Lecture 7 тсп 1

1.

07
LECTURE 7
Excavator Face
Design & Productivity
Sizing the bucket, laying out the dig zone, and matching trucks to the machine
— the geometry behind a working excavation
COURSE
TECHNOLOGY OF CONSTRUCTION
PRODUCTION
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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WHAT WE'LL COVER
From bucket size to a finished dig plan
01
02
03
04
Excavator & Truck
Selection
Backhoe Face Layout
Dragline Face Layout
Productivity & Topsoil
The exact geometry of digging,
discharging, and stepping forward
The same problem, solved with a
longer boom and a cable-hung
bucket
Rating a machine's output, then
stripping the ground before digging
starts
Matching bucket size and the
number of trucks to the volume of
work
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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SECTION ONE
Sizing the Bucket & Reading a
Spec Sheet
How wide a bucket a trench allows, and what a catalog number really promises on site
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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3.4 CHOOSING THE EXCAVATOR
A bucket can only be as wide as the trench
The bottom of a trench or pit has a fixed width. The excavator's bucket has
to fit inside it, with a little clearance either side.
b = bucket width, a = bottom (passage) width of the trench or pit
That clearance depends on how the soil behaves once it's cut:
Cohesive soils (clay, loam)
Backhoe buckets are built roughly cube-shaped: length : width
: height ≈ 1.2 : 1 : 0.8.
So once a bucket's capacity (volume) is known, its width can be
estimated — and checked against the trench it has to work in.
Getting this wrong means an excavator that physically cannot
reach the bottom corners of its own trench.
b ≤ a − 0.1 m
Loosely-cohesive soils (sand)
b ≤ a − 0.15 m
Dragline bucket
b ≤ a − 0.25 m
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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3.4 CHOOSING THE EXCAVATOR
Matching bucket size to the size of the job
Table 1. Recommended bucket capacity by total excavation volume
Excavation volume, m³
Bucket capacity, m³
Up to 500
0.15 – 0.4
500 – 1,500
0.4 – 0.5
1,500 – 3,000
0.5 – 0.8
2,000 – 8,000
0.63 – 1.0
6,000 – 12,000
0.8 – 1.6
10,000 – 18,000
1.2 – 2.5
Over 18,000
1.8 – 3.2
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
Reading this table
The ranges overlap on purpose — within a band, the final
choice depends on soil difficulty and how tight the site
access is.
The cutting edge is toothed for cohesive soils (clay, loam)
and a plain straight edge for loose sand or loam.
A bucket also needs a minimum face depth to fill properly
in one pass — too shallow a cut and it comes up halfempty.
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3.4 CHOOSING THE EXCAVATOR
The “face”: an excavator's whole working zone
The face — an excavator's whole working zone — is not just the hole being dug. It's everything the excavator needs around it to work
safely and efficiently:
The stance
The soil mass
Truck access
The dump area
where the excavator itself stands to
dig
everything reachable and dug from
one stance, without moving
room for a truck to pull in, position,
and be loaded
space to discharge soil that isn't
going straight to a truck
Hazard radius: F0 ≥ Rk + 5 m
Rk = the excavator's maximum digging radius. Nobody and nothing not involved in the work should be within this radius — it's the minimum safe standoff distance from the
machine's swing.
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3.4 CHOOSING THE EXCAVATOR
A catalog number is a best case, not a guarantee
Manufacturers publish a maximum digging depth and radius. In practice, an excavator can never quite reach either figure — the boom geometry
and the need to actually fill the bucket get in the way.
