HDD Pullback Force Fundamentals | Horizontal Directional Drilling Guide

1. Overview

Horizontal directional drilling (HDD) is a trenchless construction method used to install pipelines beneath obstacles such as rivers, roads, railroads, wetlands, and developed areas. The process involves three stages: pilot bore drilling, hole reaming to enlarge the bore, and product pipe pullback through the enlarged bore.

The pullback phase is the most critical from an engineering standpoint because the pipe must withstand the tensile forces required to pull it through the bore without exceeding its structural capacity. ASTM F1962 provides a standardized methodology for calculating the required pullback force.

Pilot Bore

Stage 1

Small-diameter drill string follows designed profile from entry to exit point.

Reaming

Stage 2

Bore enlarged to 1.5x pipe OD using back-reamers pulled from exit to entry.

Pullback

Stage 3

Product pipe attached to drill string and pulled from exit through bore to entry.

Force Analysis

ASTM F1962

Sum of friction, fluidic drag, and capstan effect determines total pullback force.

Direction of pull: In HDD, the pipe is typically pulled from the exit point toward the entry point (rig side). The drill rig at the entry provides the pulling force through the drill string attached to the pipe's leading end. Forces accumulate from the pipe tail at the exit toward the pipe head at the rig.

2. Bore Profile Geometry

The bore profile defines the path the drill follows from the entry point, through the subsurface, to the exit point. A typical maxi-HDD bore profile consists of five segments: entry ramp, entry curve, tangent (horizontal) section, exit curve, and exit ramp.

Simplified Bore Profile (sagbend model): Entry slant length: L_entry = Depth / sin(entry angle) Exit slant length: L_exit = Depth / sin(exit angle) Horizontal distance consumed: Entry: H_entry = Depth / tan(entry angle) Exit: H_exit = Depth / tan(exit angle) Straight tangent section: L_tangent = Total bore length - H_entry - H_exit Total bore length along profile: L_actual = L_entry + L_tangent + L_exit

Typical Entry and Exit Angles

Parameter	Maxi-HDD (Steel)	Maxi-HDD (HDPE)	Mini-HDD
Entry angle	8–18°	8–15°	10–20°
Exit angle	5–15°	5–12°	5–15°
Minimum depth	15–30 ft	10–20 ft	5–15 ft
Bore diameter ratio	1.5x OD	1.3–1.5x OD	1.3x OD
Typical length	500–7,000 ft	300–5,000 ft	50–600 ft

Example: 1,500-ft River Crossing

Given: Bore length (horizontal): 1,500 ft Maximum depth: 40 ft Entry angle: 12°, Exit angle: 10° Entry slant: L_entry = 40 / sin(12°) = 40 / 0.2079 = 192.4 ft H_entry = 40 / tan(12°) = 40 / 0.2126 = 188.1 ft Exit slant: L_exit = 40 / sin(10°) = 40 / 0.1736 = 230.5 ft H_exit = 40 / tan(10°) = 40 / 0.1763 = 226.9 ft Tangent section: L_tangent = 1,500 - 188.1 - 226.9 = 1,085.0 ft Total bore length: L_actual = 192.4 + 1,085.0 + 230.5 = 1,507.9 ft

3. Frictional Drag

Frictional drag is the resistance to pipe movement caused by the pipe sliding along the bottom (or top, if buoyant) of the borehole. The friction force depends on the effective pipe weight in the drilling fluid, the friction coefficient between the pipe and the bore wall, and the length of the bore.

Frictional Drag Force: F_fric = μ × W_eff × L Where: μ = Friction coefficient (pipe on bore wall) W_eff = Effective (buoyant) weight per foot (lb/ft) L = Bore segment length (ft) Effective weight: W_eff = W_pipe + W_contents + W_coating - W_displaced_mud Buoyancy: W_displaced = π/4 × D_eff² × ρ_mud × (1/144) Note: If W_eff < 0, pipe floats and presses against bore top. Friction still acts using |W_eff|.

Friction Coefficients by Soil Type

Soil Condition	μ (with mud)	μ (no mud)	Notes
Clay / Cohesive	0.25–0.35	0.40–0.60	Mud lubrication significantly reduces friction
Sand / Granular	0.30–0.45	0.50–0.70	Higher friction due to particle interlocking
Rock	0.20–0.30	0.30–0.50	Smooth bore wall, low friction with mud
Mixed	0.25–0.40	0.40–0.65	Use weighted average or most conservative

Drilling fluid is essential: Bentonite drilling mud serves multiple purposes: stabilizing the bore wall, removing cuttings, and lubricating the pipe during pullback. Loss of drilling fluid circulation during pullback can increase friction by 2-3 times, potentially causing a stuck pipe condition.

