Wind Turbine Foundation Design Ch5
Wind Turbine Foundation Design Ch5...
– Wind Turbine Foundation Design –
Wind Turbine Foundation Design
Wind Turbine Foundation Design Chapter for Civil Wind Energy Design and Construction 2 1.0 Introduction 2 1.1 Foundation Types 2 1.1.1 Shallow Octagonal Gravity Base Foundation 2 1.1.2 Shallow Rock Socketed, Rock Anchor, and Short Pier Foundations 2 1.1.3 Deep Pile and Cap Foundations 2 1.1.4. Patrick and Henderson Patented Foundations 3 1.2 What Makes Wind Turbine Foundation Design Unique? 3 1.3 Wind Turbine Driving Forces 3 2.0 Wind Turbine Foundation Design Path 4 2.1 Turbine Specific Load Document and Design Requirements 4 2.2 Geotechnical Investigation and Geotechnical Report 4 2.2.1 Ground Improvement Recommendations 4 3.0 Wind Turbine Foundation Design and Analysis 5 3.1 Preliminary Design 5 3.2 Pre-Design Check Calculations 5 3.2.1 Eccentricity 5 3.2.2 Wind Turbine Foundation Effective Area 6 3.2.3 Horizontal Wind Force Correction for Mechanical Torque 7 3.3 Wind Turbine Foundation Design Checks 7 3.3.1 Foundation Overturning 7 3.3.2 Rotational Stiffness 9 3.3.3 Bearing Capacity 13 3.3.4 Sliding 15 3.3.5 Settlement 20 References 22
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– Wind Turbine Foundation Design –
Wind turbine foundation design is unique due to untraditional loading conditions and large site and geotechnical variance. When designing a wind turbine foundation, the foundation engineer has several foundation options to choose from including shallow octagonal gravity base, rock anchors, pier-type foundations, and deep piles. Design parameters are dependent on wind turbine size, turbine and site specific loading conditions, and site specific geotechnical conditions. Furthermore, there are a series of design checks to ensure the foundation type, size, and placement is capable of withstanding the extreme loading conditions. 1.1 Foundation Types There are several options available for wind turbine generator foundation design. Depending on the localized geotechnical and the turbine specific load conditions, the best fit foundation option is chosen by the foundation design engineer for a wind turbine and wind farm project. Foundation size and type may vary throughout a wind farm. The foundations options include both shallow foundations and deep foundations. The shallow foundations include octagonal gravity base, rock socketed, rock anchor, and short pier foundations. The deep foundations include pile and cap foundations, and the patented Patrick and Henderson Tensionless Pier, Rock Anchor and Pile Anchor foundations. The deep foundations are often chosen for poor soil conditions. Mono-pile foundations are another deep foundation type that is most commonly utilized for offshore applications. 1.1.1 Shallow Octagonal Gravity Base Foundation Octagonal gravity base foundations are the most common non-proprietary foundation type used for landbased wind turbines and will be the focus of this foundation design chapter. These foundations are applicable in a broad range of soil conditions. In general, this type of foundation is a large octagonal mass of concrete and steel rebar reinforcement. Typically, octagonal gravity base foundations are 12 to 18 m in diameter, approximately 0.7 m thick at the edge, 2.5 to 3.5 meters thick at the center, contain 140 to 460 cubic meters of concrete, 125 to 360 kN of reinforcing steel, and cost $100,000 to $250,000 per foundation. This foundation type relies on the weight of the concrete and steel as well as the overburden soil to resist the overturning moment from the horizontal wind load on the turbine structure. These foundations are typically embedded 2.4 to 3 m beneath the finish grade of overlying soil. The size of these foundations is usually dictated by either the maximum allowable edge pressure or overturning due to a high groundwater table (Tinjum and Christensen, 2010). Figure 1 depicts geometry of this type of foundation and Figure 2 is an example of a shallow octagonal foundation before the overlying soil is backfilled.
Figure 1: Depiction of Geometry of Shallow Octagonal Wind Turbine Foundation
Figure 2: Example of Shallow Octagonal Wind Turbine Foundation before Overlying Soil is Backfilled
1.1.2 Shallow Rock Socketed, Rock Anchor, and Short Pier Foundations In locations where a thin layer of incompetent soil is overlying competent soil or rock, rock socketed, rock anchor, and short pier foundations can be utilized. These rock sockets, rock anchors, and short piers extend through the poor soil into the competent soil or rock. These foundation types rely on end bearing, side wall friction, tension in steel reinforcement, and lateral earth pressure on the rock sockets and anchors or short piers for stability (Morgan & Ntambakwa 2008). 1.1.3 Deep Pile and Cap Foundations Deep pile and cap foundations are applicable where competent soil or rock is located deep below the ground surface. These foundations utilize piles that are drilled deep beneath the ground surface, through the layer of incompetent soil, into the competent soil or rock. Similarly to shallow pier foundations, deep pile and cap foundations rely on end bearing, sidewall friction, and lateral earth pressure for stability (Morgan & Ntambakwa 2008).
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– Wind Turbine Foundation Design – Tensionless Pier consist of post-tensioned concrete annulus, typically 4.5 to 5.5 meters in diameter installed to a depth of between 8 and 12 m. The annulus is constructed by placing two corrugated metal cylinders in an excavated or drilled hole, and filling the annular space with concrete. The interior space is backfilled with a 1 m thick concrete plug, followed by uncompacted excavation spoil. The pier is capped with a structural slab. The exterior space between the outer corrugated cylinder and the natural soil is backfilled with sand-cement slurry or grout. The principal advantage claimed for this foundation type is cost savings. However, there are aspects to the construction of these piers that can negate the apparent savings; principally, caving soils and large grout takes (Tinjum and Christensen, 2010). A diagram of the P&H Tensionless Pier is shown in Figure 3. Patrick and Henderson also have patented Rock Anchor and Pile Anchor foundations. Figure 4 shows a diagram of the P&H Pile Anchor Foundation.
Figure 3: Patented Patrick and Henderson Tensionless Pier wind turbine foundation
Figure 4: Patented Patrick and Henderson Pile Anchor wind turbine foundation
1.1.4. Patrick and Henderson Patented Foundations The patented Patrick and Henderson (P&H) Tensionless Pier is classified as a deep foundation and is applicable where competent bedrock or non-collapsing soil is located relatively near the ground surface. The P&H
1.2 What Makes Wind Turbine Foundation Design Unique? Wind turbine foundation design is unique when compared to tradition foundation design due to untraditional loading conditions and large site and geotechnical variance. Wind turbine structures experience an unusually high horizontal wind load and thus a large overturning moment. In addition to this high overturning moment, the wind turbine structure has a low vertical or axial load. Furthermore, wind turbine foundation design is unique because wind farm projects often incorporate hundreds of wind turbines over large areas of land. Because of this, extreme variance in soil and groundwater conditions can be encountered on a single wind farm project. Wind turbine foundation design has both typical and atypical design criteria. These design criteria are based on turbine specific load documents and site specific soil and groundwater conditions. Typical design criteria include soil bearing capacity and foundation settlement. Atypical design criteria include vertical and rotational stiffness, electrical resistivity for electrical grounding, and thermal resistivity for underground electrical transmission. 1.3 Wind Turbine Driving Forces There are several driving forces that need to be accounted for in wind turbine foundation design. The wind turbine foundation needs to resist these driving forces to safely support the wind turbine structure. The most important driving forces in wind turbine foundation design are horizontal wind loads, mechanical and operation loads, vertical and axial forces, ice loads, and seismic loads. The horizontal wind loads are based on a 50 year extreme wind gust and create a large overturning moment about the foundation edge. The mechanical and operational loads are cyclic in nature and should be considered in foundation and tower fatigue calculations. The
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– Wind Turbine Foundation Design – vertical and axial forces include the weight of the wind turbine structure, the weight of the foundation, and the weight of the overlying soil. The ice and seismic loads may or may not be included in foundation design depending on the geographic location. Design loads for the above listed driving forces are typically provided by the turbine manufacturer.