So the real, required depth H and top-passage width a₃ are used to check that a machine's catalog numbers (marked with an asterisk *) leave
enough margin:
Backhoe
Dragline
Hk* ≥ H ÷ 0.7
Hk* ≥ H ÷ 0.9
Rk* ≥ a₃ ÷ 0.8 (loading into a truck)
Rk* ≥ a₃ ÷ 0.7 + 1 m
Rk* ≥ a₃ ÷ 0.8 + 1.5 m (discharging to a stockpile)
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3.4 CHOOSING THE EXCAVATOR
Reading an excavator's technical data sheet
Every excavator model comes with a technical characteristics sheet. These are the twelve numbers a planner actually needs from it — the rest of this
lecture explains how each one is used:
Soil group the machine is rated for
Height of the boom's base above the ground, hsh (m)
Bucket capacity, q (m³)
Undercarriage type (crawler / wheeled)
Digging depth, Hk (m)
Track (or wheel) base, B (m)
Maximum digging radius, Rk (m) / boom length, lᴄ (m)
Track (or wheel) gauge, K (m)
Radius of the rear of the turntable, rk (m)
Bucket-teeth breakout force, S₀ (kN)
Distance from the boom's base to the axis of rotation, rsh (m)
Working-cycle duration, Tc (seconds)
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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SECTION TWO
Selecting the Dump Truck
Matching a truck's body to the excavator, and working out how many are needed
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3.5 SELECTING THE DUMP TRUCK
How much soil actually fits in the truck?
A truck is loaded in a small number of excavator cycles — usually 3 to 9, and ideally 4 to 6. Fewer than that and the truck's body goes unused;
more, and loading simply takes too long.
Q = n×q×K
f
n
(soil volume loaded in the optimal number of cycles)
n — the chosen (optimal) number of bucket-loads, q — bucket capacity, Kn — the fill coefficient (how full each bucket-load really is, not just its rated volume).
The truck's body-fill coefficient is kept in the range 0.85 to 1.1, chosen from the manufacturer's reference tables.
The truck itself is then picked so its rated capacity Q satisfies: Q ≤ 1.1 × Qf — a little headroom, but not a wildly oversized body.
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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3.5 SELECTING THE DUMP TRUCK
Volume isn't the only limit — weight matters too
A truck body sized correctly by volume can still be overloaded by weight, especially with dense, wet soil. The actual load must satisfy:
G = Q × ρ × (1 − K ) × K ≤ 1.05 × G
g
avg
p
wet
Qavg × ρ — the soil's average bulk mass in the body; Kp — the soil's initial bulking (swell) after digging; Kwet — a correction for moisture content.
G — the truck's rated payload from its own spec sheet. The rule allows the loaded weight to run up to 5% over G, but no more — beyond that, the truck
(and the road) simply isn't built for it.
This is exactly why wet, heavy clay fills a truck's rated volume long before it reaches its rated weight.
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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3.5 SELECTING THE DUMP TRUCK
How many trucks keep the excavator busy?
An idle excavator waiting on trucks is the single most expensive mistake on an earthmoving site. The fleet size is set so the machine never has to stop:
Loading from two sides
Loading from one side
N ≥ Ta ÷ tp
N ≥ Ta ÷ (tp + tm)
tp — loading time; tm — the extra time a truck needs to reposition when only one side of the excavator is used for loading.
Ta — one full truck cycle: Ta = tp + 2 × (haul distance ÷ average speed) + turnaround time + tm.
Empty trucks typically travel 10–20% faster than loaded ones, which is factored into the average speed used.
The result N is always rounded up to the next whole truck — a fleet of 4.2 trucks means 5 trucks on site.
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
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3.5 SELECTING THE DUMP TRUCK
Two special cases worth knowing
Working two jobs at once
Bringing soil in, instead of taking it away
Sometimes the same excavator splits its output: part of the soil goes
onto a stockpile beside the trench, part goes straight into trucks.
The truck count then also depends on how the total dug volume is
divided between the two destinations, and on how much faster the
excavator can dump beside itself than load a truck.
When backfill soil has to be trucked in from a quarry or borrow pit
rather than reused on site, delivery time is checked the same way, in
reverse.
Delivery time depends on the volume needed and the trucks' average
delivery rate, and is rounded up to the nearest half work-shift — never a
fraction of a shift.
In short: trucks are only needed for the transported share of the work,
not the whole volume being dug.
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3.5 SELECTING THE DUMP TRUCK
Planning trucks' movement on paper first
A simple time-distance chart like this lays out exactly when each
truck is on-site being loaded, when it's travelling loaded, and when
it's returning empty.
