 0.07 0.46 0.71 77

TABLE 28 -- "X" SHAFT DATA, continued

Sample Porosity Grain Size Alteration No. No. %/100 (mm.) Code

1 29 0.02 0.070 3 2 32 0.03 0.070 2 3 35 0.05 0.100 4 4 36 0.01 0.090 4 5 41 0.03 0.080 3 6 71 0.04 0.080 4 7 26 0.01 0.170 3 8 34 0.09 0.180 3 , 9 43 0.06 0.170 2 10 44 0.13 0.150 3 11 70 0.04 0.150 3 12 75 0.15 0.150 4 13 76 0.09 0.150 3 14 33 0.14 0.500 3 15 65 0.06 0.400 4 16 69 0.06 0.300 4 17 28 • 0.01 0.003 2 18 31 0 .01 0.003 3 19 38 0.01 0.003 4 20 39 0.02 0.003 3 21 40 0.04 0.003 4 22 45 0.18 0.003 2 23 63 0.04 0.003 4 24 66 0.02 0.003 4 25 67 0.09 0.002 4 26 68 0.02 0.002 4 27 27 0.01 0.040 2 28 37 0.02 0.040 4 29 42 0.04 0.030 4 30 54 0.03 0.050 3 31 55 0.02 0.010 3 32 61 0.04 0.018 4 33 64 0.06 0.050 4 34 72 0.04 0.020 4 35 74 0.05 0.060 4 36 46 0.07 0.004 2 37 56 0.04 0.003 2 38 57 0.03 0.020 2 39 58 0.03 0.050 2 40 59 0.04 0.030 2 78

TABLE 28 — "X" SHAFT DATA, continued

Sample __ Composition (%/100) No. No. Quartz Kspar Clay Sericite Plagi'oclase Chert

1 29 0.56 0.20 0.11 0.03 0.02 0.01 2 32 0.77 0.10 0.04 0.02 0.00 0.00 3 35 0.57 0.15 0.11 0.14 0.00 0.00 4 36 0.55 0.14 0.15 . 0.09 0.00 0.00 5 41 0.48 0.09 0.31 0.07 0.00 0.00 6 71 0.41 0.00 0.49 0.01 0.02 0.02 7 . 26 0.38 0.12 0.07 0.02 0.02 0.06 8 34 0.62 0.19 0.17 0.02 0.00 0.00 9 43 0.70 0.12 0.16 0.00 0.01 0.01 10 44 0 .67 0.10 0.20 0.01 0.01 0.01 11 70 0.44 0.09 0.39 0.01 0.04 0.00 12 75 0.65 0.07 0.07 0.02 0.09 0.01 13 76 0.64 0.12 0.03 0.04 0.06 0.01 14 33 0.65 0.19 0.09 0.03 0.01 0.02 15 65 0.42 0.01 0.56 0.00 0.01 0.00 16 69 0.43 0.13 0.40 0.00 0.01 0.01 17 28 0.05 0.00 0.92 0.00 0.00 0.00 18 31 0.10 0.00 0.69 0.02 0 .00 0.00 19 38 0.15 0.08 0.49 0.09 . 0.00 0.00 20 39 0.16 0.03 . 0.62 0.00 0.00 0.00 21 40 0.06 0.02 0.70 0.01 0 .00 0.00 22 45 0.03 0.00 0.81 0.00 0.00 0.00 23 63 0.19 0.05 0.48 0.14 0.01 0.00 24 66 0.14 0.01 0.82 0.00 0 . 00 0.02 25 67 0.01 0.00 0.95 0.00 0.00 0.00 26 68 0 .03 0.00 0.90 0.00 0.00 0.00 27 27 0.70 0.00 0.22 0.00 0.00 0.00 28 37 0.35 0.10 0.14 0.01 0.00 0.00 29 42 0.42 0.08 0.30 0.03 0.00 0.00 30 54 0.29 0.13 0.42 0.02 0.00 0.00 31 55 0.09 0.06 0.53 0.00 0.00 0.00 32 61 0.53 0.02 0.37 0.03 0.01 0.00 33 64 0.39 0.06 0.37 0.06 0.03 \ 0.02 34 72 0.16 0.01 0.78 0.00 0.00 0.01 35 74 0.34 0.05 0.49 0.03 0.00 0.00 36 46 0.01 0.00 0.15 0.00 0.00 0.06 37 56 0.00 0.00 0.31 0.00 0.00 0.00 38 57 0.00 0.00 0.18 0.00 0.00 0.00 39 58 0.00 0.00 0.16 0.00 0.00 0.00 40 59 0.00 0.00 0.18 0.00 0.00 0.01 79

TABLE 28 — ,!X" SHAFT DATA, continued

Composition (%/100) Sample Volcanic No. No. Limonite Pyrite Fragments Carbon Calcite

1 29 0.07 0.00 0.00 0.00 0.00 2 32 0.07 0.00 0.00 0.00 0.00 3 35 0.00 0.01 0.00 0.00 0.00 4 36 0.02 0 .01 0.00 0.04 0.00 5 41 0.03 0.01 0.00 0.00 0.01 6 71 0.00 0.00 0.02 0.02 0.00 7 26 0.00 0.00 0.00 0.00 0.33 8 34 0.00 0.00 0.00 0.00 0.00 , 9 43 0 .00 0.00 0.00 0.00 0.00 10 44 0.00 0.00 0.00 0.00 0.00 11 70 0.00 0.00 0.03 0 . 00 0.00 12 75 0.00 0.00 0.06 0.01 0.00 13 76 0.00 0.00 0.06 0.03 0.00 14 33 0.00 0.00 0.00 0.00 0.00 15 65 0.00 0.00 0.00 0.00 0 .00 16 69 0.00 0.00 0.02 0.00 0.00 17 28 0.00 0.00 0.00 0.03 0.00 18 31 0.19 ' 0.00 0.00 0.00 0.00 19 38 0.02 0.02 0.00 0.05 0.10 20 39 0.02 0.00 0 .00 0.11 0.06 21 40 0.04 0.00 0.00 0.06 0.11 22 45 X 0.03 0.02 0.00 0.06 0.04 23 63 0.01 0.00 0.00 0.07 0.05 24 66 0.00 0.00 0.00 0.00 0.01 25 67 0.04 0.00 0.00 0.00 0 .00 26 68 0.02 0.02 0.00 0.03 0.00 27 27 0.01 0.01 0.00 0.05 0.00 28 37 0.04 0.01 0.00 0 .08 0.27 29 42 0.03 ■ 0.00 0.00 0.14 0.00 30 54 0.02 0.00 0.00 0.06 0.06 31 55 0.05 0.00 0.00 0.09 0.18 32 61 0.02 0.00 0.00 0.02 0.00 33 64 0.02 0 .00 0.00 0.05 0.00 34 72 0.01 0.00 0.00 0.03 0.00 35 74 0.00 0.00 0.01 0.03 0.00 36 46 0.00 0.02 0.00 0.05 0.71 37 56 0.03 0.02 0.00 0.09 0.55 38 57 0 .03 0.00 0.00 0.04 0.74 . 39 58 0.04 0.02 0.00 0.03 0.73 40 59 0.04 0.07 0.00 0.07 0.61 80

TABLE 28 — "X" SHAFT DATA, continued

Sonic Velocities Sample VP1 VP 2 VP3 VS1 VS 2 No. No. (ft./sec.) (ft./sec.) (ft./sec.) (ft./sec.) (ft./sec.)