2.0 Wind Turbine Foundation Design Path
When designing a wind turbine foundation the design path shown in Figure 5 should be followed. The path includes obtaining the turbine specific load document and design requirements, obtaining a site specific geotechnical report, creating a preliminary design, completing the required geotechnical deign checks, completing the structural design, and evaluating the field and construction quality control.
ments include subsurface conditions that are provided in the sites geotechnical report, location specific environmental restrictions, a wind modeling and resource assessment report, and a seismic risk analysis. The owner and O&M requirements are specific to the project owner and utility company that the electricity will supply. The current codes and regulatory standards include the design loads and load factors, ultimate limit state (ULS) and serviceability limit state (SLS) requirements and checks, stability and overturning checks, and fatigue checks. The loads that control the design need to be evaluated by the foundation engineer and can be any of the following, wind, ice, operational, fatigue, seismic, or wave action for offshore applications. Load cases can be found listed in IEC-61400 (2005).
2.2 Geotechnical Investigation and Geotechnical Report The geotechnical investigation and report are important documents needed for wind turbine foundation design. There are several purposes of the geotechnical investigation, analysis, and report. First, it is meant to explore the subsurface soil, rock, and groundwater conditions. Second, it reports the results of field and laboratory testing that characterize the subsurface soils and bedrock properties. Lastly, it provides geotechnical recommendations for the design and construction of the foundation systems.
Figure 5: Wind Turbine Foundation Design Path
2.1 Turbine Specific Load Document and Design Requirements The wind turbine manufacturer provides turbine specific load documents and design requirements to the project’s foundation engineer. These load documents include both characteristic and extreme conditions. The extreme conditions are based on a 50-year extreme wind gust. The loads and design requirements include the overturning moment, the vertical load, the horizontal wind load, the allowable tilt or differential settlement, the overall allowable settlement, the horizontal, vertical, and rotational foundation stiffness, and the design life of the wind turbine generator. Further design requirements that are not turbine specific must also be obtained. These include site conditions, owner requirements, operation and maintenance (O&M) requirements, current codes and regulatory standards, and an evaluation of loads that will ultimately control the design of the foundation. The site condition require-
There are several parameters that are typically collected by a combination of field and laboratory test prior to the design of wind turbine foundations. Data and specimens that are collected in field testing include soil borings, rock coring, grab samples from test trenches and thin walled Shelby Tubes, cone penetrometer test (CPT), standard penetrometer test (SPT), and geophysical testing that includes resistivity arrays and seismic surveys. A minimum of one boring or CPT at each turbine location as well as several borings for access roads and substation locations are required. Data and parameters collected in lab test include soil data classifications such as unit weight, Atterburg limits, moisture content, unconfined compressive strength, compressive strength rock core, consolidation test, permeability test, thermal resistivity test, chemical compatibility tests, and electrical resistivity for electrical ground (Tinjum and Christensen, 2010). 2.2.1 Ground Improvement Recommendations The geotechnical report may also include ground improvement recommendation for areas with poor soil conditions. This is done through methods of over exca-
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– Wind Turbine Foundation Design – vation and replacement, dynamics compaction, rammed aggregate piers and stone columns. Over excavation and replacement can be economical up to depths of 3 m or so beneath the base of the foundation. It is not uncommon for the over excavation to be replaced with a concrete slurry rather than using an engineered subgrade soil for replacement. Dynamics compaction can be effective to depths of 7 to 10 m. Dynamic compaction is limited to course-grained soil. Rammed aggregate piers (RAP) are increasingly used in conjunction with conventional spread footings. This technique is applicable where the soil profile contains a soft or loose upper later underlain by more competent material. Pier lengths up to about 7 m can be installed with auger rigs; greater lengths may be achieved with casing and mandrel systems (impact piers) (Tinjum and Christensen, 2010).
3.0 Wind Turbine Foundation Design and Analysis
3.1 Preliminary Design After the turbine specific load document, design requirements, and site specific geotechnical report have been obtained and evaluated, a preliminary foundation design can be created. When creating a preliminary design, the foundation type, dimensions, and embedment depth must be chosen. For most foundation engineers the preliminary design draws on past experience of foundation design for similar geotechnical conditions. Past experience is helpful, but if an inexperienced engineer creates a preliminary design that is over or under designed, the foundation design checks will show if the design needs to be altered. It is again noted that this foundation design chapter will focus on the shallow octagonal gravity base wind turbine foundation. 3.2 Pre-Design Check Calculations Before completing the foundation design checks, three calculations are required. First, the wind turbine system’s eccentricity is determined. Next, the wind turbine foundation’s effective loading area is calculated. Last, a correction to the horizontal force on the wind turbine, due to the presence of a mechanical torque on the structure and foundation, is needed.
3.2.1 Eccentricity Before the foundation’s effective area is calculated, the eccentricity of the wind turbine structure and system needs to be determined. Due to the large horizontal wind loads on the wind turbine and tower, the foundation load center is offset from the center of the foundation by a distance referred to as the eccentricity (e). This distance can be calculated with Equation 1 if the design overturning moment and design vertical forces are known. Figure 6 shows a diagram of eccentric loading on a wind turbine foundation. It is important to note that the ec-
Figure 6: Diagram of Eccentric Load of a Wind Turbine Foundation
centricity varies with horizontal wind force. In foundation design calculations, extreme wind conditions are used in calculation to ensure the foundation will not fail.  Md e = ___ Vd where: e = eccentricty Md = design overturning moment Vd = design vertical load
Example 3.2.1 If an extreme overturning moment is given as 52,500 kNm and a design vertical load of 11,800 kN the eccentricity is calculated below in meters.
Md e = ___ Vd e = 52,500 kNm 11,800 kN e = 4.45 m from center of wind turbine structure
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– Wind Turbine Foundation Design – 3.2.2 Wind Turbine Foundation Effective Area When wind loading is present, the load center is at the center of the effective foundation area, a distance equal to the eccentricity from the center of the system. The effective area is important to determine the maximum applied pressure to ensure adequate bearing capacity is available. The effective foundation area for a shallow gravity base octagonal wind turbine foundation is approximated to an ellipse and then later simplified to a rectangle with the following equations. It may not be immediately apparent why the ellipse needs to be approximated to a rectangle, but the rectangle will appear in design calculations later in the chapter. The effective area, approximated to an ellipse, can be calculated using Equation 2.
Aeff = 2[R2 cos-1 ( Re ) - e√R2 - e2]
where: Aeff = effective foundation area R = radius of inscribed circle of polygon e = eccentricity
Figure 7: Diagram of the Octagonal Foundation Footprint, the Ellipse Approximation, and the Rectangular Approximation
The major axes of the approximated ellipse can be calculated with Equations 3 and 4.
be = 2(R - e)
le = 2R√1-(1- 2Rb )2
where: be = width of ellipse le = length of ellipse
Example 3.2.2 Wind Turbine Foundation Effective Area For a wind turbine foundation with a diameter of 15 m and a calculated eccentricity of 4.45 m the effective loading area is calculated. The effective area, approximated to an ellipse. Aeff = 2[R2 cos-1 ( Re ) - e√R2 - e2] 4.45m Aeff = 2[(7.5m)2 cos-1 (7.5m ) - (4.45m)√(7.5m)2 - (4.45m)2]
The approximated ellipse is simplified to a rectangle with the dimensions from Equations 5 and 6.
