HELICAL FOUNDATIONS AND ANCHORS

HELICAL FOUNDATIONS AND TIE BACKS

State of the Art

Richard W. Stephenson Professor of Civil Engineering

University of Missouri-Rolla Rolla, Missouri 65409

INTRODUCTION... 3

HISTORY ... 3

Modern Usage ... 4

HELICAL PILE DESIGN ... 7

Prototype ... 7

Theoretical ... 8

Semi -empirical ... 8

Empirical ... 8

UPLIFT CAPACITY OF HELICAL PILES ... 9

General ... 9

Semi-Empirical Helical Pile Capacity ... 9

Individual Plate Capacity Method ... 9

Kulhawy Method ... 10

Clemence Method ... 15

Uplift capacity of shallow anchors in sand ... 16

Uplift capacity of deep anchors in sand ... 24

Uplift capacity of helical anchors in clay ... 27

Uplift capacity of shallow helical anchors in clay ... 27

Uplift capacity of deep helical anchors in clay ... 30

Empirical Method. ... 32

BEARING CAPACITY OF HELICAL PILES... 33

Bearing Capacity Design of Helical Piles ... 33

LATERAL CAPACITY OF HELICAL PILES ... 37

Analysis Based on Limiting Equilibrium or Plasticity Theory ... 37

Analysis Based on Elastic Theory ... 38

Analysis Based on Nonlinear Theory ... 38

Simplified Method for Nonlinear Analysis of Helical Piles in Clay ... 39

BIBLIOGRAPHY ... 46

EXAMPLE PROBLEMS ... 48

Uplift Capacity ... 48

Shallow Anchor in Sand ... 48

Deep Anchor in Sand ... 49

Shallow anchor in Clay ... 51

Deep anchor in Clay ... 52

Anchor in Sand ... 53

Anchor in Clay ... 54

Lateral Capacity of a Laterally Loaded Helical Pile in Soft Clay ... 56

HELICAL FOUNDATIONS AND ANCHORS STATE OF THE ART

March 2, 2010

R.W. Stephenson, P.E., Ph.D. INTRODUCTION

Helical piles (helical anchors) are finding increasingly widespread use in the geotechnical market. These foundations have the advantages of rapid installation and immediate loading capabilities that offer cost-saving alternatives to reinforced concrete, grouted anchors and driven piles. The last 12 years have seen the rapid development of rational geotechnical engineering-based design and analysis procedures that can be used to provide helical pile design solutions

HISTORY

Helical foundations have evolved from early foundations known as Ascrew piles or screw mandrills.@ The earliest reported screw pile was a timber fitted with an iron screw propeller that was twisted into the ground(1). The early screw mandrills were twisted into the ground by hand similar to a wood screw. They were then immediately withdrawn and the hole formed was filled with a crude form of concrete and served as foundations for small structures. Conventional screw piles have been in use since the 18th century for support of waterfront and in soft soil conditions for bridge structures as early as the 19th century.

The first commercially feasible helical anchor was developed in the early 1900's to respond to a need for rapidly installed guy wire anchors. The anchors were installed and used primarily by the electrical power industry. The development of reliable truck mounted hydraulic torque drive devices revolutionized the anchor industry. These advances allowed the installation of helical anchors to greater depths and in a wider variety of soil conditions than ever before(1).

Modern Usage

Modern helical anchors are earth anchors constructed of helical shaped circular steel plates welded to a steel shaft (Figure 1). The plates are constructed as a helix with a carefully controlled pitch. The anchors can have more than one helix located at appropriate spacing on the shaft. The central shaft is used to transmit torque during installation and to transfer axial loads to the helical plates. The central shaft also provides a major component of the resistance to lateral loading.

A typical helical anchor installation is depicted in Figure 2. These anchors are turned into the ground using truck mounted augering equipment. The anchor is rotated into the ground with sufficient applied downward pressure (crowd) to advance the anchor one pitch distance per revolution. The anchor is advanced until the appropriate bearing stratum is reached or until the applied torque value attains a specified value. Extensions are added to the central shaft as needed. The applied loads may be tensile (uplift), compressive (bearing), shear (lateral), or some combination.