1 29 9,981 10,467 10,164 5,936 6,466 2 32 12,378 12,034 12,650 7,448 ' 6,511 3 35 7,816 8,827 7,759 5,213 5,597 4 36 7,953 8,515 7,735 5,266 5,213 5 41 8,574 8,496 8,411 4,932 5,707 6 71 7,490 9,446 10,963 5,248 6,135 7 26 12,133 11,446 12,476 7,005 7 ,337 8 34 5,899 6,287 6,172 3,548 3,925 9 43 7,839 . 7,193 8,182 3,924 4,099 10 44 10,180 10,087 11,276 4,101 4,386 11 70 8,667 10,889 10,271 5,723 6,554 12 . 75 5,288 5,375 7 ,055 3,495 3,922 13 76 4,546 4,838 4,740 2,572 2,742 14 33 13,652 13,015 13,636 5,408 7,095 15 65 9,906 11,209 7,639 4,565 5,209 16 69 8,274 5,952 7,322 4,918 4,099 17 28 8,196 11,758 11,448 4,447 5,673 18 31 9,923 8,608 9,823 5,282 5,563 19 38 8,655 9,620 9,641 4,878 5,264 ' 20 39 6,150 8,663 8,518 5,193 3,914 21 40 5,502 10,110 . 9,901 3,778 6,001 22 45 4,256 8,794 8,713 2,994 3,954 23 63 6,935 11,400 11,451 3,219 4,513 24 66 13,023 10,047 12,641 10,433 9 ,000 25 67 5,972 10,075 8,925 - 2,970 5,713 26 68 10,144 9 ,970 12,651 6,190 6,062 27 27 7,477 8,197 8,054 5,163 5,263 28 37 8,539 10,085 10,533 6,183 6,202 29 42 8,381 10,134 9 ,783 5,632 6,397 30 54 4,302 6,893 8,388 2,300 4,045 31 55 5,673 9,065 9,820 2,594 4,927 32 61 11,791 9,931 10,387 8,549 8,179 33 64 4,879 10,887 10,926 . 4,422 6,533 34 72 5,209 8,441 8,922 2,732 4,494 35 74 5,828 9,618 9,676 4,330 5,504 36 46 7,401 12,704 11,951 5,273 7 ,031 37 56 9,718 9,858 10,180 2,774 4,420 38 57 6,489 10,167 10,241 4,480 4,767 39 58 9,958 13,306 12,828 5,763 7,350 40 59 6,129 9,396 9,978 5,256 6,130 81

TABLE 28 — "X" SHAFT DATA, continued

Sonic Velocities Sample VB1 VB2 VB3 No. No. (ft./sec.) (ft./sec.) (ft./sec.)

1 29 9,044 7,302 7,895 2 32 7,696 9,251 9,924 3 35 : 7,014 7,748 5,827 4 36 6,137 7 ,009 6,651 5 41 6,560 6,810 6,825 6 71 6,270 7 ,539 8,363 7 26 8,450 8,247 8,577 8 34 3,673 4,028 3,935 9 43 . 4,489 5,645 4,888 10 44 3,772 4,444 5,635 11 70 . 6,961 8,484 7,893 12 75 4,348 4,406 5,031 13 76 2,930 3,122 3,075 14 33 5,430 7,926 8,164 15 65 7,839 8,345 5,915 16 69 5,542 4,213 6,338 17 28 5,388 8,499 8,278 18 31 7,474 7,367 7,238 19 38 6,549 6,353 7,711 20 39 5,832 4,926 6,676 21 40 4,289 6,452 6,826 22 45 2,775 5,995 6,359 23 63 4,167 8,564 10,537 24 66 10,698 8,778 11,839 25 67 3,811 6,279 6,627 26 68 8,961 6,265 9,957 27 27 6,393 7,697 6,955 28 37 7,392 7,822 7,884 29 42 6,397 7,642 8,696 30 54 2,792 4,721 4,500 31 55 3,621 7,002 7,872 32 61 10,480 9,899 9,954 33 64 4,463 8,871 7,877 34 72 4,249 5,865 7,629 35 74 4,978 7,398 8,948 36 46 4,524 7,455 8,958 37 56 5,099 9,091 8,197 38 57 4,055 8,151 9,599 39 58 6,676 11,291 10,998 40 59 5,523 8,386 9,2 28 82

TABLE 28 — "X" SHAFT DATA, continued

Concrete Cumulative Length of Sample Per 7-Ft. Pour Water Inflow Avg. No. Men Round No. No. (cubic yds.) (g.p.m.) On Bottom (feet)

1 29 20.0 2 3.00 8.5 2 32 22.6 2 3.00 8.0 3 35 21.4 5 4.00 6.5 4 36 18.3 5 4.00 11.0 5 41 25.0 3 2.00 10.0 6 71 36.0 400 4.00 8.0 7 26 20 . 3 1 4.00 8.0 8 34 . 19.0 . 2 4.00 8.0 9 43 25.0 2 3.00 7.0 10 44 . 25.0 2 2.67 10.0 11 70 32.0 55 4.00 10.0 12 75 39.0 500 3.00 8.0 13 76 24.0 1,000 4.00 8.0 14 33 20.0 2 4.00 8.5 15 65 26.0 25 5.00 8.0 16 . 69 34.0 25 3 .33 8.0 17 28 20.0 1 4.00 7.0 18 31 26.7 2 2.50 9.0 19 38 21.0 4 3.43 9.0 20 39 29.6 4 4.00 6.0 21 40 29.6 3 3.00 9.0 22 45 25.0 2 4.00 8.0 23 63 24.0 25 3.00 8.0 24 66 20.0 25 4.00 8.0 25 67 20.0 25 4.00 8.0 26 68 20.0 25 4.00 8.0 27 27 23.4 1 4.00 8.0 28 37 22.0 5 4.00 9 .0 29 42 22.0 2 1.40 10.0 30 54 21.0 2 3.50 10.0 31 55 21.0 2 4.00 10.0 32 61 20.0 2 4.00 10.0 33 64 26.0 25 3.00 8.0 34 72 30.0 400 4.00 8.0 35 74 30.0 400 3.00 8.0 36 46 18.0 2 2.00 10.0 37 56 18.0 2 4.00 10.0 38 57 18.0 2 4.00 12.0 39 58 18.0 . 2 3.00 10.0 40 59 18.0 2 4.00 7.0 83

TABLE 28 — "X" SHAFT DATA, continued

Man-Hours/Round Btm. Crew Avg. Man-Hours/Foot Sample Drill & Experience Drill &. No o No. Blast Mucking Total (Man-Hrs/Rnd.) Blast Mucking Total

1 29 12 28 40 1,118 1.41 3.29 4.71 2 32 12 22 34 1,402 1.50 2.75 4.25 3 35 16 12 28 2,109 2.46 1.85 4.31 4 36 24 16 40 1,900 2.18 1.45 3.64 .5 41 10 34 44 2,294 1.00 3.40 4.40 6 71 16 32 48 5,625 2.00 4.00 6.00 7 26 12 18 30 730 1.50 2.25 3.75 8 34 16 26 42 1,409 2.00 3 . 25 5.25 9 43 12 36 48 2,634 1.71 5.14 6.86 10 44 28 24 52 2,912 2.80 2.40 5.20 . 11 70 8 44 52 8,006 0.80 4.40 5.20 12 75 12 36 48 5,619 1.50 4.50 6.00 13 76 16 16 32 6,484 2.00 2.00 4.00 14 33 12 18 30 1,414 1.41 2.12 3.53 15 65 19 24 43 5,516 2.38 3.00 5.38 16 69 20 23 43 3,977 2.50 2.87 5.38 17 ;-28 16 36 52 825 2 . 29 . 5.14 7.43 18 31 20 24 44 1,362 2.22 2.67 4.89 19 38 24 44 68 2,455 2.67 4.89 7.56 20 39 16 40 56 2,933 2.67 6.67 9.33 21 40 8 36 44 3,255 0.89 4.00 4.89 22 45 12 20 32 3,986 1.50 2.50 4.00 23 63 12 16 28 1,964 1.50 2.00 3.50 24 66 16 32 48 6,494 ' 2.00 4.00 6.00 25 67 16 24 40 5,648 2.00 3.00 5.00 26 68 16 24 40 4,627 2.00 3.00 5.00 27 27 16 16 32 950 2.00 2.00 4.00 28 37 16 40 56 2,400 1.78 4.44 6.22 29 42 16 44 58 2,884 1.40 4.40 5.80 30 54 28 28 56 5,965 2.80 2.80 5.60 31 55 16 40 56 4,966 1.60 4.00 5.60 32 61 32 12 44 8,097 3.20 1.20 4.40 33 64 12 28 40 5,807 1.50 3.50 5.00 34 72 16 24 40 7,889 2.00 3.00 5.00 35 74 . 12 28 40 6,783 1.50 3.50 5.00 36 46 8 30 38- 4,449 0.80 3.00 3.80 37 56 16 32 48 , 4,544 1.60 3.20 4.80 38 57 16 44 60 5,807 1.33 3.67 5.00 39 58 16 28 44 6,582 1.60 2.80 4.40 40 59 16 28 44 5,834 2.29 4.00 6.29 84