The major axes of the approximated ellipse.
leff beff = ___ be le
leff = √Aeff
Aeff = 51.5 m2
where: beff = width of rectangle leff = length of rectangle Aeff = effective foundation area A diagram of the octagonal foundation footprint, ellipse approximation, and rectangular approximation is shown in Figure 7.
be = 2(R - e) be = 2(7.5m - 4.45m) be = 6.1 m
le = 2R√1-(1- 2Rb )2 6.1m 2 le = 2(7.5m)√1-(1- 2(7.5m) )
le = 12.1 m The dimensions of the rectangle approximated from the ellipse. leff = √Aeff
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– Wind Turbine Foundation Design – 12.1m leff = √51.5 m2 (6.1m )
H1 = 9,640.5 kN
Ieff = 10.1 m
3.3 Wind Turbine Foundation Design Checks After a preliminary design is created and the pre-design check calculations have been completed, there are several design checks that must be evaluated to both ensure that the foundation is suitable to support the wind turbine structure and to ensure that the foundation is not over designed for cost purposes. There are five main design checks that must be evaluated: foundation overturning, rotational stiffness, soil bearing capacity, sliding, and settlement.
leff beff = ___ be le
10.1 m 6.1m beff = _______ 12.1 m
beff = 5.09 m
3.2.3 Horizontal Wind Force Correction for Mechanical Torque Before completing the design checks, the horizontal load needs to be adjusted due to the presence of a mechanical torque on the structure and foundation. Most modern wind turbines are designed to orientate the turbine to face the direction of the incoming wind. This mechanical action creates a mechanical torque about the Z-axis of the system. The mechanical torque can be seen as Mz in Figure 8. The mechanical torque needs to be accounted for in the design calculations by adjusting the horizontal load on the system with Equation 7.
2M z leff
3.3.1 Foundation Overturning Foundation overturning is often one of the first design checks evaluated. This design check is meant to ensure the destabilizing forces of the wind turbine system, from an extreme loading case, do not exceed the stabilizing forces. The destabilizing forces include the horizontal wind load adjusted with mechanical torque, and any other mechanical forces the turbine may create. The stabilizing forces include the mass of the turbine structure, the mass of the concrete foundation, and the overburden soil mass and pressure. Some important geometric foundation parameters, shown in the Figure 9, will be required for this design check calculation. After these geometric parameters have been identified, several steps must be followed to complete the design check.
Figure 8: Diagram of Forces and Resultant Moment on Wind Turbine System
+ H2 + (
Example 3.2.3 Correction for Mechanical Torque If a mechanical torque of 27,000 kNm is applied to a system with an already existing horizontal force of 900 kN and a foundation radius of 15 m, determine the adjusted horizontal force.
2(27,000 kNm) 10.1 m
+ H2 + (
+ (900kN)2 + (
2(27,000 kNm) 10.1 m
2. Calculate the total volume (Vc) and weight of concrete (Wc) in the foundation. 3. Calculate the soil dead load (WT). The soil dead load is the weight of the soil that is above the octagonal foundation.
where: H1 = adjusted horizontal force Mz = mechanical torque leff = length of approximated rectangle of octagonal foundation
1. Determine the foundation geometry, soil properties, concrete properties and the extreme factored turbine loads. The foundation geometry will come from the preliminary design. The soil properties can be found in the geotechnical report. The concrete properties will come from the concrete supplier for the specific concrete that is to be used. Lastly, the extreme factored turbine loads can be found in the manufacturer supplied load document.
4. Calculate the total resisting moment (MR). The total resisting moment is a function of the weight of the concrete, the weight of the soil, and the vertical or axial forces of the turbine structure. The combination of these weights and forces are multiplied by the foundation radius to obtain the total resisting moment. 5. Calculate the total overturning moment for the extreme conditions (MOE). The total overturning moment is the combination of the existing overturning moment at the base of the wind turbine tower cou-
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– Wind Turbine Foundation Design – Extreme Factored Turbine Loads Fxy = 163 kips horizontal Fz = 497 kips vertical Mxy = 36,587.2 ft · kips Operational Loads Fxy = 45.0 kips horizontal Fz = 509 kips vertical Mxy = 11,300 ft · kip
2. Determine the volume and weight of concrete that will be installed. Figure 9: Important geometric foundation parameters for overturning calculation
pled with the horizontal wind force multiplied by the height of the foundation. 6. Determine the factor of safety against overturning. This is the ratio of the total resisting moment to the extreme condition overturning moment. A factor of safety of 1.5 or greater is commonly accepted for foundation overturning. Note: If the water table is above base of foundation, total resisting moment (MR) needs to be adjusted with a buoyancy calculation. Example 3.3.1 Design Check Wind Turbine Foundation Overturning 1. Determine foundation geometry, soil properties from the geotechnical report, the properties of the concrete that is to be used, and the extreme factored turbine loads from the manufacturer supplied load document.
Octagonal2 Foundation Area Ao = 8R1 tan(π/8) Ao = 8(25ft)2tan(π/8) = 2071.1 ft2 Volume of Flat Octagon Vo = (hb+hc ) × Ao Vo = (1.83ft+3.75ft) × 2071.1 ft2 = 11,557 ft3 Deduction of Wedges Rectangular wedges (4) total VWR = ½ hc (R1- B⁄2) B VWR = ½ (3.75ft)[25ft - ((20.7ft)⁄2)](20.7ft) = 568.7 ft3 EA Triangular wedges (4) total VWT = 1/3 × ½ Bhc (R1- (B⁄2) √2) VWT = 1/3 × ½ (20.7ft)(3.75ft)(25ft - (20.7ft⁄2)√2) VWT = 134.0 ft3 EA Total Wedge Volume VW = 4 × (VWR + VWT) VW = 4 × (568.7 ft3 + 134.0 ft3) = 2810.8 ft3 Pedestal Area AP = π(R2)2 AP =π (8.5ft)2 = 227.0 ft2
Foundation Geometry hp = 4.0 ft hc = 3.75 ft hb = 1.83 ft hg = 3.5 ft R = 27.1 ft R1 = 25 ft R2 = 8.5 ft X1 = 13.0 ft B = 20.7 ft
Pedestal Volume VP = AP × hP VP = 227.0 ft2 × 4.0 ft = 907.9 ft3 Total Concrete Volume Vc = Vo - VW + VP Vc = 11,557 ft3 - 2810.8 ft3 + 907.9 ft3 = 9,659.8 ft3 or 357.8 YD3
Concrete Properties Weight = 150 lb/ft3 f'c = 5000 psi Taper rate = 0.256
Weight of Concrete Wc = Vc × 150 lb/ft3 Wc = 9,659.8 ft3 × 150 lbs⁄ft3 = 1,449.0 kips
Soil Properties Weight = 120 lb/ft3 Allowable Bearing = 5440 psf Extreme Allowable Bearing = 6400 psf Friction Coefficient, μ = 0.35 Water table height = 20 ft
3. Determine the soil dead load. Change in soil height, ∆g. Soil grade at ¼" per foot. ∆g = ¼ in × 1 ft/12 in × (R1 - R2) ∆g = ¼ in × 1 ft/12 in × (25.0ft - 8.5 ft) = 0.344 ft
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– Wind Turbine Foundation Design –
Average height of soil above flat octagon, hg_ave hg_ave = [hg + (hg - ∆g)]/2 hg_ave = [3.5ft + (3.5ft-0.344ft)]/2 = 3.33 ft Soil Area without Pier As = Ao - AP As = 2071.1 ft2 - 227.0 ft2 = 1,844.1 ft2 Soil Weight Above Flat Octagon, Ws Ws = As × hg_ave × үs Ws = 1,844.1 ft2 × 3.33 ft × 120 lb/ft3 = 736.5 kips Wedge Soil Weight, Wws Wws = VW × үs Wws = 2810.8 ft3 × 120 lb/ft3 = 337.3 kips Total Soil Weight, WT WT = Wws + Ws WT = 337.3 kips + 736.5 kips = 1073.8 kips 4. Determine the total resisting moment, MR. MR = (Wc + WT + FZ) × R1 MR = (1,449.0 kips + 1073.8 kips + 497.0 kips) × 25.0 ft MR = 75,495 ft · kips 5. Calculate the total overturning moment for the extreme conditions, MOE. MOE = Mxy + Fxy(hb + hc + hp) MOE = 36,587.2 ft · kips + 163 kips (1.83 ft + 3.75 ft + 4.0ft) MOE = 38,148.7 ft · kips MOO = Mxy + Fxy (hb + hc + hp) MOO = 11,300ft · kips + 45.0 kips (1.83 ft + 3.75 ft + 4.0 ft) MOO = 11,731.1 ft · kips 6. Determine the factor of safety against overturning. FS = MR / MOE FS = (75,495 ft · kips) / (38,148.7 ft · kips) = 1.98 1.98 > 1.5 Foundation Design Passes Overturning Check Summary of steps to check foundation overturning: 1. Determine geometry, properties, and extreme loads of the system 2. Determine the volume and weight of concrete that will be installed 3. Determine Soil Dead Load 4. Determine the total resisting moment, MR
5. Determine the total overturning moment, MOE 6. Determine the factor of safety against overturning Buoyancy Calculation Two changes take place when the water table is above the base of the foundation. First, an uplift force from the water pressure occurs at the base of the foundation. Second, if the water table is above the upper edge of the foundation base, the soil above the foundation, below the water table, becomes saturated. The uplift force due to the water pressure can be calculated with Equation 8.