Helical anchors are rapidly installed in a wide variety of soil formations using a variety of readily available equipment. They are immediately ready for loading after installation. Large

multi-helix anchors develop capacities of up to 100,000 lbs. (450 kN).

In the past 20 years, the use of helical anchors has expanded beyond their traditional use in the electrical power industry. The advantages of rapid installation, immediate loading capability and resistance to both uplift and bearing loads have resulted in their being used more widely in traditional

geotechnical engineering applications. Reported uses include tiebacks for soil retaining walls, foundations for lightly loaded structures such as transmission line towers, light poles, tiedowns for manufactured housing, temporary structures, etc., and for underpinning lightly loaded structures such as single family dwellings. Because of these uses, there has been an increase in research into the

geotechnical principals governing the behavior of helical piles. They have published reports of their studies of helical anchors under loading and proposed design procedures by which helical pile performance can be predicted. By far, the majority of this work has been in the anchoring (uplift) capacity of helical piles(1). However, studies in the lateral and bearing (compression) load performance are reported as well.

HELICAL PILE DESIGN

The methods available to design helical pile systems and to predict their performance under load can be divided into four broad categories: prototype (load test), theoretical, semi-empirical and empirical.

Prototype

In the prototype design method, helical pile capacities are determined by testing a helical pile identical to the production pile in identical subsurface conditions (5). The results of the prototype test (load test) are then extrapolated to the rest of the helical piles used at the site. Advantages of this approach lie in the fact that actual piles are evaluated in their field use conditions. However, this method requires the a priori selection of helix size and configurations as well as installation depth. The testing of several helical pile configurations to determine optimum size and spacing is usually too costly. Consequently, prototype testing is used primarily for proof testing semi-empirical and empirical designs.

Theoretical

Theoretical methods utilize soil mechanics theories of the interaction behavior of foundations and earth materials. The theories use the basic properties of the foundation (strength and deformability) as well as the basic properties of the soil (strength and compressibility) to create design procedures that can be applied to different soil structures and different helical pile configurations. Ideally, the procedures are independent of particular installation equipment and can be applied to all realistic combinations of helical piles and soil stratigraphies.

Semi -empirical

Unfortunately, because of the complexity of soil stratigraphy and the inability of current soil mechanics theories to fully describe the actual field performance of a soil, most geotechnical design procedures are theoretical procedures modified by experience (semi-empirical).

Empirical

Empirical methods are most often developed and used by helical pile manufacturers who have access to vast quantities of pile behavior data. Empirical methods are based on statistical correlations of anchor uplift capacity with other, easily measured, parameters such as standard penetration test (N) values, installation torque, or other indices. The methodology for development of these correlations and the data on which they are based is usually considered proprietary by the manufacturers. Results obtained from these methods are highly variable (1)(1)(1)(1).

By far the majority of the research has been directed toward the uplift behavior of helical piles (helical anchors). This is due primarily to their traditional use as guy line anchors and as tie downs for transmission towers and tiebacks for retaining structures. Considerably less work has

work is available on laterally loaded piles that could possibly be applied to helical piles. Even less data is reported on the performance of helical piles under bearing (compressive) loading. This is becoming more important since helical piles are gaining wide use for underpinning and supporting lightly loaded structures. The following sections will address each of the three design loading conditions.

UPLIFT CAPACITY OF HELICAL PILES General

The behavior of any deep foundation is highly complex. Consequently, it is important to understand the the behavior of helical piles is influenced by the same factors that influence the behavior of drilled piers and driven piles: i.e., strength and deformation properties of soils, soil non-homogeneities, groundwater levels, soil plasticity and volume change potential as well as installation procedures and equipment.

Semi-Empirical Helical Pile Capacity

Individual Plate Capacity Method. One method of computing uplift capacities of helical piles is the individual plate capacity method. In this method, the uplift capacities are computing using:

helices

of

number

the

is

n

where

,

Qui is the ultimate uplift capacity of the individual helix. Qui can be computed from bearing capacity

theory as: where:

The first term of equation three is the contribution of soil cohesion to the uplift capacity. The

second term is the contribution of soil friction to the capacity and the third term is the contribution of soil overburden to the capacity. Nc *, Nγ* and Nq* are bearing capacity factors on cohesion, friction

and surcharge respectively.