Staggering trucks this way is what keeps the excavator continuously
fed without any truck queuing unnecessarily at the face.
The haul distance itself splits into two legs — the short run across
the site, and the longer run to wherever the soil is being taken
(disposal or stockpile grounds).
Figure 1. Truck movement schedule: distance (L) vs. time (T) for two trucks on one haul route
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SECTION THREE
Laying Out the Backhoe's Face
The exact geometry that keeps a backhoe safe, efficient, and able to reach where it
needs to dig
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3.6 BACKHOE FACE LAYOUT
Keeping the machine back from the edge
The excavator must stand back far enough from the crest of the slope that its own weight can't trigger a collapse, or tip it into the excavation.
That minimum safety berm, l-min, depends on how wet the ground is:
0.5 – 1 m
dry soils, dig depth up to 7 m
l-min = H(mv − m) + 0.5 m, ≥ 1.5 m
wet soils — mv is the slope coefficient of moistened soil, always steeper-sided
than dry soil (m)
Wet soil slumps at a shallower angle than dry soil, so on a wet site the safe standoff distance grows well beyond the flat 0.5–1 m rule — sometimes several times
over.
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3.6 BACKHOE FACE LAYOUT
The whole face, drawn to scale
rk — turntable rear radius; rsh, hsh — the boom's pivot position; l0
— the machine's own footprint clearance; l-min — the safety berm
just discussed.
Rst — distance from the rotation axis to the slope edge; Hm — depth
times the slope coefficient; Rn-min — the smallest usable digging
radius at the bottom of the pass.
Lp — the recommended step the whole machine advances between
passes; Rn, Rp — the digging radius actually achievable at the
required depth.
Every later formula in this section is really just working out one
piece of this same drawing.
Figure 2. Longitudinal section through a backhoe's face and its dimension chain
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3.6 BACKHOE FACE LAYOUT
l0: how far the machine itself reaches forward
For a crawler machine: l0 = B÷2 + (0.1–0.15) m (B = the machine's
track base length)
For a wheeled machine: l0 = B÷2
Rst ≥ l0 + l-min
Figure 3. Determining the distance from the front support to the slope crest on wet ground
TECHNOLOGY OF CONSTRUCTION PRODUCTION · LECTURE 7
This is simply the rule that the excavator's own footprint (l0) plus the
safety berm (l-min) together fix the minimum distance from the
rotation axis to the edge of the slope.
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3.6 BACKHOE FACE LAYOUT
From the stance to the digging radius
Minimum bottom radius
Rn-min ≥ Rst + H·m
the smallest radius that still clears the slope at full depth
Realizable vs catalog radius
Rp = (0.85–0.95) × Rk
a machine never quite reaches its own catalog maximum
Maximum radius at depth H
Rn ≤ √(l² − (H+hsh)²) + rsh
l = the effective boom-and-bucket reach
Boom reach, l
l = √((Rp − rsh)² + hsh²)
back-calculated from the realizable radius
Recommended step
Lp ≥ Rn − Rn-min
how far the whole machine advances between passes
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3.6 BACKHOE FACE LAYOUT
Discharging straight into a truck
Rvt ≤ √(l² − (hvt − hsh)²) − lk÷2 + rsh — the reach needed to swing the
loaded bucket over the truck body.
hvt = htruck + hgap, where hgap is a clearance reserve above the truck's
own soil pile: 0.3 m for the pile's natural overheight, plus 0.1–0.3 m
(hydraulic excavators) or 0.3–0.5 m (mechanical excavators) so the bucket
teeth never catch the truck body.
A minimum 1 m gap is always kept between the excavator's own body and
the truck, so neither the swinging boom nor the counterweight can ever
strike the cab or the load.
Figure 4. Cross-section: a backhoe loading a truck
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3.6 BACKHOE FACE LAYOUT
Discharging to a stockpile instead
The reach and height needed depend on the stockpile's own
shape — a simple triangular pile needs less reach than a flattopped trapezoidal one.
hvn = hpile + hgap, where hgap is 0.1–0.3 m for a mechanical
(cable) excavator, or at least half the bucket length plus 0.1 m for a
hydraulic one — hydraulic buckets need more headroom to clear
the growing pile.