SHAFT (CIRCULAR SECTION) STARTING TIME DATE SHIFT FOR ITEMS

1. Number of Hen in Bottom Crew:

2. Buckets Hoisted/Round (Hoistman’s Tally) : ( > .... . _ . . ( : )

3. Holes/Rounds and Length: ( ) ( : )

4. Grout Holes (Number of and Length): ( ) ( : >

5. Concrete - Forming from to depth: ( : )

- Pouring from to depth: ( : )

- Cubic Yards Poured:

6. Installing Steel of Set Nos.: ( ) ( : )

7. Powder Consumption (Circle Whole Cases): 1, 2, 3, 4, 5, 6, 7, 8

(Circle Fraction of Case) : 1/4, 1/2, 3/4

8. Vent line Installed (Feet): ( _) ______< : >

9. Electrical Cable Installed (Feet) - Temporary: ...... ( :)

Permanent:

10. Pipe installed (Feet and Diameter):

11. Water Inflow (GPM): ______12. Fault Encountered @ Set No.: _____

13. Rock Bolts Installed (Number of): j[_

14. Wire Mesh Installed (Square Feet):

15. Overbreak (Average Feet):

"X" Dimension (inside concrete) "Y" Dimension

16. Man-Hours: Bottom Crew Support Crew Drilling and Blasting^ Hoisting_____ Mucking . Toplander_ Set Installation __ Rock Disposal ____ Shaft Fittings Placement Engineering (In-Shaft 0nly)_ (Guides, Pipe , Vent, etc.)_ Supervision (In-Shaft Only) Rock Bolting______Mechanic (In-Shaft Only)___ Other______Electrician (In-Shaft OnlyJi_ CHECK THE APPROPRIATE ITEM (ITEMS) UNDER A, B, AND C BELOW 1 2 3 4 5 6 7 8 Ventilation ------Mechanical ------Electrical ------NOTE: For each major delay Supply ------insert its starting hour under Form Leakage ------the appropriate duration-time Injury ————————— heading. Thunder Storm ------Other (Note the Type) - - _____ B. Maintenance and/or Repair Required C. Rock Type of Current Round Pumps Electric Cable Sandstone______Drills, Compressors______Shale Jumbo Sinking Bucket^_____ Clay, Cryderman, Headframe Components, Other Fans______Hoist Components Pipe,_____ Other ______

Figure 9 -- Shift Report Form for Circular Concrete Shaft 85

SHAFT (RECTANGULAR SECTION) STARTING TIMES DATE SHIFT FOR ITEMS

1. Number of Men in the Bottom Crew:

2 . Buckets Hoisted/Round (Hoistman's Tally): ( 1

3. Holes/Round and Length: j( ) ______4. Installing Set Nos. , Is this a bearer set? L. _L 3. Powder Consumption (Circle Whole Cases): 1, 2, 3, 4, 5, 6, 7,

(Circle Fraction of Case): 1/4, 1/2, 3/4

6. Concrete - Forming @ Set No.: ( )______

- Pouring @ Set No.: Jl - Cubic Yards Poured:

7. Grout Holes (Number of and Length):__^_

8. Vent Line Installed (Feet):__j£______

9. Electrical Cable Installed (Feet) - Temporary:

- Permanent:

10. Pipe Installed (Feet and Diameter):______

11. Water Inflow (GPM):______

12. Fault Encountered @ Set No.:______

13. Rock Bolts Installed (Number of):

14. Wire Mesh Installed (Square Feet):

15. Overbreak (Average Feet):

"X" Direction = "Y" Direction =

16. Man-Hours: Bottom Crew Support Crew, Drilling and Blasting^ Hoistingy Mucking _ Toplander^ Set Installation Rock Disposal^ Shaft Fittings Placement Engineering (In-Shaft Only)_ (Guides, Pipe, Vent, etc .)_ Supervision (In-Shaft Only)_ Rock Bolting Mechanic (In-Shaft Only)__ Other _____ ■______Electrician (In-Shaft Only%_

CHECK THE APPROPRIATE ITEM (ITEMS) UNDER A , B, AND C BELOW: A. Major Cycle Delays: (Hours) 1 2 3 4 5 6 7 8 Ventilation ------Mechanical ------Electrical NOTE: For each major delay Supply ------insert its starting hour Form Leakage ------under the appropriate Injury duration-time heading. Thunder Storm ------Other (Note the Type), - - Maintenance and/or Repair Required: C. Rock-Type of Current Round: Pumps_____ Electric Cable Sandstone______Drills_ Compressors______Shale Jumbo_ Sinking Bucket______Clay______Fans__ Headframe Components^ Others______Pipe__ Hoist Components____ Cryderman_ Other______

Figure 10 -- Shift Report Form for Rectangular Shaft 86

TIM E SHEET Mine______Roy Period From______To

Work Item 8 S h i f t MT w T F s s M TWT F S s Tot. 1 Drill 2 3 2 2 f 4 4

1

MUCK 2

3 6 4 2 a ,2 4 4 4 1 A) fb rtf? 5 2 3 2 f 4 1 0 Goicl&s 2 2 3 3 1 C o n c re te 2 3 4-

1

S f e e / 5c- 2

3 0 1

¥ip e 2 r 3 f 0 4 1

Vent P i P e 2

3 0 1 Ulire 't'&o/ts 2 3 £

1

2

3

8 8 8 / o j Tot. Contract Time 8 8 6 8 8 8 8 M 8 Tot. Company Time 2 * Tot. Overtime 4 a Name ! (Job# P o &______Classification :

Figure 11 — Example Time Sheet Illustrating How It Is to Be Filled Out 87 distribute labor to the correct shift, assuming three shifts, and to identify the type of work to credit with the man-hours. As shown, overtime is commonly noted by circling the respective hours. When a man works overtime in one day, it is often difficult to ascertain what he did on which shift.

Since the author was not in close contact with the "X11 Shaft project, the specially prepared forms were not used consistently enough to be incorporated in the data. They are described in conjunc­ tion with the time sheet to suggest the range of cycle description that would be of use in fully developing the history of a particular shaft.

Further, this detail obtained from several shafts would be a basis for quite detailed models for shaft sinking.

A brief discussion of data measurements from the ftXn Shaft will complete the background on its models. Electric logs measuring self­ potential and single-point resistance throughout the proposed length of the shaft were obtained from a core hole at the site. Since the core was not available, rock samples were obtained as the various rock types were penetrated during sinking, and the author correlated these samples to electric log readings at the approximate depth of the sample.

Each rock type sampled was submitted to the U. S. Bureau of

Mines in Denver, Colorado, for sonic velocity measurements. . The object was to include a measure of rock quality in terms of elastic constants which can be calculated from the velocities. The samples were oriented by bedding planes before measuring the velocity vertically and in two orthagonal horizontal directions. As an example, consider the P-wave velocity in the vertical direction to be VP1 and the corresponding horizontal measures to be VP2 and VP3, The significance of VP2 rel­ ative to VPS is merely to denote the two readings to be perpendicular to one another. In addition to the P-wave velocity, the longitudinal- bar velocity (VB) and the shear velocity (VS) were obtained. Only one horizontal orientation was used in the shear velocity measurement,

Lucius Pitkin, Incorporated, Grand Junction, Colorado, per­ formed the petrographic work. All remaining data, which is operational, came from the foreman's daily report and personal communications with the owner of the property.

The two models presented from the nXn Shaft data illustrate the extent to which geology explains changes in sinking performance.