4. Fluidic Drag

Fluidic drag results from the viscous shear stress of drilling fluid acting on the pipe surface as the pipe moves through the bore. Even with lubrication, the drilling mud exerts a resistive force proportional to the pipe surface area and the apparent shear stress of the fluid.

Fluidic Drag Force: F_fluid = π × D_pipe × L × τ_s Where: D_pipe = Pipe outside diameter (ft) L = Bore length along profile (ft) τ_s = Apparent shear stress (psf) Typical shear stress values: Bentonite slurry (9 ppg): 2.0–3.0 psf Polymer mud (10 ppg): 3.0–4.0 psf Heavy mud (12+ ppg): 4.0–6.0 psf τ_s increases with mud weight and viscosity. Heavier muds provide better bore stability but increase fluidic drag on the pipe.

Fluidic drag is typically the smallest of the three force components for steel pipe installations, representing 5-15% of total pullback force. However, for long bores with heavy mud, it can become significant.

5. Capstan (Belt Friction) Effect

The capstan effect is one of the most important and often underestimated force components in HDD pullback analysis. Named after the rope-around-a-capstan principle in maritime engineering, it describes how friction at curved sections of the bore amplifies the pulling force exponentially.

Euler-Eytelwein Capstan Equation: F_out = F_in × e^(μ × θ) Where: F_out = Force on the pulling side of the bend F_in = Force on the pipe-tail side of the bend μ = Friction coefficient θ = Bend angle (radians) e = Euler's number (2.71828...) Additional force due to capstan: F_capstan = F_in × (e^(μθ) - 1) Total capstan amplification factor: e^(μθ) — this is always > 1.0 Example (μ = 0.30, θ = 22° = 0.384 rad): Factor = e^(0.30 × 0.384) = e^(0.115) = 1.122 Force increases by 12.2% at this bend

Capstan Effect at Multiple Bends

A typical HDD bore has at least two significant bends: the transition from the entry slant to the horizontal tangent, and the transition from the horizontal to the exit slant. Each bend amplifies the accumulated force from the previous sections.

Force accumulation through bore profile: Starting at exit (pipe tail): 1. Exit slant friction: F_1 = μ × W_eff × L_exit 2. Exit-to-horizontal bend: F_2 = F_1 × e^(μ × θ_exit) 3. Horizontal friction: F_3 = F_2 + μ × W_eff × L_tangent 4. Horizontal-to-entry bend: F_4 = F_3 × e^(μ × θ_entry) 5. Entry slant friction: F_5 = F_4 + μ × W_eff × L_entry 6. Add fluidic drag: F_total = F_5 + F_fluid The capstan multiplier is cumulative across all bends.

Sensitivity Analysis: Capstan Effect

Total Bend Angle	μ = 0.20	μ = 0.30	μ = 0.40	μ = 0.50
10° (0.175 rad)	1.036	1.054	1.072	1.091
20° (0.349 rad)	1.072	1.110	1.150	1.191
30° (0.524 rad)	1.110	1.170	1.233	1.300
45° (0.785 rad)	1.170	1.265	1.369	1.482
60° (1.047 rad)	1.233	1.369	1.521	1.690

Exponential growth: The capstan equation produces exponential force growth. With a friction coefficient of 0.40 and combined entry/exit angles of 30 degrees, the pulling force at the rig is 23% higher than the base friction force alone. For tight-radius bores with high friction, the capstan effect can double the required pullback force.

6. Pipe Tensile Capacity and Safety Factor

The pipe being pulled through the bore must have sufficient tensile strength to withstand the total pullback force without yielding or rupturing. The allowable tensile load depends on the pipe material, grade, and wall thickness.

