3D Hill Topographic Effects

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Understanding 3D Hill Wind Loads

Three-dimensional axisymmetric hills are isolated topographic features that create wind speed-up effects from all horizontal directions. Unlike 2D ridges where wind direction matters significantly, 3D hills amplify wind loads regardless of wind approach angle, making them particularly important for structural design. These rounded, isolated hills are characterized by similar dimensions in all horizontal directions and include features like volcanic cones, drumlin hills, isolated mountain peaks, and man-made features like waste mounds and storage facilities.

What is a 3D Axisymmetric Hill?

In ASCE 7 terminology, a 3D (three-dimensional) axisymmetric hill is a topographic feature that is relatively uniform in all horizontal directions—essentially circular or oval in plan view. The term "axisymmetric" means the hill has rotational symmetry about a vertical axis through its peak. Wind approaching from any horizontal direction encounters similar slopes and experiences similar speed-up effects, distinguishing 3D hills from directionally-dependent 2D ridges.

Defining Characteristics

• Isolated feature - Stands alone, not part of a ridge or mountain range
• Circular/oval plan - Similar dimensions in all horizontal directions (length ≈ width)
• Omnidirectional effects - Wind speed-up occurs from all approach angles
• Summit at center - Peak centrally located with slopes radiating outward
• Lower K1 values - Generally less speed-up than equivalent 2D ridges

ASCE 7 Requirements for 3D Hills

ASCE 7 Section 26.8 addresses 3D axisymmetric hills with specific K1 values in Table 26.8-1 that are typically lower than those for 2D ridges and escarpments, reflecting the three-dimensional flow patterns.

Topographic Factor Calculation for 3D Hills

The topographic factor for 3D axisymmetric hills uses the same formula structure but with 3D-specific K1 values:

Calculation Procedure

1. Measure H - Height of hill above surrounding terrain
2. Determine Lh - Average radial distance from summit to half-height contour
3. Calculate H/Lh - Confirm ≥ 0.2 for topographic effects to apply
4. Select K1 - Use 3D axisymmetric hill values from ASCE 7 Table 26.8-1
5. Determine K2 - Based on radial distance from summit (x/Lh)
6. Calculate K3 - Based on height above local ground (z/Lh)
7. Compute Kzt - Apply formula for all wind directions

Wind Flow Patterns Around 3D Hills

Understanding how wind behaves around isolated hills helps engineers appreciate why topographic factors matter:

• Windward slope - Wind accelerates as it climbs toward summit
• Summit zone - Maximum speed-up typically at or just downwind of peak
• Leeward slope - Complex flow with separation, recirculation, and reattachment
• Wake region - Turbulent wake extends 5-10H downwind
• Lateral flow - Some wind diverts around sides rather than over top

Real-World 3D Hill Examples

• Volcanic cones - Mt. Fuji, Vesuvius, Hawaiian volcanoes
• Isolated peaks - Lone mountains rising from plains
• Drumlin hills - Glacially-formed rounded hills in northern regions
• Landfills and waste mounds - Man-made elevated storage facilities
• Mining spoil piles - Conical waste rock accumulations
• Radar domes and observatories - Facilities on isolated hill summits
• Communication towers - Structures on prominent isolated peaks

Engineering Best Practices

Key Considerations for 3D Hill Design:

• Verify hill is truly axisymmetric—if elongated, treat as 2D ridge instead
• Measure Lh in multiple directions to confirm approximately circular plan
• 3D hills generally have lower Kzt than equivalent 2D ridges (less severe)
• Consider all wind directions since effects are omnidirectional
• Document hill geometry with contour maps and cross-sections
• Account for seasonal variations (snow, erosion) affecting H
• Site visit critical to confirm isolated nature and freedom from upwind obstructions

3D vs 2D Classification

Determining whether a topographic feature is 2D or 3D is critical for accurate Kzt calculation:

• Use 3D approach when: Length/width ratio < 2:1, circular or oval plan view
• Use 2D approach when: Length/width ratio > 4:1, elongated crest, part of range
• Intermediate cases: Use engineering judgment or analyze as both and take worst case

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