The first one considered, Excavating Man-Hours Per Foot, refers to the excavation portion (drill and blast plus mucking) of the cycle and includes only the men on the bottom with major delays, such as mucker breakdowns, and hoist failures, omitted. Time cards were coded onto punched cards and manipulated on a computer in securing the excavation man-hours. In Table 29, the minimum number of variables which were felt to adequately explain the variation in man-hours per foot for excavation alone are summarized with a brief explanation of why each affects the model. Understanding of the correlation explanations in

Table 29 is aided by Table 30 which summarizes all of the input data in terms of the six general rock types encountered, At a glance, one can see which rock types possess the highest or lowest values, on the average, for a particular variable. Knowing the relative magnitude of TABLE 29 -- MODEL ANALYSIS — TOTAL EXCAVATING MAN-HOURS PER FOOT

Correlation T-Value No. Variable Name Coefficient Significance Explanation of Correlation 1 % Sericite**3 -0.2319 -3.8966 An alteration product possibly acting to improve self-supporting nature. 2 % Porosity**(l/3) -0.2166 -3 .3484 Sandstones are more porous and offer more rapid advance than clays, etc. 3 (VP2/1000)**3 -0.2562 3.0596 Higher velocity indicative of more dense : material, increased self-support. 4 % Kspar**3 -0.2140 2.5243 Mostly present in sandstones which gen­ erally are less troublesome than clays or siltstone. 5 (VB2/1000)**! -0.2283 2.3241 (See Variable 3) 6 % Clay Cement**(l/3) 0.3376 2.2314 Higher clay contents cause plugged steels and slower cycle in general. 7 % Clay Cement^( 1/2) 0.3310 -2.2015 (See Variable 6) 8 Ohm Log**3 -0.2056 -2.1522 Higher resistance indicates less water content and generally sandstone rock type. 9 % Total Cement**(l/2) 0.2254 -2.1284 Clay generally composes largest portion of cement, (See Variable 6). 10 Grain Size**(l/3) -0.2099 2.0677 Higher grain size indicative of sandstone (See Variable 2). 11 % Carbon**2 0.3316 1.9975 Higher carbon in clays arid siltstone which are more troublesome (See Variable 6). 12 % Chert**3 -0.2685 -1.9136 Present in sandstones and micrite which generally are more self-supporting. 13 Length of Round**(1/3) -0.3648 -1.7332 Longer.drill-rounds require less setup time per foot of advance. 14 (VS2/1000)**3 -0.3112 -1.7169 (See Variable 3) 15 % Carbon**! 0.2827 -1.6956 (See Variable 11) 16 Length of Round**(l/2) -0.3591 1.6159 (See Variable 13) 17 % Quartz**3 -0.2213 -1.3939 Higher quartz in sandstones which gen­ erally are less troublesome. TABLE 30 — AVERAGES OF VARIABLES AT "X" SHAFT FOR EACH ROCK TYPE

Very Fine Fine Medium- Grain Grain Coarse Grain Clay- Silt- Sandstone Sandstone Sandstone Stone Stone Micrite

% Cement: Clay 20 16 35 74 40 20 Quartz 6 5 0 0 0 0 Carbon 2 0 0 5 5 5 Calcite 0 5 0 2.0 6 54 Total % Cement 27.7 25.7 35.0 81.2 51.1 79 ,0 % Porosity 3.0 8.1 9.3 4.4 . 3.4 4.2 Grain Size 0.082 0,160 0.400 0.003 0.035 0.021 Alteration Code 3.3 3.0 3.7 3.4 3.6 2.0 % Composition: Quartz 56 59 50 9 36 0 Kspar 11 12 11 2 6 0 Clay 20 16 35 74 . 40 20 Sericite 6 2 1 3 2 0 Plagioclase 1 3 1 . 0 1 0 Chert 1 1 1 0 0 1 Limonite 3 0 0 4 2 3

Pyrite 1 0 0 . 1 0 3 Volcanic Fragments 0 2 1 0 0 0 Carbon 2 i : 0 " 5 6 6 Calcite 0 . 5 0 4 6 67 Resistance Log 46.3 39.3 41.0 37.3 38.0 19.6 Self Potential Log 28,7 32.6 42.0 26.8 30.8 22.8 Specific Gravity 2.131 2.055 2.180 2.303 2.254 2.306 TABLE 30 -•*' Continued

Very Fine Fine Medium- Grain Grain Course Grain Clay- Silt- Sandstone Sandstone Sandstone Stone Stone Micrite

Sonic Velocities (ft./sec.) VP1 9,032 7,793 10,611 7,876 6,898 7,939 VP2 9,631 8,017 10,059 9,904 9,250 11,086 VPS 9,614 8,452 9,532 10,371 9,610 11,036 VS1 5,674 4,338 4,964 4,938 4,656 4,709 VS2 5,938 4,709 5,468 5,566 5,727 5,940 VB1 7,120 4,946 6,270 5,994 5,641 5,175 VB2 7,610 5,482 6,828 6,948 7 ,435 8,875 VB3 7,581 5,576 6,806 8,205 7,813- 9,396 Concrete/7’-Pour (YD ) 23.9 26.3 26.7 23.6 23.9 18.0 Cunrni. G.P.M. Water Inflow 69.5 223.1 17.3 11.6 93.2 2.0 Avg. No. Men On Bottom 3.3 3.5 4.1 3.6 3.4 . 3.4 Length of Round 8.7 8.4 8.2 8.0 9.0 9.8 Avg. Experience/Shaftman(Hrs.) 2,408 3,971 3,636 3,355 5,082 5,443 Man-Hours/Round Drill & Blast 15.0 14.9 17.0 15.6 18.0 14.4 Muck 24.0 28.6 21.7 29.6 28.9 32.4 Total 39.0 43.4 38.7 45,2 46.9 46.8 Man-Hours/Foot Drill & Blast 1.76 1.76 2.10 1.97 1.98 1.52 Muck 2.79 3.42 2.66 3.79 3.20 3.33 Total 4.55 5.18 4.76 5.76 5.18 4.85 .92 a variable in one rock type relative to another often allows explanation of correlation in terms of a variable not even in the data. An example is variable number 4 (% KSPAR**3) in Table 29. It correlates negatively with man-hours per foot for excavation. By itself, one has difficulty in explaining this, but by looking at Table 30, one finds it most prevr elant in sandstones which generally are less troublesome from the drilling, blasting, and mucking viewpoint. In knowing the relationship of KSPAR to the various rock types an explanation is obtained.

Figure 12 graphically depicts the tests conducted in justifying the model. The 40 observations of data are sufficient to give a standard error of residual (SER) of 0.50 man-hour per foot which relates to confidence limits of + 0.16 man-hour per foot for the estimate.

Nomographs for this model are in Appendix E and relate to the following:

Y = 110.64 + 26.94CLYCM1/3 -22.79CLYCM1/2 -5.59POROS1/3

-3.00GRAIN1/3 -0.0000049RESIS3 -4.66T0TCM1/2 -4.15QTZ3

-207.03KSPAR3 -1086.37SRGIT3 -7316.69CHERT3 -18.63CRBN

-KL59.89CRBN2 -K).0012VP23 -0.0028VS23 -0.34VB2

-131.12LNGRD1/3 +57.06LNGRD1/2

Definitions of the variable abbreviations are given in Table 31 which also summarizes the correlations of each variable term. The importance of heeding these intercorrelations is especially evident in the nomo­ graphs in Appendix E where one finds the range of values on particular nomographs restricted to shaded or specially marked areas. Here again STANDARD ERROR OF ESTIMATE (Syx) MAN HOURS PER FOOT iue 2- Ecvtn a-or PrFo oe Selection ModelFoot Per Man-Hours 12-- Excavating Figure 0.8 0.2 0.6 0.4 i.o 0 0 o < £ 5 o O ec UJ => o o w tc £ =>2 or < z il a

5 (B) Adequacy of Dataof(B) Adequacy (A) Plot 0.8 0.4 0.6 1.2 1.0 20 10 UBR F OBSERVATIONS OF NUMBER q £ R n Sy^ and R ERSIN STEP REGRESSION 15 (A) 0.66 0.83 (B) 20 Syx 25 4025 35 30 30 35 0.6 0.8 0.4 0.2 1.0 93