For cohesive (clay) soils, Nc* is normally taken as 9.0 for H1/D1 > 3. For H1/D1 3, Nc* is

normally taken as 5.7. Nγ* and Nq* are taken as 0 and 1 respectively.

For helical foundations embedded in cohesionless (sand) soils, c is zero and Nγ* and Nq*

vary as a function of the coefficient of friction (Φ) of the sand. Meyerhof=s values of Nγ* and Nq*

are often used and are presented as Table 1, below.

Kulhawy Method. Kulhawy (1) described a method of analysis of the uplift capacity of helical anchors by describing their behavior as intermediate between the grouted and spread anchors. In his model, the upper helix develops a cylindrical shear surface that controls its behavior. The soil between the helices becomes an effective cylinder if the helices are sufficiently close together. The

helix above soil of weight unit effective = helix to surface ground from Depth = H helix of diameter = D helix of area = A N H + N D 2 1 + cN = q i i * q i * i * c ui xA q = Q_{u u} i i

in the disturbed cylinder of soil above the anchor. This disturbance effect can be approximated by relating the disturbed properties to the in-situ properties in the following equations:

Qu = Ultimate uplift capacity

Qp = Top plate (cone breakout) capacity

Qf = Cylinder friction capacity

Wf = Weight of helical pile (often neglected)

For cohesionless (sand) soils, Kulhawy recommended the following equations:

Table 1 Meyerhof@s Bearing Capacity Factors

Φ (deg) Nc* Nq* Nγ* 0 5.1 1.0 0.0 5 6.5 1.6 0.1 10 8.4 2.5 0.4 15 11.0 3.9 1.1 W + Q + Q = Qu p f f

25 20.7 10.7 6.8 26 22.3 11.8 8.0 28 25.8 14.7 11.2 30 30.1 18.4 15.7 32 35.5 23.2 22.0 34 42.2 29.4 31.1 36 50.6 37.7 44.4 38 61.4 48.9 64.0 40 75.3 64.1 93.6 45 133.9 134.7 262.3 50 266.9 318.5 871.7 where:

Qp(max) = Top plate capacity limit

Af = Area of top helix

qq = effective surcharge= H1 Q + W + ) N q ( A = ) ( Qp max f q q qr qs qd f _tu

Qtu = Tip capacity in uplift (usually neglected)

The Nq term is a bearing capacity factor given by:

2 + 45 e = Nq tan tan2 _

The ζ terms are modification factors for soil rigidity (ζqr), anchor shape (ζqs), and anchor depth (ζqd)

as given below.

with the tan-1 term in radians.

G = soil shear modulus

E = soil elastic modulus

The cylinder friction capacity, Qf , is computed from the following equation:

where:

P = helix perimeter

v = effective vertical stress

k = coefficient of horizontal earth pressure

tan tan q 1 ) + 2(1 E = q G = I i i r tan + 1 = qs tan + 1 = qs D H ) -(1 2 + 1 = 1 1 -2

qd tan sin tan

(z) (z) k P(z) k k = )(z)dz (z)( k P(z) = Q o v H H o u v H H f 1 1 tan tan

= effective interface friction angle ko = Coefficient of earth pressure at rest

= Effective stress soil friction angle __/__ = 0.9

k/ko = 5/6

The friction capacity of the helical pile system is reduced due to disturbance caused by pile installation. Kulhawy accounted for this by using a reduced uplift capacity according to the following equation:

Clemence Method. A significant series of studies on helical anchor uplift capacity was done by Clemence (1), and later summarized in Mitsch and Clemence (1) and Mooney, Adamczak, and Clemence (1). They extended the work of previous researchers with extensive full scale field tests, scale model laboratory tests, and theoretical analysis. These researchers suggested that helical pile uplift capacity could be divided into two broad categories: shallow anchors and deep anchors. They stated that the uplift capacity is provided by:

0 r f f(reduced)=Q Q tan k = 3 + 2 = o o o r

Uplift capacity of shallow anchors in sand:

The weight of the soil, Ws can be expressed as:

Das non-dimensionalized these equations into:

Q + Q = Qu p f W + 3 2 H + 2 H D 2 k = Q s 3 1 2 1 1 2 u u tan cos tan 2 H 2 + D ) D ( + 2 H 2 + D + ) D ( H 3 = W 1 1 1 1 1 2 2 1 1 s tan tan

Similarly: Let

Combining:

Fq is called the breakout factor by Das. To determine Fq the value of ku must be determined. Mitsch

and Clemence(11) showed that this value varies with the soil friction angle, Φ. Their values can be expressed as: H A Q = F 1 p q1 2 0.33 + D H 0.5 D H 2 ) ( k 4 = H A Q = F 1 1 1 1 2 2 u 1 p

q1 tan cos tan

2 D H 8 + 2 D H 5.33 + 4 = H A W = F 1 1 2 2 1 1 2 1 s q2 tan tan R = D H 1 1 2 8R + 2 R 5.33 + 4 + 2 0.33 + R 0.5 2 ) ( k R 4 = H A Q = F 2 2 2 u 2 1 p q tan tan tan cos tan

The variation of m is given below.

Table 2 Variation of m

Soil friction angle, Φ (degrees) m 25 0.033 30 0.075 35 0.180 40 0.250 45 0.289

The magnitude of ku increases with H1/D1 up to a maximum value and remains constant after

that. This maximum value is attained at (H1/D1)cr = Rcr . The variation of ku with H1/D1 and Φ are

plotted in Figure 4. Substituting the appropriate value of ku and R into the previous equation, the

D H m + 0.6 = k 1 1 u H D F 4 = H A F = Qp q 1 q 12 1

Da = average helix diameter.

Therefore the ultimate uplift capacity for a shallow anchor in sand

is: tan k ) H -H ( D 2 = Qf a 2n 12 u tan k ) H -H )( ( 2 D + D 2 + H D F 4 = Qu q 12 1 1 n 2n 12 u

Table 3: Variation of Breakout Factor Fq for Shallow Anchor Condition Fq R =H1/D1 Φ = 25 Φ=30 Φ=35 Φ=40 Φ=45 0.5 5.27 5.54 5.87 6.23 6.61 1.0 6.74 7.38 8.25 9.18 10.17 1.5 8.41 9.54 11.16 12.91 14.77 2.0 10.27 12.01 14.64 17.49 20.53 2.5 12.33 14.82 18.72 22.99 27.54 3.0 14.6 17.97 23.44 29.46 35.94 3.5 21.48 28.84 36.99 45.74 4.0 25.35 34.95 45.64 57.13 4.5 41.81 55.44 70.18 5.0 49.46 66.56 85 5.5 78.97 101.68

6.5 108.01 141.06 7.0 124.78 163.98 7.5 189.14 8.0 216.69 8.5 246.73 9.0 279.34

Uplift capacity of deep anchors in sand:

The magnitude of the Fq = Fq* is determined by setting R = Rcr and ku = ku(max) in equation 25.

Fq* has been plotted in Figure 8.

The frictional resistance Qf is

computed using:

The two equations can be combined to yield the net ultimate uplift capacity for deep anchors in sand:

If the helices are placed too close to each other, the average net ultimate uplift capacity of each anchor may decrease due to the overlapping and interference of the individual failure zones.

0 = resistance friction shaft = Q helices the between cone the of resistance frictional = Q helix top the of capacity bearing = Q Q + Q + Q = Q s f p s f p u factor breakout anchor deep = F where H D F 4 = Q * q 1 2 1 * q p 2 D + D = D where k ) H -2 H ( D 2 = Q n 1 a u 2 1 n a u maxtan tan max k ) H -H ( 2 D + D 2 + H D F 4 = Qu *q 21 1 1 n 2n 21 u

It is recommended that the optimum spacing of the helices be about 3D1 apart. A factor of safety of

2.5 or more should be applied to the ultimate uplift capacity to determine the allowable or working uplift capacity.