FH2O = үw hw Afoundation
where: FH O = uplift force due to water pressure 2 үw = unit weight of water hw = height of water above foundation base Afoundation = area of foundation footprint The moment the uplift force creates about the edge of the foundation must be subtracted from the total resisting moment (MR) previously calculated. In the scenario that the water table is above the upper edge of the foundation base, the weight of the overlying soil must be recalculated using the saturated unit weight. 3.3.2 Rotational Stiffness There are several types of foundation stiffness checks. However, rotational stiffness is almost always the design controlling stiffness parameter, and is often the overall design controlling parameter. Vertical, horizontal, and torsional stiffness rarely control the design. The turbine manufacture provides a nominal minimum value of rotational stiffness that is required in the foundation design. Foundation rotational stiffness is defined as the ratio of the applied moment to the foundations angular rotation in radians as shown below. kф ≡ M/ѳ where: kф = rotational stiffness M = applied moment ѳ = rotation in radians For a rigid circular foundation resting on an elastic halfspace and subjected to rocking motion, Richart et al. (1978) provides Equation 9 for rotational stiffness.
kф = 8GR3 / 3(1-v) = M/ѳ
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– Wind Turbine Foundation Design – Modulus reduction = G / Gmax
where: G = shear modulus R = foundation radius v = Poisson's ratio It is important to note there are two key soil parameters needed for a stiffness check, Poisson’s ratio (v), and shear modulus (G). Poisson’s ratio is usually estimated based on the type of soil and details in the geotechnical report. Figure 10 from Tinjum and Christensen, 2010 shows commonly used values for Poisson’s ratio. In unsaturated soils, Poisson’s ratio can be determined from equation: v = [0.5(Vp ⁄ Vs) -1] / [(Vp ⁄ Vs) - 1] where Vp = compression wave velocity Vs = shear wave velocity v = poisson's ratio There are empirical correlations in DNV Riso, 2002 from which you can obtain shear modulus (G) values. However, in current US based practice the shear modulus is often determined from testing such as cone Figure 10: Commonly used values for penetrometer testing Poisson's Ration by soil type from (CPT), seismic testTinjum and Christensen, 2010 ing, or surface geophysical testing. Through these test, the shear wave velocity (Vs) can be obtained. Once the shear wave velocity is obtained, the maximum shear modulus (Gmax) can be calculated with the following equation.
Gmax = ρVs2 = E / [2(1 + v)]
where: G = reduced shear modulus Gmax = nonreduced modulus Figure 12 shows the variation of modulus reduction factors for normally consolidated soil based on plasticity index (PI) and granular soil as a function of cyclic shear strain (after Sykora et al. 1992 and Vucetic and Dobry, 1991). It is recommended Figure 11: Common values for shear by DNV Riso, 2002 wave velocity (Vs) are shown in Figure to assume a cyclic 3.6 from Tinjum and Christensen, 2010 shear strain value of 0.1% for wind turbine foundation stiffness calculations. DNV Riso, 2002 also gives recommended cyclic shear strain values for rotating machines, wind and ocean waves, and earthquakes. These ranges can be seen shaded on Figure 12. The reduced shear modulus obtained from Figure 12 is to be used in the rotational stiffness calculation.
where: ρ = soil density Vs = shear wave velocity E = modulus of elasticity Common values for shear wave velocity (Vs) are shown in Figure 11 from Tinjum and Christensen, 2010. Because soil behaves with a non-linear response to stress, the shear modulus obtained from the previous equation needs to be reduced by a reduction factor. The modulus reduction factor is a function of cyclic shear strain (үc), and can be defined as the ratio of the reduced shear modulus to the unreduced maximum shear modulus as shown below.
Figure 12: Variation of modulus reduction factors for normally consolidated soil based on plasticity index, PI and granular soil as a function of cyclic shear strain (after Sykora et al. 1992 and Vucetic and Dobry, 1991)
The equations to evaluate foundation stiffness for an embedded foundation on a medium above bedrock are shown in Figure 13 from DNV Riso, 2002. These equations are modified in DNV Riso, 2002 for other geotechnical conditions including foundation, which are not embedded, placed on soil over bedrock or a two layer infinite half-space. The equation to calculate rotational stiffness for an embedded foundation on soil over bedrock is shown below.
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– Wind Turbine Foundation Design – Example 3.3.2 Design Check – Rotational Stiffness A wind turbine is to be constructed where the soil profile is a very uniform, poorly graded sand where the bedrock is generally at depths of 200 ft and deeper. The subsurface profile for this location is shown in Figure 14.
Figure 13: Equations to evaluate foundation stiffness for an embedded foundation on a medium above bedrock from DNV/Riso 2002
Embedded Foundation with Soil Over Bedrock kф = (8GR3 / 3(1 - v))(1 + R/6H)(1 + 2D/R)(1 + 0.7 D/H)  where: H = depth to bedrock d = depth of embedment R = foundation radius range of validity: D⁄R < 2 and D⁄H < ½ If the bedrock is located 200 feet or deeper below the surface the (1 + R/6H) and (1 + 0.7 D/H) terms can be ignored in the above equation. Maximum Foundation Inclination The maximum inclination that the foundation will encounter can be determined once the rotational stiffness of the system is determined. From the definition of rotational stiffness along with the maximum applied moment, the rotation in radians can be determined by rearranging the definition of rotational stiffness as seen below.
ѳ = M / kф
where: kф = rotational stiffness M = applied moment ѳ = rotation in radians Using geometry the maximum deflection of the edge of the foundation can be determined.