MULTIPLE CORRELATION COEFFICIENT SQUARED (Rl ) TABLE 31 -- CORRELATION MATRIX __ EXCAVATING MAN-HOURS PER FOOT

CLYCM1/2 POROS1/3 CRAIN1^3 RESIS3 T0TCM1/2 qrz3 KSPAR3 SRCIT3 CHERT3 CRBN CRBN2 VP23 VS23 VB2 LNCRD1/3 LNCRD1^2

CLYCMl/3 40.99 -0.17 -0.58 -0.26 40.72 -0.66 -0.47 -0.07 -0.26 40.17 40.12 -0.07 -0.21 40.01 -0.11 -0.11 40.34

CLYCM1^2 -0.16 -0.59 -0.25 40.73 -0.65 -0.47 -0.08 -0.26 40.15 40.10 -0.07 -0.22 -0.01 -0.14 -0.14 -0.22

POROS1/3 40.37 -0.21 -0.24 40.28 40.17 -0.05 -0.07 -0.19 -0.14 -0.07 -0.15 -0.37 -0.10 -0.10 -0.21

CRAIN1/3 40.19 -0.77 40.60 40.54 -0.07 40.01 -0.51 -0.36 -0.05 40.06 -0.19 -0.05 -0.06 -0.21

RES IS3 -0.39 40.51 40.15 40.19 40.12 -0.13 -0.08 40.07 40.01 40.07 -0.37 -0.37 -0.23

TOTCM1/2 -0.84 -0.61 -0.23 40.08 40.38 40.25 40.15 -0.07 40.19 40.07 40.07 -0.22

QTZ3 40.44 -0.01 -0.13 -0.41 -0.30 -0.14 -0.01 -0.21 -0.13 -0.14 -0.21

KSPAR3 951 Confidence 40.09 -0.02 -0.34 -0.23 -0.03 -0.05 -0.23 -0.07 -0.07 -0.23 SRCIT3 N - 40 -0.08 40.02 -0.01 40.02 -0.10 40.12 -0.19 -0.18 -0.23

CHERT3 Zr/ 1 0.312 -0.07 -0.07 40.36 40.38 40.10 40.06 40.06 -0.27

CRBN 40.92 -0.03 -0.09 40.06 40.13 40.13 40.28

CRBN2 -0.04 -0.07 40.03 40.09 40.09 40.33 VP23 40.65 40.72 40.16 40.16 -0.26

VS23 40.64 40.22 40.22 -0.31

VB2 40.20 40.20 -0.23 LNGRD1^3 40.99 -0.36

LNCRD1^2 -0.36

CLYCM - % CLAY CEMENT SRC IT X SERICITE POROS - X POROSITY CHERT X CHERT CRAIN - GRAIN SIZE CRBN X CARBON

RESIS - RESISTANCE LOG VP2 VP2/1000 TOTCM - X TOTAL CEMENT VS2 VS2/1000

QTZ - X QUARTZ VB2 VB2/1000 KSPAR - X KSPAR LNCRD LENGTH OF ROUND Y TOTAL MAN-HOURS PER FOOT to illustrate, it would be ridiculous in a sedimentary environment to assume a rock type of 90% clay composition to possess 50% porosity and have a grain size of 0.5 millimeter. Under such assumptions the model falls apart because one is exceeding the range of sample data included in the model. In other words, no rock of this type exists and therefore could not be included in the data.

To this point in discussing modeling, nothing has been specifically directed at the materials aspect of capital cost esti­ mation. The second model from "X" Shaft looks at the variation of concrete in cubic yards per pour. In the case of the "X" Shaft, the pours were made in multiples of 7 feet. Here the geologic variables again explained the variation to a remarkable degree of satisfaction.

Table 32 summarizes the variables included in the model, and Figure 13 depicts the tests for justifying the model in terms of the 40 obser­ vations. A standard error of residuals (SER) of 2.37 cubic yards per

7-foot pour gives 95% confidence of + 0.76 cubic yards which is close to estimating within 10% of the actual pour (see Table 28 on page 82).

Intercorrelation aspects of the concrete model are given in Table 33 and need to be consulted in using the nomographs in Appendix F . These nomographs relate to the following mathematical relationship:

Y = 99.2 +0.88DEPTH -0.0046DEPTH3 +36134.21PLAG3

-8.25PYRIT1/3 -5471.19V0LC -2109 .51V0LC1/3

+4319.27VOLC1/2 -7.23CALC2 -0.19VB2 +8.13GPM1/3

Definitions of the abbreviated variables are found in Table 33. TABLE 32 — MODEL ANALYSIS — CUBIC YARDS OF CONCRETE PER 7-FOOT POUR

Correlation T-Value No. Variable Name Coefficient Significance Explanation of Correlation

1 7 . Plagioclase**3 0.4812 4.6002 Most prevalent in sandstone where water inflow may be higher increasing concrete washing. 2 (Cumm. GPM/100)**(l/3) 0.6096 2.9874 Increased water flow increases washing out of concrete during pouring. 3 7o Volcanic Fragments**! 0.5680 -2.9301 Highly correlated with cumm. GPM water inflow and thus concrete washing. 4 7. Vol. Fragments**( 1 /2) 0.6423 2.4482 (See Variable 3) 5 7o Vol. Fragments**(l/3) 0.6618 -2.2786 (See Variable 3) 6 (Depth/100)**3 0.4658 -2.0116 Cumm. GPM water increases with depth and washing increases accordingly. 7 7» Calcite**2 -0.4226 -1.8275 Higher calcite formations are generally more self-supporting with less slough. 8 (Depth/100)**l 0.3683 1.7325 (See Variable 6) 9 7. Pyrite**(l/3) -0.4007 -1.2571 High pyrite in micrite which is also high in calcite. (See Variable 7) 1 0 (VB2/1000)**! -0.3684 -0.5405 Higher sonic velocity generally means more dense material, possibly less over­ break.

a. Computer language (FORTRAN) nomenclature is used for representing the power of a variable. 7e Plagioclase**3 represents the cube of % Plagioclase.

vo ov iue 3 -CbcYrs fCnrt e 7Fo orMdl Selection ModelPour 7-Foot Per 0fConcrete 13--Yards Cubic Figure STANDARD ERROR OF ESTIMATE (Syx) CUBIC YARDS 4 0 2 5 3 5 0 5 0 5 0 35 30 25 20 15 10 5 0 (B) Adequacy of Dataof(B) Adequacy (A)of Plot O m o 3 20 0 5 0 35 30 25 20 2.75 0.80 UBR F OBSERVATIONS OF NUMBER and and ERSIN STEP REGRESSION SyX (A) (B) 40 97

MULTIPLE CORRELATION COEFFICIENT SQUARED (Rz) 98

TABLE 33 -- CORRELATION MATRIX CUBIC YARDS OF CONCRETE PER 7-FOOT POUR

DEPTH3 PLAC3 PYRIT1^3 VOLC VOLC1/3 VOLC1/2 CALC2 VB2 GPM1/3 Y

DEPTH +0.96 +0.30 -0.05 +0.46 +0.52 +0.51 +0.13 -0.04 +0.67 +0.37

DEPTH3 +0.39 -0.16 +0.58 +0.64 +0.63 -0.01 -0.07 +0.80 +0.47

PLAC3 -0.14 +0.81 +0.69 +0.73 -0.09 -0.33 +0.54 +0.48

PYRIT1^3 -0.21 -0.24 -0.24 +0.49 -0.22 -0.27 -0.40

VOLC +0.96 +0.98 -0.14 -0.42 +0.77 +0.57

VOLC1^3 +0.99 -0.16 -0.38 +0.79 +0.66

VOLC1^2 -0.16 -0.39 +0.79 +0.64

CALC2 95% Confidence -0.39 -0.23 -0.42

VB2 N 40 -0.34 -0.37

GPM1/3 /r/ 0.312 +0.61

DEPTH DEPTH/100

PLAC % P LAG IOC LAS E

PYRIT % PYRITE

VOLC % VOLCANIC FRAGMENTS

CALC 1 CALCITE

VB2 VB2/1000

GPM CUMULATIVE GPM/100

Y CUBIC YARDS OF CONCRETE PER 7*-POUR . 99

The Models in Retrospect

The sole purpose of this chapter is in answer to a "shotgun" estimate need arising in Chapter 3 * Where has the discussion gone since asserting this need? Four different sets of data acquired through separate sources have been used to produce 13 models, seven of which have been converted into nomographs for easy solution of complex mathematical relationships. Table 34 summarizes these 13 models in terms of the sign (positive or negative) determined for each variable in the models. Thirty-six variables in all were found to produce models that showed considerable accuracy in estimation of capital cost items. Out of these 36, only 2 variables seem to be contradictory and are marked with a question mark (?) in Table 34, Additional data are especially warranted relative to these two items.