20

30

40

50

Soil Friction Angle (deg)

10

100

D

ee

p

A

nc

ho

r

B

re

ak

ou

t

F

ac

to

r,

F

q*

Uplift capacity of helical anchors in clay. Failure of helical piles in clay soils is

normally analyzed using the Φ= 0 condition. The soil shear strength is then characterized as: Uplift capacity of shallow helical anchors in clay. For shallow anchors (H1/D1 7), the

failure surface at ultimate load extends from the top helix to the ground surface (Figure 9 ). If the H1/D1 ratio is relatively large then the failure zone will not extend to the ground surface and the deep

anchor situation controls.

For shallow anchors:

where: Qp = bearing capacity of the top helix

Qf = bearing due to friction along enclosed cylinder between helices.

Where A1 = area of the top helix

Fc = breakout factor

γ = unit weight of soil above top helix

H1 = distance between the ground surface and the top helix

c = su u Q + Q = Q_{u p f} ) + F c ( A = W + F c A = Qp 1 c s 1 u c

The variation of the breakout factor Fc is plotted as a function of (H1/D1)/(H1/D1)cr in Figure 10.

The frictional resistance of the cylinder of soil between the helices can be computed from:

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (H1/D1)/(H1/D1)cr 0 1 2 3 4 5 6 7 8 9 F c 7 2.5 + c 0.107 = D H = R u 1 1 cr cr ) H H ( c 2 D + D = Qf 1 n u n 1

Uplift capacity of deep helical anchors in clay. For the deep anchor condition (H1/D1)> (H1/D1)cr deep anchor criteria holds (Figure 11). The capacity for this

case is given below.

Where Qs = resistance due to adhesion at the interface of the clay and the anchor shaft located

above the top helix.

Where ca is the adhesion and varies from about 0.3cu for stiff clays to about cu for soft clays and Ds is

the shaft diameter. Combining:

c ) H -H ( 2 D + D + ) H + F c ( D 4 = Qu 21 u c 1 1 n n 1 u Q + Q + Q = Qu p f s ) H + c )(9 D ( 4 = Qp 21 u 1 ) H H ( c 2 D + D = Qf 1 n u n 1 c H D = Qs s 1 a

c H D + c ) H -H ( 2 D + D + ) H + c )(9 D ( 4 = Qu 12 u 1 1 n n 1 u s 1 a

All ultimate uplift capacities should be divided by an appropriate factor of safety to set the

allowable(working) factor of safety, i.e., Empirical Method.

Empirical methods are most often developed and used by anchor manufacturers who have access to vast quantities of anchor behavior data. These methods are based on statistical correlations of anchor uplift capacity with other, easily measured, parameters such as standard penetration test (N) values, installation torque, or other indices. The methodology for development of these correlations and the data on which they are based are usually considered proprietary by the manufacturers. Results obtained from these methods are highly variable.

The most widely used correlation is with installation torque. In this method, the total anchor

capacity is computed from the installation torque as:

where: Kt is the empirical factor relating installation torque and uplift capacity and T is the average

installation torque. Currently, Kt values are reported between 3 feet-1 for large (8 inch) extension

shafts to around 10 feet-1 for all small (3 inch) shafts. 10 feet-1 is most widely used in the industry.

FS Q = Q u allow xT K = Qu t

BEARING CAPACITY OF HELICAL PILES

Although helical piles have been used as tower foundations for many years, the design loading for these foundations is not bearing (compression) but uplift. It is only relatively recently that helical piles have been used in primarily bearing conditions. In particular, these foundations are being used in the retrofit or underpinning of distressed lightly loaded structures.

There are several advantages of helical piles for foundation underpinning(1). Of particular importance is the general relationship between installation torque and helical pile capacity. It is possible to develop site-specific Kt values from preliminary field load testing and use the results as

quality control values for the production piles. Other advantages include the ease of extending pile length by adding on extension shafts, the lack of influence of water table or caving soils, ability to install in low-overhead, low noise or other restricted areas. Helical anchor shafts are relatively small in diameter and by that develop low lateral stresses and low drag along their lengths. This makes them particularly applicable in expansive soil conditions.