Figure 14: Subsurface profile for example problem 3.3.2
The turbine load document includes the following design loads: M = 45,000 ft-kips KΨ(min) = 33 GNm/rad For a preliminary design of a foundation equivalent diameter of 48.0 ft and an embedment depth of 8.0 ft, answer the following: a. What is the available rotational stiffness? b. Does the rotational stiffness meet the minimum requirements provided by the manufacturer? c. What is the maximum displacement at the out edge of the foundation? 1. Select appropriate approach. For this scenario of a circular footing embedded in stratum over bedrock, the
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– Wind Turbine Foundation Design – Equation 11 from Figure 13 should be used. kф = (8GR3 / 3(1 - v))(1 + R/6H)(1 + 2D/R)(1 + 0.7 D/H) where: G = reduced shear modulus R = foundation radius v = Poisson's Raio H = depth to bedrock D = embedment depth Because the bedrock is located at 200 feet or deeper below the surface the (1 + R/6H) and (1 + 0.7 D/H) terms can be ignored. 2. Estimate Poisson’s ratio based off of the soil description and soil profile.
Figure 15: Determination of correct modulus reduction factor from given soil information for example 3.3.2
For a poorly graded sand a Poisson’s ratio of v = 0.35 is a reasonable approximation.
H = 200 ft D = 8.0 ft
3. Determine a shear wave velocity, Vs from the soil profile. The effective zone for a foundation maybe considered to be the foundation diameter divided by two. Thus, only the first 24 ft. of the soil profile below the base should be evaluated for shear wave velocity. A conservative estimate of shear wave velocity, Vs = 150 m/s or 492 ft/s, should be used.
Kф = [8(259.4 ksf)(24.0 ft)3 / (3(1 - 0.35)] (1 + 2(8.0 ft)/(24.0 ft)) Kф = 24,519,286 kip · ft ⁄ rad or 33.24 GN · m⁄rad 7. Does the available rotational stiffness meet the design requirements? 33.24 GN · m⁄rad > 33 GN · m⁄rad Design Passes Rotational Stiffness Check
4. Calculate the maximum shear modulus, Gmax though the correlation with shear velocity and soil density.
8. Determine the maximum displacement of the outer edge of the foundation.
Moist/Wet Loose Poorly Grade Sand (SP) has a unit weight of approximately 115 pcf.
Kф ≡ M / ѳ
Gmax = ρVs
Gmax = [(115 pcf) / (32.2 ft⁄s2 )] × (492 ft/s)2 = 864.5 ksf 5. Determine the correct modulus reduction factor from the given soil information and reduce the shear modulus. This is shown in Figure 15. G ⁄ Gmax = 0.3 G = Gmax × G ⁄ Gmax G = 864.5 ksf × 0.3 = 259.4 ksf 6. Enter all the known parameters into the stiffness equation and calculate the available rotational stiffness. G = 259.4 ksf R = 24.0 ft v = 0.35
where: Kф = rotational stiffness M = applied moment ѳ = rotation in radians ѳ = M / Kф ѳ = (45,000 ft · kips) / (24,519,286 kip · ft⁄rad) ѳ = 0.001835 radians Once the maximum rotation is known, the maximum vertical displacement of the out edge of the foundation can be determined. vert disp = R sin ѳ vert disp = 24 ft × sin (0.001835 rad) = 0.044 ft or 0.528 in Summary of steps to check foundation stiffness: 1. Select appropriate approach. 2. Estimate Poisson’s ratio based off of the soil description and soil profile.
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– Wind Turbine Foundation Design – 3. Determine a shear wave velocity, Vs from the soil profile. 4. Calculate the maximum shear modulus, Gmax though the correlation with shear velocity and soil density. 5. Determine the correct modulus reduction factor from the given soil information and reduce the shear modulus. 6. Enter all the known parameters into the stiffness equation and calculate the available rotational stiffness. 7. Check if the available rotational stiffness meets the design requirements. 8. Determine the maximum displacement of the outer edge of the foundation. 3.3.3 Bearing Capacity When calculating a soil’s ultimate bearing capacity the engineer must determine whether the soil condition will be drained or undrained. Because it cannot often be assumed that a soil will remain in the drained condition for the life of the wind turbine or wind turbine foundation, the more conservative undrained bearing capacity calculation is most often used in wind turbine foundation design. It is noted that in the case of extreme eccentric loading, e > 0.3B, where B is the diameter of the foundation, an additional bearing capacity calculation needs to be evaluated. If extreme eccentricity is present, there is a possibility of failure according to rupture 2 in Figure 16. A rupture 2 failure indicates failure of the soil under the unloaded part of the foundation as well as the loaded area
(DNV Riso 2002). Although there are additional calculations to evaluate the stability of a system with extreme eccentricity, other design checks will often show that the size of the foundation needs to be increased to a point that extreme eccentricity no longer exist. Fully Drained Bearing Capacity Assuming that the wind turbine foundation is not extremely eccentric and the potential failure would occur along rupture 1 in Figure 16, Equation 13 can be used to evaluate the drained bearing capacity. Equation 13 is the general form of the ultimate bearing capacity equation with a few adjustments for the shape and inclination of a shallow octagonal wind turbine foundation. qи = ½ ү' beff Nү Sү iү + Nq Sq iq Po + cd Nc Sc ic  where: qи = ultimate foundation bearing capcity ү' = effective (submerged) unit weight of soil beff = width of rectangle Nү, Nq, Nc = bearing capacity factors,which depend on the soil effective friction angle Sү, Sq, Sc = shape influence factors iү, iq, ic = inclination influence factors cd = effective cohesion of supporting soil The three terms on the right hand side of Equation 13 represent the contribution to soil weight, overburden pressure, and cohesion. The bearing capacity factors may be found in charts or tables in text books or manuals or may be computed by a variety of equations or charts in foundation engineering textbooks or manuals. In practice, Equation 13 is rarely applied in its complete form (Tinjum and Christensen, 2010). The more commonly used forms are: For Granular Soil:
qи = ½ ү' beff Nү Sү iү + Nq Sq iq Po
For Cohesive Soil:
qи = cd Nc Sc ic + Po
The shape and inclination factors, for shallow octagonal wind turbine foundations on fully drained soil, can be determined with the following equations from DNV Riso 2002.
Sү = 1 - 0.4 (beff / leff)
Sq = Sc = 1 + 0.2 (beff / leff)
iq = ic = [1 - Hd / (Vd + Aeff cd cotØd)]2  Figure 16: Bearing capacity failure planes for normal (rupture 1) and extreme eccentricity (rupture 2) failure
iү = iq2
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– Wind Turbine Foundation Design – Undrained Bearing Capacity Again assuming the foundation is not experiencing extremely eccentric loading, and potential failure would occur along rupture 1 of Figure 16, Equation 20 can be used to determine the ultimate bearing capacity for a shallow octagonal wind turbine foundation on undrained soil conditions.
qи = sи NcScic0 + P0
where: qи = ultimate foundation bearing capcity sи = undrained shear strength Nc = shear strength bearing capacity factor, Nc = π + 2 Sc = shape factor ic0 = inclination factor P0 = effective overburden stress The shape and inclination factors, for shallow octagonal wind turbine foundations on undrained soil, can be determined with the following equations from DNV Riso 2002.
Sc = 1 + 0.2 (beff / leff)
ic = 0.5 + 0.5√(1 - H / AeffSи)
Upon making the appropriate substitutions into the bearing capacity equation it transforms into the following.  qи = sиNc(1 + 0.2 beff / leff)(0.5 + 0.5√[1- (H /(AeffSи)] + P0)
1. Determine the bearing capacity factor, the shape factor, the inclination factor, and the effective overburden pressure. Bearing Capacity Factor, Nc = π + 2 Shape Factor, Sc Sc = 1 + 0.2 (beff / leff) = 1 + 0.2 [(6.45 m) / (12.8 m)] = 1.1 leff = √82.0 m [(12.1 m) / (6.1 m)] = 12.8 m beff = [(12.8 m) / (12.1 m)] 6.1 m = 6.45 m Inclination Factor, ic ic = 0.5 + 0.5 √(1-H'/AeffSи) ic = 0.5 + 0.5 √1-(9,640.5 kN) / [(51.5 m2)(240 kPa)] ic = 0.73 2. Determine the effective overburden pressure. P0 = σ - μ where: σ = hsoilүsoil μ = hwaterүwater P0 = (2 m × 18.5 kN ⁄m3) - (0.5 m × 9.8 kN ⁄ m3) = 32.1 kPa 3. Determine the ultimate bearing capacity of the soil.