In Chapter 4 it has been demonstrated that models can be pro­ duced for shaft sinking and undoubtedly any other phase of mine de­ velopment , and that these models function as follows:

1, They allow the introduction of probability for cost esti­

mation within confidence limits.

2, They permit quantitative interpolation within the range

of data in the model and qualitative extrapolation outside

u .

3, They disseminate information from past experience to the

young engineer coming into the field and thereby advance

technological development of the mining industry at an

accelerated rate. 100

TABLE 34 -- GENERAL CAUSE-AND-EFFECT SUMMARY IN SHAFT SINKING ECONOMICS

Lining & Tot. Drill & Blast Muckln ft Fittings X Cost S/Ft Yd3 Mh/Ft No. Variable Name A B CD EF G H IJ KL M 1 Avg. Advance/Day - + 2 Shaftoen/Shift + + + + 3 Shifts/Day + + 4 Year of Sinking . 5 No. Compartments + + 6 Rock Type Code + 7 Length of Round - +7 6 Hoisting Distance 9 Lining Code + 10 Shaft Area (see 5) + + + 11 Depth Sunk + + + + 12 Water Inflow (gpm) -? + + 13 Length/Width Ratio 14 Lbs Explosives/Ft 15 Skip Capacity 16 Sonic Velocity (VB2) 17 X Pyrite 18 X Calcite 19 X Quartz 20 Sonic Velocity (VS2) 21 X Chert (see 19) 22 Grain Size 23 X Kspar 24 Sonic Velocity (VP2) 25 X Porosity 26 X Sericite 27 X Carbon + 28 X Total Cementation + 29 Ohm Log 30 X Clay Cement + 31 Months To Sink + 32 X Wet Depth + 33 Sustained TPD Rate + 34 X Volcanic Fragments + 35 X Plagloclase +

Model Codes

Labor Dlttrlbutlon For The Sinking Cycle In General A. Drill and Blast (Man-Hours Per Foot) C. Drill and Blast (% of Cycle Man-Hours) D. Mucking (Man-Hours Per Foot) F. Mucking (% of Cycle Man-Hours) C . Lining and Fittings (Man-Hours Per Foot) H. Lining and Fittings (1 of CycleMan-Hours)

Co*wr d'Alene Shafts B. Bottom Crew Drill and Blast Man-Hours Per Foot B. Bottom Crew Mucking Man-Hours Per Foot I. Bottom Labor and Supervision (I of Total Shaft Cost) J. Total Labor and Supervision (X of Total Shaft Cost)

Shafts Accessing Sandstone Type Uranium Deposits K. Dollars Per Foot of Shaft (Including Stations and Pockets)

"X” Shaft L. Cubic Yards of Concrete Per 7-Foot Pour M. Excavating Man-Hours Per Foot They retain relationships for which the details may readily be forgotten and maintain them in a readily useable form as nomographs. CONCLUSION

Shaft sinking methods will become of increasing importance as it becomes necessary to exploit deeper deposits. The problems associated with increasing depth, which South African shaft sinkers have been involved with for the past 20 years, are now facing several companies in the United States. There are at least half-a-dozen new discoveries under evaluation this year requiring shafts in excess of

4,000 feet to reach and develop them.

Current U. S. Economic and political factors reflected in increasing inflation necessitate rapid shaft sinking relative to the

time-value of capital invested. Labor costs in the United States prohibit utilization of manpower as used in South Africa to attain advance rates in excess of 1,000 feet per month. In the U, S., con­

tinued adaptation of mechanization along with development of new and novel excavating techniques will have to be relied upon to decrease development timing.

The question of using contractor crews or owner crews to

sink a shaft is answered by inquiry into which alternative will provide

the necessary facility more efficiently in terms of total cost, work­ manship, and timing. Increased mechanization and changing techniques

require a different scale of requirements in a shaftman than 30 years

ago. With the general manpower shortage in the mining industry, it is

quite difficult to obtain a shaft crew through hiring competent men or ■ • ■- ' : . 103:

finding interested men to train♦ Also, training several men at a time

on the job slows down the project„ Thus, one finds the increasing

demand for bigger and deeper shafts along with increased mechanization

and diminishing supply of shaftmen placing the demand for shaft con­

tractors on an upward trend. The contractor strives to maintain

competent crews and efficient performance in view of his competition.

Large-diameter shaft drilling (f 10 feet in diameter) is not a panacea to be thought of as capable of matching South African advance

rates. It is doubtful, considering the difference in economics between here and there, that 1,000 feet per month in the U. S. is foreseeable

in the near future even though the desire is present. The only

similarity that is relevant today is in the South African problems

encountered with depth. Faced with these problems, the question is

one of vying drilled shafts of up to 25 feet in diameter against the

same shaft sunk conventionally to depths in excess of 4,000 feet. At

the present time, two major hurdles confront shaft drilling as follows:

1. The need for increased capacity in drilling equipment and

improved techniques for drilling and casing large diameter

holes.

2. The need for increased strength characteristics for casing

material and/or new casing construction developments.

To remain competitive, drilling must obtain these goals, because U.S.

demand for larger and deeper shafts will undoubtedly become a reality within the next 10 years. y ■■ 104

It has been standard practice in the earlier stages of property evaluation to obtain initial cost estimates for the new shaft from other shafts sunk under similar conditions• Even after costs and con­ ditions have been acquired, trying to adjust them to the new shaft conditions poses many questions. It is common to rationalize, 11 An increase in water inflow increases cost1’ and r,Bad ground will slow the advance rate," but this is merely a qualitative appraisal and of little help in adjusting the estimate.

Relative to the time-value of money, management is seeking methods or techniques providing tools to optimize the use of their funds. In this thesis presentation the author has proposed a procedure based on the conviction that canse-and-effeet relationships exist be­ tween shaft sinking conditions and cost, and that these relationships can be expressed quantitatively through statistical modeling techniques.

Analysis of several data sets support the thesis, but due to the gen^ eralizing nature of standard modeling techniques used, the shaft sinking models are of a "shotgun" nature and of most use in earlier stages of property evaluation, Since the quantification of a cause-and-effect relationship requires a mathematical equation, using the model is enhanced by converting the equation into nomographs requiring only a straight-edge for reaching a solution in a fraction of the time. The effect of varying one or more variables is visually apparent on the nomographs.

The models answer questions of why sinking performance varies, and these answers can be applied to developing new sinking techniques or innovations to current ones. If one knows precisely what variables 105 affect current practice, the problems can be efficiently approached0

This is particularly relevant to equipment design. In economic terms, the author concludes that it is most important to know how and why changes in conditions affect sinking performance in order to adapt to future shaft sinking demands.

Models developed for shaft sinking or any other phase of mine development represent the experiences of the past to be applied to the needs of the present, and current data reflecting changes in technology and productivity must be fed into the model. With the inclusion of these current data, the models must be regenerated.

Once preliminary evaluation of a project shows merit, detailed estimates need to be made according to an extensive check list of items involved in the particular project. There is no "black box" method for turning out a detailed estimate of shaft cost, but there is no argument that defeats model analysis for its purpose of quantitatively documenting cause-and-effeet relationships and the retention of past experience for usage as an initial estimating tool. It is with regard to this experience retention that models of complicated systems are to be considered the closest approximation of brain transplanting that is possible today.

It will be found, too, that the greatest technological advance­ ment has been in those areas or fields, such as physics, where cause- and-effect could be quantified and passed on to a multitude of minds for 106 further consideration» In mining, this is exemplified by the intensive work and development in the fields of explosives application and rock mechanics. Similar advancement in understanding the economics of shaft sinking or any other phase of mine development is keyed to cause-and- effeet studies.

In a model study of the nature presented here, the identity of data sources need not be reported. The conditions or variables reported describe the environment of the model, and this is what one looks to in using the model. The argument of many companies in the mining industry that they cannot provide the data requested because the models will divulge their confidential position is not valid.

While pursuing this thesis, the author selected several items as major points of consideration for continued research. Directly related to modeling is the need for establishing a division within a government or private, non-profit institution to be charged by the mining industry with the collection of cost data on all phases of mine development. This data would be converted into models, such as in­ dicated in this thesis, and disseminated to industry in a fashion not to divulge any one company's economic position but in a manner to assist all those concerned with capital cost estimation when they have determined basic conditions encountered on their particular projects.