Bearing Capacity Design of Helical Piles

The bearing capacity of helical piles in compression is based upon the general bearing

capacity equation:

where: c = soil cohesion

1) -N q( + cN = qult c q

Nc= and Nq= are bearing capacity factors for circular plates at varying H/D values.

Although there are some minor differences in these values depending upon the particular theory adopted, in general Nc= and Nq= are taken from Figure 11(1).

The bearing capacity of a multi-helix system is the sum of the individual capacities of the individual helices if they are spaced appropriately far apart, i.e., three times the plate diameter or greater.

Ai = individual plate area

ci = cohesion of soil at and beneath helix I

qi = γiHi = overburden pressure at helix i

Nci= = Bearing capacity factor on cohesion for helix i(Figure 11)

1)] -N ( q + N c A = Q i i ci i qi n i ult

[

0 5 10 15 20 25 30 35 40 45 50

Soil Friction Angle (deg)

1 10 100 1000

N

c*

a

nd

N

q*

Nc

Nq

1

4

7

H/D

7 4 1

LATERAL CAPACITY OF HELICAL PILES

Lateral loads and moments may be transferred to helical pile foundations by the supported structures due to a variety of reasons. The load can come from wind loading, line breakage for tower structures, axial load eccentricities in underpinning foundations and from other sources. Since the extension shafts used with these piles have diameters less than about 2.0 inches and may be as long as 50 feet or more, the slenderness ratios roughly 100 to 200 are typical. These values of slenderness ratios make buckling of the shaft a matter of concern. On the other hand, the applied loads are generally a small fraction of the shaft=s compressive yield load and the connection hardware between the shaft and the supported foundation provides significant restraint against rotation. The available approaches for the analysis of laterally loaded vertical piles can be broadly grouped under the following categories:

A. Analysis based on limiting equilibrium or plasticity theory. B. Analysis based on elastic theory.

C. Analysis based on nonlinear theory.

Analysis Based on Limiting Equilibrium or Plasticity Theory. The theories of Brinch Hansen(1) and Meyerhof and Ranjan(1) were developed for rigid piles assuming that the limiting or maximum soil resistance is acting against the pile (Figure 12) when it is subjected to the ultimate lateral load. The pile is assumed to deflect sufficiently to develop full soil resistance along the length considered. This is not true for small deflections. Because of the diameter of the extension shafts

Analysis Based on Elastic Theory. Methods based on elastic theory commonly assume that the soil behaves as a series of closely spaced independent elastic springs (Winkler=s assumption). Using the beam-on-elastic-foundation approach, basic equations have been developed by various investigators (Reese and Matlock(1), Davisson and Gill(1) for different variations of modulus of

subgrade reaction (k). The governing equation is:

Non-dimensional coefficients have been given for the solution of the pile problem to obtain deflection, moment and shear, etc., along the pile lengths (Stephenson and Puri(1).

Analysis Based on Nonlinear Theory. In general, because of the inherent complexities of determining soil-structure interaction using nonlinear theories, most of the solutions are computer based. The most widely used computer program is a finite difference model LPILEPLUS _{developed by}

Lyman Reese and his colleagues at the University of Texas(1). The computer model uses the

following equation:

where: y = lateral displacement x = distance along the axis

EI = the bending stiffness of the pile, and

Es = the secant modulus of the soil response curve.

If a distributed lateral load w acts along some portion of the shaft length, the final equation becomes:

-ky = dx y d EI 4₄ 0 = y E + dx y d Q + dx y d EI ₂ s 2 4 4

The advantages of the computer solutions are:

The bending stiffness EI of the pile can be varied along its length.

The soil secant modulus can vary from point to point along the pile=s length and as a function of deflection (nonlinearly).

The effect of the axial load on deflection and bending moment can be considered.

The effect of bending on compression loaded helical anchors was studied by Hoyt, et. Al. (20). They used LPILEPLUS to model three full-scale loading tests. The modeling showed that buckling is a practical concern only in the softest soils, and this agrees with past analyses and experience on other types of piles (Sowers and Sowers(1). They presented a figure (Figure 13) that can be used to decide whether a particular application is clearly stable (well to the right and below the applicable boundary line), clearly unstable (well to the left of or above the boundary), or questionable (close to the boundary). Their criteria for soil classification is given in Table 4. They suggested that load tests could be used to resolve questionable applications.