Factor of Safety for Bearing Capacity The ultimate bearing capacity represents the capacity at which the soil will fail. In wind turbine foundation design, a factor of safety equal to 2.25 is used to obtain an allowable bearing capacity.
qи = sиNcScic + P0 qи = 240 kPa × (π + 2) × 1.1 × 0.73 + 32.1 kPa = 1023.0 kPa
qall = qи / FS
Max pressure = max vertical load /Aeff
where: qall = allowable bearing capacity qи = ultimate bearing capacity FS = factor of safety for bearing capacity, 2.25 Example 3.3.3 Design Check – Undrained Bearing Capacity Determine the ultimate and allowable bearing capacity for a site with an average undrained shear strength, sи = 240 kPa, a soil unit weight of 18.5 kN/m3, a foundation embedment depth of 2 m, and a water table 0.5 m above the base of the foundation. Is the site suitable for construction of a wind turbine with a maximum vertical load of 18,000 kN (inclusive of foundation weight) and an equivalent dimensions, effective area, horizontal load, and overturning moment as Example 3.2.1.
4. Determine the maximum overburden pressure.
Max pressure = (18,000 kN) / (51.5 m2) = 349.5 kPa 5. Check if the maximum overburden pressure is greater than the allowable bearing capacity. 349.5 kPa < 454.7 kPa Design Passes Bearing Capacity Check Summary of steps to check foundation bearing capacity: 1. Determine the bearing capacity factor, the shape factor, the inclination factor, and the effective overburden pressure 2. Determine the effective overburden pressure 3. Determine the ultimate bearing capacity of the soil
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– Wind Turbine Foundation Design – 4. Determine the allowable bearing capacity of the soil 5. Determine the maximum overburden pressure 6. Check if the maximum overburden pressure is greater than the allowable bearing capacity 3.3.4 Sliding Due to the large horizontal wind load that is applied to the wind turbine and tower, sliding resistance must be investigated to ensure sliding will not occur. The frictional resisting force (Fs), must be greater than the horizontal force by a factor of at least 1.5. This is a conservative calculation because the later earth pressure on the sides of the embedded foundation greatly reduces any chance of foundation sliding. To determine the frictional resisting force, the sum of the vertical loads is multiplied by the frictional coefficient. The frictional coefficient can be obtained from Equation 25. The equations to calculate the frictional resisting force and factory of safety against sliding are shown below as Equation 26 and 27.
μ = tanδ
where: μ = frictional coefficient δ = interfacial friction angle of disimilar materials
Fs = μ × (Wconcrete + Wsoil + Fz)
where: Fs = frictional resisting force μ = frictional coefficient Wc = weight of concrete Ws = weight of overlying soil Fz = vertical or axial load
FS against sliding = Fs / FH
where: Fs = frictional resisting force FH = horizontal wind load corrected for mechnical torque Example 3.3.4 Design Check – Foundation sliding Using the known parameters from the previous example problems and an interfacial friction angle of 20 degrees, determine the factor of safety against sliding.
FRF = 1,087.0 kips FH = 509 kips FS against sliding = 1,087.0 kips / 509 kips = 2.14 2.14 > 1.5 Foundation Design Passes Sliding Check 3.3.5 Settlement In the case of wind turbine foundations, settlement can occur as a result of compression of the underlying soil. Given the magnitude of the vertical loads from the wind turbines and the typical size of the spread footings, the contact pressure from vertical loads is quite low; typically in the range of 50 to 75 kPa. Most soil profiles that have adequate bearing capacity and stiffness will settle less than 2.5 cm (Tinjum and Christensen, 2010). Foundation Settlement Analysis There are several methods available to calculate foundation settlement. For cohesive soils, consolidation settlement is utilized. This type of settlement calculation relies on laboratory test of undisturbed soil samples to obtain the compression index (Cc) and recompression index (CR) of the soil. The classical method of calculating consolidation settlement is described in the following section of this design chapter. For granular soils, wind turbine foundation settlement is often calculated using the Schmermann at al. (1978) procedure or some other form of ‘elastic’ analysis. Elastic settlement calculations relies on a variety of geotechnical parameters including SPT blow counts (N), CPT tip resistance (qc), strain influence factor, Poisson’s ratio (v), unconfined compressive strength (qu), constrained modulus (M), and the modulus of elasticity (E). The Schmermann method of calculating granular soil settlement is described later in this section. Other than the elastic half-space analysis, the methods are incremental, allowing the compressibility of the soil layers within the zone of influence of the foundation to be incorporated into the analysis. The downside of conventional settlement analysis for shallow octagonal wind turbine foundation design, is that the size of the foundation influences the soil profile to a considerable depth, and even small strains summed over large depths can result in what may appear to be unacceptable settlements. Cutting off the computations at depths where the stress increases is 10 to 20 percent of the overburden pressure generally solves the problem (Tinjum and Christensen, 2010).
μ = tanδ μ = tan20 = 0.36 Frictional Resisting Force, FRF = μ × (Wconcrete + Wsoil + FZ) FRF = 0.36 × (1,449.0 kips + 1,073.8 kips + 497 kips)
On most wind energy projects, the elastic properties of the soil are measured at small strain, either by CPT or surface methods. By properly reducing the small strain values obtained by the field measurements, settlements could be computed using elastic methods. A reduction of the small strain values on the order of 6 percent is
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– Wind Turbine Foundation Design – recommended for use in settlement calculations (Tinjum and Christensen, 2010). The Classical Method – Lab Testing (Conduto, 2010) The classical method of foundation settlement analysis uses Terzaghi’s theory of consolidation and the compression index (Cc) and recompression index (Cr) data from laboratory testing. In this method it is assumed that all settlement is one-dimensional and all of the strain is vertical. This method divides the soil beneath the footing into layers, computes the settlement of each layer, and then sums the settlement of the all layers for the total foundation settlement. To obtain a high degree of accuracy, the soil layers closest to the surface are the thinnest and progressively get thicker as they get farther from the surface. To obtain the highest degree of accuracy, thin layers throughout the computation are used. Using computer analysis greatly simplifies the settlement computation for numerous thin layers. When computing settlement for a spread footing, such as a shallow octagonal gravity base wind turbine foundation, the octagonal foundation is simplified to a circle for calculation. Furthermore, a rigidity factor (r), must be added into the consolidation settlement equations. The rigidity factor used for octagonal gravity base foundations is equal to 0.85 implying a perfectly rigid spread footing. The settlement equations for normally consolidated and overconsolidated soil with the rigidity factor are shown as Equations 28 through 30. Settlement equations for normally consolidated soils (σ'z0 ≈ σ'c)
δc = r∑ [Cc / (1 + e0)] Hlog [(σ'zf) / (σ'z0)]  For overconsolidated soil – Case I (σ'zf < σ'c)
δc = r∑ [Cr / (1 + e0)] Hlog [(σ'zf) / (σ'z0)]  For overconsolidated soil – Case II (σ'z0 < σ'c < σ'zf)
Cr σ'zf σ'zf Cc ___ ____ ___ δc = r∑ ____ 1 + e0 Hlog ( σ'z0 ) + 1 + e0 Hlog ( σ'z0 ) 
where: δc = ultimate consolidation settlement r = rigidity factor (0.85 for octagonal gravity base foundations) Cc = compression index Cr = recompression index e0 = initial void ratio H = thicknes of soil layer σ'z0 = initial vertical effective stress at midpoint of soil layer σ'zf = final vertical effective stress at midpoint of soil layer σ'c = preconsolidation stress at midpoint of soil layer