This organization would have to function in a manner in which it or its employees would not be allowed.to benefit financially by betraying "company confidential" material entrusted to it. 107.

Major points of consideration for continued research directly related to shaft sinking are as follows:

lo Continued development of labor saving innovations in sinking

techniques and equipment. In the face of economic inflation,

increased productivity is the major counter balance.

2. Continued research on novel rock breaking and excavation

techniques to increase productivity.

3. Development of a means of measuring the state of stress at

any point along the vertical extent of a drill hole at a

shaft site. Knowing beforehand the pressure to be en­

countered would allow one to better estimate the support

system cost.

4o Development of a means of determining the in-situ strength

properties of the rock to be penetrated during sinking.

Shaft lining specifications could be optimized knowing the

extent to which the rock would be self-supporting.

5. Development of a rapid means of determining grout injectivity

during site investigation by some dowrni-the-hole tool pro­

viding continuous readout. Combined with porosity and

permeability measurements one would have a basis for a com­

plete assessment of grouting requirements.

Items 1 and 2 are important links in the supp 1 y - demand chain in view of the diminishing near-surface reserves. Items 3 through 5 are considered essential in bringing the science of rock mechanics into frequent use as a tool for improving the estimate of time involved! in completing a shaft project. APPENDIX A

NOMOGRAPH FOR BOTTOM CREW DRILL AND BLAST

MAN-HOURS PER FOOT (COEUR D' ALENE DATA)

/

108 Figure 14 -- Bottom Crew Drill and Blast Man-Hours Per Foot Nomograph Foot Per Man-Hours and Blast Drill Crew -- Bottom Figure 14

STARTING YEAR 54 49 50 48 56 47 52 53 55 46 57 2.0 Starting Year Versus Number ofCompartments Number Versus Starting Year (CoeurData)d'Alene 2.5 UBR F COMPARTMENTS OF NUMBER 3.0 , 4.0 3,5 109

APPENDIX B

NOMOGRAPHS FOR BOTTOM CREW MUCK

MAN-HOURS. PER FOOT (COEUR D' ALENE DATA)

\

110 SHAFT AREA iue 5 - otmCe ukMnHus e Fo Nomographs Foot Per Man-Hours Muck Crew Bottom -- 15 Figure

FEET2 200 220 240 230 160 140 130 150 170 120 190 180 210 110 0 30 0 70 0 10 10 10 1700 1500 1300 1100 900 700 500 300 100 (A) Shaft Area Versus Maximum Hoisting Distance Hoisting Maximum Versus ShaftArea (A) (Coeur (Coeur d AIU HITN DISTANCE HOISTING MAXIMUM 1 Data) Alene FEET

111 FIRST CUMULATION iue1 - Bto rwMc a-or e ot Nomographs FootPer Man-Hours Muck Crew -- Bottom Figure 15 BOTTOM-CREW MUCK MAN-HOURS PER FOOT 20 24 23 22 25 26 (B) First Cumulation Versus Average Length ofRound Length VersusAverage Cumulation First (B) CerdAeeDt) continued.(CoeurData), d'Alene . 5.04.04.5 VRG LNT O ROUND OF LENGTH AVERAGE FEET

6.0 6.5 112 APPENDIX C

NOMOGRAPHS FOR TOTAL LABOR PLUS SUPERVISION

(PERCENT OF TOTAL SHAFT COST) COEUR D' ALENE DATA

113 iue1 - oa Lbr ls uevso (ecn of Shaft Total (Percent Supervision Plus Labor -- Total Figure 16 SKIP CAPACITY YARD3 20 30 34 24 22 26 28 32 36 10 18 12 14 16 (A) . 45 . 55 . 6.5 6.0 5.5 5.0 4.5 4.0 ot Nmgah (Coeurd'Alene Data) Nomographs Cost) Skip Capacity Versus Average Length of Roundof Length Average Versus Capacity Skip o. VRG LNT O ROUND OF LENGTH AVERAGE FEET

114 iue 6 Ttl ao Pu Spriin Pret of Shaft (PercentTotal Supervision Plus Labor Total — 16Figure

FIRST CUMULATIVE TOTAL LABOR PLUS SUPERVISION PERCENT TOTAL SHAFT COST 59 67 57 63 69 73 75 65 (B) First Cumulation Versus Pounds of Explosives Per Foot Per of Explosives Pounds Versus Cumulation First (B) 15 '6o. ot Nmgah (Cocur Data)>d'Alene continued. Nomographs Cost) ONS F XLSVS E FOOT PER EXPLOSIVES OF POUNDS 20 25 30 540 35 To 115 APPENDIX D

NOMOGRAPHS FOR BOTTOM LABOR PLUS SUPERVISION

(PERCENT OF TOTAL SHAFT COST) COEUR D' ALENE DATA

116 iue1 — Bto ao ls uevso (ecn o oa Shaft ofTotal (Percent Supervision PlusLabor Bottom — Figure 17

AVERAGE LENGTH OF ROUND FEET 4.5 5.5 6.0 4.0 5.0 6.5 6 8 0 52 50 48 46 (A) Average Length 0f Round Versus Starting Year Starting 0fVersusRound Length Average (A) ot Nmgah Cer ’AleneData) d Nomographs (CoeurCost) TRIG YEAR STARTING 4 5

55 117 iue1 -- Bottom LaborPlus Supervision (Percent Figure of17 Total Shaft FIRST CUMULATIVE BOTTOM LABOR PLUS SUPERVISION PERCENT TOTAL SHAFT COST 40 50 30 60 0 10 4 10 8 20 2 240 220 200 180 160 140 120 100 (B) Cost) Nomographs (Coeur d'AleneData),continued. FirstCumulation Versus Shaft Area HF AREA SHAFT FEET2 'SO

118 APPENDIX E

•NOMOGRAPHS FOR TOTAL MAN-HOURS PER FOOT

("X"-SHAFT DATA)

119 iue1 - TtlMnHus e Fo Nmgah (X-ShaftData) Nomographs Foot Per Man-Hours -- Total Figure 18 CLAY CEMENT PERCENT A PercentClay Cement Versus Percent Porosity (A) 4 8 0 2 4 6 18 16 14 12 10 8 6 4 2 XM CIE .\> \ . CRITEC M X V POROSITY PERCENT 120 iue 8 Ttl a-or PrFo oorps (X-ShaftData), Nomographs Foot Per Cont. Man-Hours Total — 18Figure FIRST CUMULATION TOTAL MAN HOURS PER FOOT 114 115 112 113 (B) First Cumulation Versus Grain SizeGrain Versus Cumulation First (B) 0.1 Clays 0.2 n/os o^xed .0mm) m 0.003m not^exceed one/does MILLIMETERS in a r g ' ze iz s ANDSTQ. 0.4 121 0.50.3 iue1 - oa MnHus e otNmgah (X-ShaftData), Nomographs cont. Foot Per Man-Hours --Total Figure 18 SECOND CUMULATION

TOTAL MAN-HOURS PER FOOT 113 HO 114 112 C SecondCumulation Versus Resistance Log (C) SANDSTONE SILTSTONE CLAYSTONB 30 EITNE LOG RESISTANCE 40 OHMS 50

070 60 122 123

114

113

MICRITE; SANDSTONE

112 u_ SILTSTONE o re 7- L U

III O

o 110

109

108

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 TOTAL CEMENT PERCENT

Figure 18 -- Total Man-Hours Per Foot Nomographs (X-Shaft Data) , continued. (D) Third Cumulation Versus Percent Total Cement 124

(MICRITE-POESZNOT

110 •HO

u. i09' V QC

AYSTONE. TONE

iOQ' o 108

cc <

106

104

20 30 40 50 60 70 0UART2 composition p e r c e n t Figure 18 -- Total Man-Hours Per Foot Nomographs (X-Shaft Data) , continued. (E) Fourth Cumulation Versus Percent Quartz Composition 8 12 KSPAR COMPOSITION PERCENT ure 18 continued. (F) Total Man-Hours Per Foot Nomographs (X-Shaft Data)

Fifth Cumulation Versus Percent KSPAR Composition iue1 - oa a-or e otNmgah (X-ShaftData), Nomographs Foot Per --Man-Hours Total 18Figure SIXTH CUMULATION

100 TOTAL MAN-HOURS PER FOOT 105 110 G SixthCumulation Versus Percent Sericite Composition (G) SILTSTONE otne. * continued. EIIE COMPOSITION SERICITE PERCENT ,06

126 127

110 >//C?