This is exactly the same logic as loading a truck (previous slide),
just aimed at a pile of soil instead of a truck body.
Figure 5. Cross-section: a backhoe piling soil beside the trench, for a triangular and a trapezoidal
stockpile
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3.6 BACKHOE FACE LAYOUT
Looking down on the face from above
The plan view is what shows the excavator's largest possible stockpile length, and how close a
fixed obstacle (a wall, a pole, a neighbouring structure) can safely sit to the working face.
The turning angle 2γ₀ (the swing between digging and discharging) should stay between:
55° ≤ 2γ₀ ≤ 110°
Below 55°, the excavator chosen is simply too big for the job — more swing capability than the layout
ever uses, at extra cost.
Turning angles are capped by convention at 135° for discharge to one side, or 270° for discharge split
between both sides.
Figure 6. Plan view of the face and its swing arc
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3.6 BACKHOE FACE LAYOUT
Working a wide pit in successive passes
A pit wider than one pass is dug strip by strip. The very first strip's bottom width, ap, is set at a fixed 4 m
or 7 m simply to let equipment drive in and out.
Each subsequent strip's top width, a₃, must satisfy: a₃ ≥ ap + 2H·m
Discharging to one side: 0.8Rp ≤ a₃ ≤ 1.6Rp
Discharging to both sides: 1.3Rp ≤ a₃ ≤ 2Rp
In short, the wider the strip, the more the excavator can discharge to both sides at once — fewer, wider
passes rather than many narrow ones.
Figure 7. Pass scheme for a wide pit
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SECTION FOUR
Laying Out the Dragline's Face
The same layout problem, solved by a machine with a longer reach and a cable-hung
bucket
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3.7 DRAGLINE FACE LAYOUT
A longer boom, and a bucket on a cable
A dragline also digs below its own stance, just like a backhoe. But its boom is significantly
longer, and the bucket hangs from a flexible cable rather than a rigid arm.
That flexible connection changes what the machine can do: greater reach and depth, but less
precise control over exactly where the bucket cuts.
The same rk, rsh, l0, l-min, Rst, Rn-min, and Lp dimensions from the backhoe layout carry over
directly — only the reach itself, l, is now measured along the boom's own angle α.
Figure 8. Longitudinal section through a dragline's face
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3.7 DRAGLINE FACE LAYOUT
Wider swings, and a bigger safety margin
Turning angle, 2γ₀
Safety berm, l-min
50° ≤ 2γ₀ ≤ 100° (discharging to a stockpile)
≥ 1.5 m on stable, dry ground
30° ≤ 2γ₀ ≤ 110° (discharging into transport)
3 – 5.5 m on wet ground, depending on the bucket's capacity
A dragline's minimum digging depth is effectively unrestricted — its long boom simply reaches over any obstruction. The real limit on maximum depth
is the length of cable the winch can pay out.
Rst (distance from the rotation axis to the slope crest) is worked out exactly the same way as for a backhoe.
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3.7 DRAGLINE FACE LAYOUT
How far a dragline can actually reach
Rp = lᴄ·cosα + (lᴄ·sinα + hsh)·tanβ + rsh
lᴄ — the boom's length, chosen from the catalog for the required depth and trench-top width; α — the boom's working angle, typically 30–60°.
β — the angle the bucket's own cable makes as it swings out, kept to 10–15° or less so the cable-and-pulley rigging still works correctly.
Recommended step: Lp = Rp − Rn-min — the same idea as the backhoe's step, just built from the dragline's own reach.
Discharge radius (into transport or onto a stockpile — it works out the same either way): Rv = rsh + lᴄ·cosα − hk÷2, where hk is the dragline bucket's own height,
roughly hk ≈ 0.8 × ³√q.
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3.7 DRAGLINE FACE LAYOUT
How high a dragline can lift its load
The maximum discharge height, hv, is set by the boom's length and angle, minus however much of that reach the bucket-and-cable rigging itself takes
up:
hv ≤ (lᴄ·sinα + hsh) − lku
lku — the combined length of the bucket plus its cable harness, roughly lku ≈ 1.8 × ³√q.