The compression index, recompression index, and preconsolidation stress should be provided with the soil data in the geotechnical report and preliminary foundation design. The initial and final vertical effective stresses can be calculated using the Equations 31 and 32. If the compression index, recompression index, and the preconsolidation stress are not provided in the geotechnical report, they can be acquired from the geotechnical lab testing information and procedures described in detail in geotechnical engineering manuals and textbooks. Initial Vertical Effective Stress
σ'z0 = ∑ үH - μ
where: ү = unit weight of soil stratum H = thickness of soil stratum μ = pore water pressure Final Vertical Effective Stress
σ'zf = σ'z0+ ∆σz
where: σ'z0 = initial vertical effective stress at midpoint of soil layer ∆σz = induced vertical stess due to load from foundation Induced Vertical Effective Stress
∆σz = Iσ (q - σ'zD)
where: ∆σz = induced vertical stess Iσ = stress influence factor q = bearing pressure along bottom of foundation σ'zD = vertical effective stress at a depth D below the ground surface Induced Vertical Stress The induced vertical stress for shallow foundations can be determined several ways, either by the Boussinesq method, the Westergaard method, or by the simplified method which produces induced vertical stress values within 5 percent of the Boussinesq values. Both the Boussinesq and simplified method for determining induced vertical stress are covered in this chapter. Boussinesq Method for Determining Induced Vertical Stress The bearing pressure along the bottom of the foundation (q), reflects the vertical stress from the structure on the foundation and the weight of the foundation. The vertical effective stress (σ'zD), represents the reduction in vertical stress from the soil removed for excavation and installation of the foundation. In the case of with turbine foun-
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– Wind Turbine Foundation Design – dation design, σ'zD would be determined for a depth (D), equivalent to the embedment depth of the foundation. The induced vertical stress (∆σz), represents the net result of the two effects. Immediately below the foundation, the stress influence factor (Iσ), is equal to 1. However, as depth beneath the foundation increases, the vertical stress is distributed over an increasingly large area. Because of this, the induced vertical stress (∆σz) and stress influence factor (Iσ) decrease with depth. In 1885, Joseph Valentin Boussinesq a French physicist and mathematician developed a classic solution for the induced vertical stress in an elastic material due to an applied load. This classic solution was later integrated by Nathan Mortimore Newmark in 1935 to produce equations for the stress influence factor beneath a foundation as a function of the foundations geometry and depth to the point of interest. These equations have been used to create stress bulb charts to determine the stress influence factor and can be seen in Figure 17. Simplified Method for Determining Induced Vertical Stress The Boussinesq equations used to create the stress bulb charts shown in Figure 17 are tedious to solve by hand. Because of this, the simplified method for determining induced vertical stress has been created for use when a quick answer is needed or when a computer is not available. For shallow octagonal wind turbine foundations approximated to a circle, Equation 34 adapted from Poulos and Davis 1974, offers a simplified approach to the induced vertical stress calculation.
For circular foundations (adapted from Poulos and Davis 1974)
1 ∆σz = 1- _________ 2 B ______ 1+
(q -σ'zD )
where: σ'zD = vertical effective stress at a depth D below the ground surface zf = vertical distance from the bottom of the foundation to the point of interest q = bearing pressure B = diameter of foundation Using the above equations, the total foundation settlement can be determined using the classical method and Equations 28, 29, or 30. The total foundation settlement can be compared to the allowable settlement and the design can be checked for settlement. Example 3.3.4 Design Check – Foundation Settlement Classical Method The allowable settlement for the shallow octagonal spread wind turbine foundation described in Example 3.3.1 is 1 inch. Using the classical method and a simplified soil layer division, compute the settlement of the foundation and determine if it satisfies the allowable settlement requirement. Information from geotechnical report and preliminary design: Embedment depth = 9 ft Soil is Overconsolidated - Case I ү = 115 pcf-Silty Clay Depth to water table = 20 ft σ'c (psf) = 5,000 psf Cc / (1 + e0) = 0.11; Cr / (1 + e0) = 0.015
Figure 17: Stress bulbs based on Newark’s solution of Boussinesq’s equation for square and continuous footings
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– Wind Turbine Foundation Design – Solution Fz = 497 kips
(qc) data, the equivalent modulus of elasticity (Es) of the soil, and the strain influence factor (I€). The analysis can be adapted to use other in-situ geotechnical parameters other than CPT data including standard penetration test (SPT), dilatometer test (DMT), and pressuremeter test (PMT) data.
Weight of Concrete Wc = Vc × 150 lb/ft3 Wc = 9,659.8 ft3 ×150 lbs⁄ft3 = 1,449.0 kips
The Schmertmann method uses an equivalent modulus of elasticity (Es) for settlement calculation. Because the equivalent modulus of elasticity is a linear function, it simplifies the settlement computation when compared to the classical method that uses the compression index (Cc) and recompression index (CR), which are logarithmic parameters.
Total Soil Weight, WT WT = Wws + Ws WT = 337.3 kips + 736.5 kips = 1073.8 kips q = [(Fz + Wsoil + Wc) / A] q = [(497 kips + 1,073.8 kips + 1,449.0 kips)] / π(25 ft)2 q = 1,539.0 psf σ'zD = ү × D = 115 pcf × 9 ft = 1,035.0 psf σ'zf = σ'z0 + ∆σz σ'z0 = ∑ үH - μ
1 ∆σz = 1- _________ 2 ______ B 1+
r zf ___ Total Settlment δc = r∑ ____ 1 + e0 Hlog ( σ'z0 )
Soil behaves with a non-linear response to stress. Because the response is non-linear (stress is not proportional to strain), the modulus of elasticity cannot be used in computation; the equivalent modulus of elasticity must be used. The Equivalent modulus of elasticity represents a modulus that is equivalent to an unconfined linear material such that the computed settlement will be the same as the actual soil settlement. The equivalent modulus of elasticity (Es) represents the lateral stain in the soil and thus is larger than the modulus of elasticity (E), but smaller than the confined modulus (M). Determining Equivalent Modulus of Elasticity (Es) from CPT Tip Resistance Cone penetrometer tests (CPT) provide continuous tip resistance data for the entire depth of the CPT analysis. Empirical correlations between the equivalent modulus of elasticity (Es) and the cone tip resistance (qc) have been developed. A range of recommended design values of Es / qc are shown in Figure 18 adapted from Schmertmann, et Cc Cr δc al. (1978) and Robertson and Com1 + e0 1 + e0 (in) panella (1989). When applying CPT 0.11 0.015 0.25 data to the Schmertmann method, 0.11 0.015 0.32 do not apply an overburden correc0.11 0.015 0.26 tion to the cone tip resistance (qc).
Because the soil is overconsolidated case 1, there is no need to compute σ'c or Cc / (1 + e0).
Strain Influence Factor In shallow spread footings, the Total 0.89 greatest vertical strains do not occur immediately below the footing. As determined by Schmertmann, the greatest strain occurs at a depth equal to ½ B, where B is the width
δc ≤ δallowable The settlement criterion has been satisfied The Schmertmann Method – Field Testing (Conduto, 2010) The Schmertmann method is one of the more common methods for calculating foundation settlement in granular soils. The method is based on a physical model that is calibrated using empirical data. This method of settlement analysis relies primarily on CPT cone resistance
Figure 18: Es – Values from CPT Results [Adapted from Schmertmann, et al. (1978) and Robertson and Campanella (1989)]
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– Wind Turbine Foundation Design – or diameter of the footing. This distribution of strain is described by the strain influence factor (IƐ). For shallow octagonal wind turbine foundations, the distribution of the strain influence factor is shown as two straight lines in Figure 19. The peak value of the strain influence factor (IƐp) can be calculated with Equation 35.