Steel Pipe Tensile Capacity: F_tensile = A_metal × SMYS × 0.90 Where: A_metal = Cross-sectional metal area (in²) SMYS = Specified Minimum Yield Strength (psi) 0.90 = Utilization factor (90% of yield) A_metal = π/4 × (OD² - ID²) Example (12.750" OD, 0.375" wall, X52): A_metal = π/4 × (12.750² - 12.000²) = 14.57 in² F_tensile = 14.57 × 52,000 × 0.90 = 681,400 lbs

Safety Factor Requirements

Pipe Material	Minimum SF	Basis
Carbon Steel (API 5L)	2.0	ASTM F1962, ASCE MOP 108
HDPE (PE4710)	3.0	ASTM F1962, PPI TR-46
PVC (DR 18)	3.0	ASTM F1962
Ductile Iron	2.0	ASCE MOP 108

Safety Factor Calculation: SF = F_tensile / F_total_pullback Requirement: SF ≥ SF_min If SF < SF_min: - Increase wall thickness - Use higher grade pipe - Reduce bore length (multiple shorter bores) - Reduce friction (better drilling fluid) - Increase bore diameter (reduce tight spots)

7. Practical Considerations

Rig Selection

The HDD rig must provide sufficient pullback force with adequate margin. Industry practice is to select a rig with capacity of at least 125% of the calculated total pullback force. This margin accounts for unexpected conditions such as bore collapse, mud loss, or higher-than-anticipated friction.

Common HDD Rig Capacities

Rig Class	Pullback (lbs)	Typical Pipe Size	Bore Length
Mini	10,000–40,000	2"–6"	50–600 ft
Midi	40,000–200,000	6"–16"	300–2,000 ft
Maxi	200,000–500,000	12"–36"	1,000–5,000 ft
Mega	500,000–2,000,000	24"–48"	2,000–10,000 ft

Factors Affecting Pullback Force

Several field conditions can cause actual pullback forces to differ significantly from calculated values. Conservative design accounts for these uncertainties through the safety factor and by using upper-bound estimates for friction coefficients and mud properties.

Factor	Effect on Pullback Force	Mitigation
Bore collapse	Dramatic increase (can double force)	Maintain mud circulation, appropriate mud weight
Mud loss	Increased friction (2-3x)	Lost circulation material, increase pump rate
Pipe stalling	Static friction higher than kinetic	Maintain continuous motion, avoid stops
Tight spots	Localized high friction	Multiple reaming passes, larger bore diameter
Water table	Changes buoyancy profile	Account in design, may help if pipe floats

Pipe Stress During Pullback

Beyond tensile stress from the pulling force, the pipe experiences additional stresses during HDD installation: bending stress from conforming to the bore curvature, external pressure from the hydrostatic head of drilling fluid, and combined stress from all sources acting simultaneously.

Bending stress at bore curvature: S_bend = E × D / (2 × R) Where: E = Modulus of elasticity (29 × 10&sup6; psi for steel) D = Pipe OD (inches) R = Bore radius of curvature (inches) Example (12" pipe, R = 1,000 ft radius): S_bend = 29e6 × 12.750 / (2 × 12,000) S_bend = 15,406 psi This must be combined with tensile stress from pullback.

Critical check: The combined stress during pullback (tensile + bending + external pressure) must not exceed the pipe's allowable stress. For steel pipe, verify that the combined stress at the point of maximum bending curvature does not exceed 90% SMYS. For HDPE, the combined stress is limited by the short-term tensile strength derated for temperature.

HDD Pullback Force Analysis

≥ 2.0

F_out = F_in × e^μθ

1.5 × OD

Contents

Use this guide when:

1. Overview

Stage 1

Stage 2

Stage 3

ASTM F1962

2. Bore Profile Geometry

Typical Entry and Exit Angles

Example: 1,500-ft River Crossing

3. Frictional Drag

Friction Coefficients by Soil Type

4. Fluidic Drag

5. Capstan (Belt Friction) Effect

Capstan Effect at Multiple Bends

Sensitivity Analysis: Capstan Effect

6. Pipe Tensile Capacity and Safety Factor

Safety Factor Requirements

7. Practical Considerations

Rig Selection

Common HDD Rig Capacities

Factors Affecting Pullback Force

Pipe Stress During Pullback

HDD Pullback Force Analysis

≥ 2.0

Fout = Fin × eμθ

1.5 × OD

Contents

Use this guide when:

1. Overview

Stage 1

Stage 2

Stage 3

ASTM F1962

2. Bore Profile Geometry

Typical Entry and Exit Angles

Example: 1,500-ft River Crossing

3. Frictional Drag

Friction Coefficients by Soil Type

4. Fluidic Drag

5. Capstan (Belt Friction) Effect

Capstan Effect at Multiple Bends

Sensitivity Analysis: Capstan Effect

6. Pipe Tensile Capacity and Safety Factor

Safety Factor Requirements

7. Practical Considerations

Rig Selection

Common HDD Rig Capacities

Factors Affecting Pullback Force

Pipe Stress During Pullback

F_out = F_in × e^μθ