A clearance reserve, hgap, is still added on top — the same idea as the backhoe's own clearance: 0.6–0.8 m when discharging into transport, or 0.5–0.6 m
onto a stockpile.
Every other face parameter — first-pass width, discharge turning angle, and so on — is worked out exactly as it was for the backhoe in the previous section.
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SECTION FIVE
Rating an Excavator's Productivity
Turning a face layout into an honest estimate of how much soil a machine actually
moves per shift
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3.8 EXCAVATOR PRODUCTIVITY
Rated productivity: the standard reference number
Once a machine is finally chosen, its output is estimated two ways — a rated (catalog / reference) productivity first, then a more realistic
operational figure.
Π = (t ÷ H ) × 100 m³ / shift
n
shift
norm
tshift — the length of the work shift, in hours.
Hnorm — a standard labor-time norm for the machine and soil-group combination, looked up from a standard construction labor-time reference table.
For a backhoe or dragline, this rated figure is then adjusted downward for soil that sticks to the bucket, a wet face, and similar conditions — using the same
reference tables.
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3.8 EXCAVATOR PRODUCTIVITY
Operational productivity: what actually happens on site
Π = 3600 × (q ÷ T ) × K° × (K ÷ (1+K )) × K × t
e
c
n
p
v
shift
q ÷ Tc — bucket capacity divided by the actual working-cycle time in seconds, scaled up to an hourly rate (×3600).
K° — a coefficient for the discharge turning angle: a wider swing costs more time, so it lowers output.
Kn ÷ (1+Kp) — the bucket fill coefficient corrected for the soil's own bulking after digging.
Kv — a time-utilization coefficient: about 0.9 discharging to a stockpile, 0.83 loading one truck side, or 0.85 loading from both sides.
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SECTION SIX
Removing the Topsoil
Clearing the fertile layer before digging starts — a job excavators rarely do well
themselves
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3.9 TOPSOIL REMOVAL
Clearing the ground before anything else is dug
The fertile topsoil layer across the whole site is stripped first and moved to stockpiles, so it can later be reused for landscaping or returned to
agricultural land — not buried or hauled away as waste.
Stripping can be skipped when:
Under 10 cm
Waterlogged ground
Narrow trenches
the topsoil layer is too thin to be worth the
effort of stripping and stockpiling separately
wet, boggy sites are excluded from stripping
altogether
trenches with a top width of 1 m or less are dug
through without a separate stripping pass
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3.9 TOPSOIL REMOVAL
Why excavators rarely do this job themselves
A topsoil layer is usually too thin for an excavator bucket to fill properly — the bucket simply can't get enough soil per pass to work efficiently.
Scrapers and bulldozers are the standard tools for this job instead:
Scrapers
Bulldozers
Economical for haul distances of roughly 0.3 to 5 km — short enough
that driving to a dump and back doesn't waste the trip.
Beyond a scraper's economical range, a bulldozer instead pushes the
stripped soil to a temporary dump nearby.
Work best on cohesive soils, with a fill coefficient of about 0.8–1.1 when
stripping a layer of steady thickness.
From that temporary dump, the soil is then loaded and hauled onward
by truck — rather than one machine covering the whole distance itself.
Typically run in working strips up to 200 m long.
With a bulldozer pushing behind it, a scraper can strip a noticeably
thicker layer per pass than it can working alone.
In effect: short haul → scraper alone; medium haul → scraper assisted
by a bulldozer; long haul → bulldozer plus trucks.
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LECTURE 7 — IN SUMMARY
From a bucket size to a working excavation
1
Size the bucket to the trench, and check the truck fleet against both volume and weight
2
Lay out the backhoe's face: stance, safety berm, digging radius, and discharge reach
3
The same layout logic applies to a dragline, just measured along its longer boom
4
Rate a machine's output honestly — catalog numbers first, then real working conditions
5
Strip and stockpile the topsoil before any other digging begins
Next time, in Lecture 8: putting excavators, bulldozers, and compaction machines to work together as one coordinated earthmoving crew.
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