/yd'

’107 >

EE vys-' ± ^ DST0N ^ AND-NlTcRt¥ I S 105 - U 3 ~ CLAYS T o K F r SILTSTOr.jP- 104 ui

Ui to u

./y/-

’/ O O 100

CHERT COMPOSITION p e r c e n t

Figure 18 — Total Man-Hours Per Foot Nomographs (X-Shaft Data) , continued. (H) Seventh Cumulation Versus Percent Chert Composition Figure 18 iue 8 -Ttl a-or e ot oorps (X-ShaftData) Nomographs FootPer , Man-Hours --Total 18 Figure NINTH CUMULATION TOTAL MAN-HOURS PER FOOT 100 105 95 110 (j) Ninth Cumulation Versus Sonic Velocity VP2 Velocity SonicVersus Cumulation Ninth (j) 8 0 12 10 8 6 continued. HUAD O FE PR SECOND PER FEET OF THOUSANDS OI VLCT VP2 VELOCITY SONIC SANDSTONE SILTSTONE: CLAYSTONEi

129 iue1 - oa MnHus e Fo oorps (X-ShaftData), Nomographs Foot Per Man-Hours -- Total Figure 18 TENTH CUMULATION TOTAL MAN-HOURS PER FOOT 100 105 95 115 K TenthCumulation Versus Sonic Velocity VS2 (K) 3 116 continued. 4 HUAD O FE PR SECOND PER FEET OF THOUSANDS ^ MICRIT LS A'ND STONE- OI VLCT VS2 VELOCITY SONIC 5 10 ^ -CLAY_S_TpNEy 6 M 1 # 7 10k

7 8 130 9 (•* »*»** **/10' no

o s s p fcU •/05' 5 a '05 O •M/c r ,Tc . X x 'SandstoNf tuIf 'CL a y ^ t o n e ' M r s Tone- t>/O0» too

95* 95

(so.

FlSure

v s - @ 5 i = : - : Velo=ity VB2 iue1 --TotalMan-Hours Per FootNomographs (X-Shaft Data) , Figure 18 TWELFTH CUMULATION TOTAL MAN-HOURS PER FOOT 100 105 110 0 9 95 115 6 8 1 II 10 9 8 7 M TwelfthCumulation Versus Length of Round (M) continued. EGH F ROUND OF LENGTH FEET

132 APPENDIX F

NOMOGRAPHS FOR CUBIC YARDS OF CONCRETE PER 7-FOOT POUR

("X"-SHAFT DATA)

133 iue 9 -CbcYrso ocee e 7Fo Pu Nomographs Pour 7-Foot Per Concrete of --Yards Cubic 19Figure DEPTPH /I0 0 FEET 14 6 4 6 2 6 8 6 4 2 0 (A) Depth/100 Versus Percent Plagioclase Composition Plagioclase Percent Versus Depth/100 (A) 100 (X-ShaftData) LGOLS COMPOSITION PLAGIOCLASE PERCENT

134 3 4 PYRITE COMPOSITION figure 19 PERCENT

•- Cubic Yards of Concrete Per 7-Foot Pour Nomographs (X-Shaft Data) , continued. (B)

First Cumulation Versus Percent Pyrite Composition Figure 19 — Cubic Yards of Concrete Per 7-Foot Pour Nomographs Pour 7-Foot Per Concrete of Yards Cubic — Figure19 SECOND CUMULATION CUBIC YARDS OF CONCRETE PER 7 FT. POUR 106 102 126 12% 130 94 98 110 114 118 12 3 5 6 5 4 3 2 1 0 (C) Second Cumulation Versus Percent Volcanic Fragments Volcanic PercentVersus Cumulation Second (C) LU o LU LU e> opsto (. pret to 6.0 percent) (1.0 percent Composition (X-ShaftData) , continued. OCNC RGET COMPOSITION FRAGMENTS VOLCANIC PERCENT

136

V*

40

-J5-

JO'

-Z- V o o- ^5-

2 0 *

:.:^vc ° ; 5 ^ 4 ' ,.

s5 ’ ‘ , i i v <30

t.. . - r r ~ r 0.10 0.15 ( VOLCANIC FRAGMENTS COMPOSITION Figure 19 PERCENT wx,wrUSITION : Yards of Con/"'-~' -- Cubic Yards of Concrete Per 7-Foot Pour Nomographs (X-Shaft Data)f continued. (£!)

Second Cumulation Versus Percent Volcanic Fragments Composition (0.1 percent to 0.25 percent) 139

Q 45

ou 40 50 CALCITE COMPOSITION PERCENT Figure 19 -- Cubic Yards of Concrete Per 7-Foot Pour (X-Shaft Data), continued. Nomographs (F) Third Cumulation Versus Percent Calcite Composition Figures 19 -- Cubic Yards of Concrete of Yards -- Cubic 19 Figures FOURTH CUMULATION CUBIC YARDS OF CONCRETE PER 7 FT. POUR 30 45 60 105 15 120 90 75 + *** » »> * # A*ae**a n A !» »♦ » » > o C FourthCumulation Versus Sonic Velocity (C)VB2/1000 4 3E

(X-ShaftData), continued. J-t•'rv > t±.i »-r 5 HUAD O FEET OF THOUSANDS

OI VELOCITY SONIC 6

7

E SECOND PER e 7Fo Pu Nomographs Pour 7-FootPer 9 0 II 10 9 8 VB2

140 I tz

141

o 40

CUMULATIVE WAicn GALLONS PER MINUTE /1 0 0

Cubic Yards of Concrete Per 7-Foot Pour Nomographs

F ig u re 1 9 (X-Shaft Data), continued. Fifth Cumulation Versus Cumulative Water Inflow (K) SELECTED BIBLIOGRAPHY

Abel, J . F *, Tunnel Mechanics. Quarterly of The Colorado School of Mines, Vol. 62, No. 2, April, 1967.

Beall, J. V., "Tunnel And Staff Conference Spotlights Wider Acceptance of Boring Methods", Mining Engineering, July, 1968, p. 139—1^3.

Bilheimer, L., "Chemical Grout Technique Solves Meramec Shaft Sinking Problems", Engineering and Mining Journal, November, 1959, p« 107-109*

Bolmer, R. L ., Sinking A Large-Diameter Concrete-Lined Access Shaft: Harold D. Roberts Tunnel, Colorado. U . S. Bureau of Mines In­ formation Circular No. 8029, 19 61.

Bolmer, R . L ., Sinking Methods And Costs For A Small Vertical Shaft With Steel Supports: Keystone Mine, Crested Butte, Colo. U. S. Bureau of Mines Information Circular No. 8086, 19 62.

Bullock, R . Lo, "Fundamental Research on Burn-Cut Drift Rounds", (reprint) The Explosives Engineer, January-February and March- April, 1961.

Coates, D. F ,, Rock Mechanic Principles, Ottawa: Department of Mines And Technical Surveys Mines Branch Monograph No. 874, 1965.

Coates, D . F . and M. Dickhout, "Elements of Planning In Deep Mining", Canadian. Mining Journal, September, 1970 , p. 7^-78.

Crow, E. L., F. A. Davis and M. W. Maxfield, Statistics Manual. New York: Dover Publications, 19 60.

Deacon, D . D ., "Sinking No. 4 Shaft At Hartebeestfontein Gold Mining Company, Ltd." (reprint) The Canadian Mining And Metallurgical Bulletin, February, 1965.

Dellinger, T. B ., Economic Factors Relative To Drilling Large - Diameter Holes. Second Symposium on Salt, The Northern Ohio Geological Society, Inc., May, 1965.

Dowis, J. E., "Mining Tax Variations In North America", Mining Engi­ neering , September, 1970 , p. 82-87•

Draper, N. R. and H. Smith, Applied Regression Analysis. New York: John Wiley & Sons, 1966.

Elsing, M. J., "Cost of Shaft Sinking", Engineering and Mining Journal, October 26, 1931 ,p« 3^9-352.

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