IƐp = 0.5 + 0.1√ [(q - σ'zD) / (σ'zp )]
where: IƐp = peak strain influence factor q = bearing pressure σ'zD = vertical effective stress at a depth D below the ground surface σ'zp = initial vertical effective stress at depth of peak strain influence factor
The Schmertmann settlement analysis method accounts for empirical corrections for the depth of embedment, secondary creep in the soil, and the shape of the foundation footing. These corrections are implemented through the factors C1, C2, and C3. The equations for the empirical corrections are shown as Equations 38 and 39. Depth Factor C1 = (1 - 0.5)[(σ'zD) / (q - σ'zD)]  Secondary Creep Factor C2 = 1 + 0.2 log(t / 0.1)  Shape Factor C3 = 1 for square and circular foundations where: q = bearing pressure σ'zD = vertical effective stress at a depth D below the ground surface t = time since application of load in years, t ≥ 0.1 yr The above equations are applicable for all consistent units with the exception that time must remain in years. If the time since load application is unknown use t = 50 years, C2 = 1.54. All of the previous information can be combined into Equation 40 to determine the elastic settlement of a shallow octagonal wind turbine foundation.
δ = C1C2C3(q - σ'zD) ∑(IƐH / Es) Figure 19: Distribution of strain influence factor with depth under square and continuous footings (Adapted from Schmertmann (1978)
Compute σ'zp at depth of D + B⁄2 for square and circular foundations. The exact value of IƐ, for square and circular foundations, at any given depth can be determined using Equations 36 and 37. When dividing the soil strata into layers, be sure to divide it in a manner that the depth from the bottom of the foundation to the midpoints of the layers work for the below zf conditions and equations. For zf = 0 to ⁄2: B
IƐ = 0.1 + [(zf / B)(2IƐp - 0.2)]
where: C1 = depth factor C2 = secondary creep factor C3 = shape factor q = bearing pressure σ'zD = vertical effective stress at a depth D below the ground surface IƐ = strain influence factor H = thickness of soil layer Es = equivalent modulus of elasticity Summary of Steps for Schmertmann Method of Settlement Analysis: 1. Obtain required in-situ test data that defines the subsurface conditions
2. Divide the depth of influence, 2B for square and circular footings, into zone layers and assign an equivalent modulus of elasticity (Es) to each layer
3. Calculate the peak strain influence factor (IƐp)
For zf = B⁄2 to 2B:
IƐ = 0.667 IƐp [2 - (zf / B)]
where: zf = depth from bottom of foundation to midpoint of layer IƐ = strain influence factor IƐp = peak influence factor
4. Calculate the strain influence factor (IƐ), at the midpoint of each layer 5. Calculate the correction factors, C1, C2, and C3 6. Calculate the settlement
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– Wind Turbine Foundation Design – Example 3.3.5 Design Check – Foundation Settlement Schmertmann Method The allowable settlement for the shallow octagonal spread wind turbine foundation described in Example 3.3.1 is 1 inch. Using the classical method and a simplified soil layer division, compute the settlement of the foundation and determine if it satisfies the allowable settlement requirement. Information from geotechnical report and preliminary design: the results of a CPT sounding performed at the location where a wind turbine is to be installed are shown in Figure 20. The soils at this site are young, normally consolidated sands with some interbedded silts. Embedment depth = 9 ft Soil is Overconsolidated - Case I ү = 115 pcf - Silty Clay Depth to water table = 20 ft σ'c (psf) = 5,000 psf Cc / (1 + e0) = 0.11 Cr / (1 + e0) = 0.015
Solution Fz = 497.1 kips Weight of Concrete Wc = Vc × 150 lb/ft3 Wc = 9,659.8 ft3 ×150 lbs⁄ft3 =1,449.0 kips Total Soil Weight, WT WT = Wws + Ws WT = 337.3 kips + 736.5 kips = 1073.8 kips q = (Fz + Wsoil + Wc) / A q = (497 kips + 1,073.8 kips + 1,449.0 kips) / π(25 ft)2 q = 1,538.0 psf Using Es = 2.5 qc from Figure 18 Depth of influence = D + 2B = 9.0 ft + 2(41.4) = 91.8 ft σ'zD = ү × D = 115 pcf × 9 ft = 1,035.0 psf Compute σ'zp at depth of D + B⁄2 for square and circular foundations. σ'zp = ү(D + B⁄2) - үw (Hw) σ'zp = 115 pcf (9 ft + 20.7 ft) - 62.4pcf (9 ft + 20.7 ft - 20ft) σ'zp = 2,810.2 psf IƐp = 0.5 + 0.1√[(q - σ'zD) / σ'zp] IƐp = 0.5 + 0.1 √[(1,538.0 - 1,035.0) / 2,810.2 psf] IƐp = 0.57 For zf = 0 to B⁄2: IƐ = 0.1 + [(zf / B)(2 IƐp - 0.2)] For zf = B⁄2 to 2B: IƐ = 0.667 IƐp [2 - (zf / B)]
Figure 20: Results from CPT sounding at wind turbine proposed installation location for Example 3.35 Design Check Foundation Settlement Schmertmann Method
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– Wind Turbine Foundation Design – Depth Factor C1 C1 = 1 - 0.5[(σ'zD) / (q - σ'zD)] C1 = 1 - 0.5[(1,035.0 psf) / (2,243.4 psf - 1,035.0 psf)] = 0.572 Secondary Creep Factor C2 C2 = 1 + 0.2 log(t / 0.1) = 1 + 0.2 log(50 / 0.1) = 1.54 Shape Factor C3 = 1 for square and circular foundations δ = C1C2C3 (q - σ'zD) ∑ (IƐH / Es) δ = (0.572)(1.54)(1)(2,243.4 psf - 1,035.0 psf)(5.35E-03)
δ = 0.00404 feet = 0.58 inches δc ≤ δallowable The settlement criterion has been satisfied
The Simplified Schmertmann Method If limited subsurface data is available or if the CPT results show a relatively uniform cone tip resistance (qc), a constant equivalent modulus of elasticity (Es) can be used to simplify the Schmertmann method of settlement analysis. Equation 41 shows the simplified method of Schmertmann settlement analysis.
δ = [(C1C2C3(q - σ'zD)(IƐp + 0.025)B] / Es 
where: C1 = depth factor C2 = secondary creep factor C3 = shape factor q = bearing pressure σ'zD = vertical effective stress at a depth D below the ground surface IƐp = peak influence factor H = thickness of soil layer Es = equivalent modulus of elasticity Layer No.
IƐ H Es
0 to 9
9 to 20
20 to 40
40 to 47
47 to 52
52 to 60
60 to 79
70 to 87
87 to 92
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– Wind Turbine Foundation Design –
References Conduto, D.P. Foundation Design Principles and Practices, 2nd Edition. Prentice Hall. 2010. Det Norske Veritas. Guidelines for Design of Wind Turbinse. Risø National Laboratory, Copenhagen. 2002. International Electrotechnical Commission. Wind Turbines-Part I: Design Requirements. International Standard 61400-1, 3rd Edition. 2005. Morgan, K. and Ntambakwa, E. Wind Turbine Foundation Behavior and Design Considerations. AWEA WINDPOWER Conference. Garrad Hssan America, Inc. June 2008. Tinjum, J.M. and Chrsitensen, R.W. Site Geotechnical Characterization, Civil Design, and Construction Considerations for Wind Energy Systems. 2010.
22 – Wind Energy Site Design and Construction © James M. Tinjum Draft - Version 1.0