Simplified Method for Nonlinear Analysis of Helical Piles in Clay. Hsiung and Chen(1) have presented a simplified method for the analysis and design of long piles under lateral loads (moment) in uniform clays. The method is based on the concept of the coefficient of subgrade reaction with consideration of the soil properties in the elastoplastic range. To use their method four

0 = w(x) + y E + dx y d Q + dx y d EI ₂ s 2 4 4

required parameters are the ratio of length to diameter and the elastic modulus of the pile shaft. If

the coefficient of subgrade reaction varies with depth, then: The range of the analytical parameters are determined as follows:

1. The coefficient of subgrade reaction, kh has been compiled by Poulos and Davis(1) and are

shown in Table 5. kh is taken in the range of 4,000-26,000 kN/m3 for an overconsolidated

clay. A value of nh in the range of 200-1300 kN/m4 is used.

2. Yielding displacement of soil, u* is taken in the range of 12-25 mm according to Bowles(1). 3. Ratio of length to diameter (L/d).

4. Elastic modulus of the pile shaft, Ep.

The results of this study showed that both the load-maximum deflection and load-maximum moment relationships may be expressed by normalized curves based on regression analysis. The equations used for normalizing the Load and Moment Factors are given in Table 6. Table 7 gives the regression equations for maximum deflection and moment.

z n = kh h

Table 4: Soil Parameters for Figure 13 Description N (blows) Cu (kPa) Φ (deg) Clays Very Soft 1 10 0 Soft 3 19 0 Medium 6 38 0 Stiff 12 72 0 Very Stiff 24 143 0 Hard 32+ 287 0 Sands Very Loose 2 0 28 Loose 7 0 29 Medium 20 0 33 Dense 40 0 39 Very Dense 50+ 0 ₄₃

0.0 1.0 2.0 3.0 4.0 5.0 6.0 Shaft Length (m) 0 50 100 150 200 A x ia l L o a d ( k N ) STIF F CLA Y MEDI IUM SAND ME DIU M C LA Y & LO OSE SA ND SOFT CLA Y VE RY LO OS E S AN D VERY SOF T CL AY 178 kN BRACKET STRENGTH LIMIT

Table 5: Range of Coefficient of Subgrade Reaction

Soil Type kh (kN/m3) nh (kN/m4) Reference

Over-consolidated stiff clay 15700-31400 Terzaghi (1955) Over-consolidated very-stiff clay 31400-62800 Terzaghi (1955 Over-consolidated hard clay >62800 Terzaghi (1955 Normally consolidated soft clay

160-3260 Reese and Matlock(1965)

270-540 Davisson and Prakash (1962)

Normally consolidated organic clay

108-270 Peck and Davisson (1962)

108-810 Davisson (1970)

Peat 54 Davisson (1970)

Table 6: Formulas for Normalizing Load and Moment Factors Formula Number (1) Soil Condi-tion (2) Pile-head Condition (3) Loading Condition (4) Normalizing Load factor (5) Normalizing moment factor (6)

1 Constant kh Free-head Lateral Force

Po

Pc _{= 2EIλ}3_u*

Mc

max=0.3224Pc/λ

2 Constant kh Free-head Moment Mo Mc = 2EIλ2u* Mc_max = Mc

3 Constant kh Fixed-head Lateral Force

Po

Pc

f = 4EIλ3u* Mc_max =0.5P_fc/λ

4 Linear kh Free-head Lateral Force

Po

Pc _{= (1/249)EIλ}3_u*

Mcmax=0.7714 Pf c_/λ

5 Linear kh Free-head Moment Mo Mc =(1/1.619)EIλ2u* Mc_max = Mc

6 Linear kh Fixed-head Lateral Force

Po

Pc

f =(1/.9279)4EIλ3u* Mc_max =0.9271P_f

c_/λ

Note: For constant kh:

4 p p hd/4E I k = _{For linear k} h: 5 p p hd/E I n =

Table 7: Regression Equations for Maximum Deflection and Moment Equation Number (1) Soil Condition (2) Pile-head Condition (3) Loading Condition (4) Regression equation of load-max. deflection (5) Regression equation of load-max. Moment (6)

1 Constant kh Free-head Lateral

Force Po 0.32u/u +0.66 u u/ = P P * * c o M M 1.10 = P P c 0.52 c o max max

2 Constant kh Free-head Moment Mo

0.87 + u 0.15u/ u u/ = M M * * c o M M 1.00 = M M c 1.0 c o max max 3 Constant kh Fixed-head Lateral Force Po 0.37u/u +0.67 u u/ = P P * * c f o M M 1.07 = P P c 0.54 c o max max

4 Linear kh Free-head Lateral

Force Po 0.15u/u +0.82 u u/ = P P * * c f o M M 1.111 = P P c 0.70 c o max max

5 Linear kh Free-head Moment Mo

0.91 + u 0.075u/ u u/ = M M * * c o M M 1.00 = M M c 1.0 c o max max 6 Linear kh Fixed-head Lateral Force Po 0.19u/u +0.83 u u/ = P P * * c f o M M 1.09 = P P c 0.72 c o max max

EXAMPLE PROBLEMS Uplift Capacity

Shallow Anchor in Sand

Given the situation shown in Figure EX-1. Using equation 31:

Interpolating from Table 3, Fq = 30.06.

ku = 1.3 (Figure 5).

Qu = 5164+6021 = 11,185 lbs

FS = 2.5

Qallow = 11,185 = 4474 lbs = 4.5kips

If the water surface were at the ground surface, then:

tan k ) H -H )( ( 2 D + D 2 + H D F 4 = Qu q 21 1 1 n 2n 21 u 3.6 = 10 36 = D H = R 1 1 35 )1.3x 3 -8 (105)( 2x12 7.5 + 10 2 + 3 12 10 30.06x105 4 = Q 2 2 2 u tan

Qu = 5902 lbs

FS = 2.5

Qallow = 5902/2.5 = 2361 lbs = 2.4 kips

Deep Anchor in Sand

Given the situation shown in Figure EX-2. Using equation 31:

pcf 55.4 = 62.4 -117.8 = -= = _{sat water} 35 )1.3x 3 -8 (55.4)( 2x12 7.5 + 10 2 + 3 12 10 30.06x55.4 4 = Q 2 2 2 u tan 7.2 = 10 72 = D H = R 1 1 D H m + 0.6 = 5) (Figure 1.5 = k 1 1 cr umax

Fq* = 50 (Figure 8)

Qu = 17181+10737 = 27918 lbs

FS = 2.5

Qallow = 27918/2.5 = 11,167 lbs = 11.1 kips

If the water surface were at the ground surface, then:

Qu = 14730 lbs FS = 2.5 Qallow = 14730/2.5 = 5892 lbs = 5.9 kips R < 5 = 0.18 0.9 = D H D H + 0.6 = 1.5 1 1 cr 1 1 cr 39) (equation k ) H -H )( ( 2 D + D 2 + H D F 4 = Qu q 21 1 1 n 2n 12 utan 35 )1.5x 6 -11 (105)( 2x12 7.5 + 10 2 + 6 12 10 50x105 4 = Q 2 2 2 u tan 35 )1.5x 6 -11 (55.4)( 2x12 7.5 + 10 2 + 6 12 10 50x55.4 4 = Q 2 2 2 u tan

Shallow anchor in Clay

Given the situation shown in Figure EX-3. Using equation 38 Fc = 9 D1 = 12 in = 30.5 cm Qu = 33.6 + 66.3 = 99.9 kN ) + F c ( A = W + F c A = Qp 1 c s 1 u c 7 2.5 + c 0.107 = D H = R u 1 1 cr cr =0.107(49)+2.5=7.7 D H = R R 1 1 cr cr kN 33.6 = 19.5) + (49x9 100 30.5 4 = Q 2 p ) H H ( c 2 D + D = Qf 1 n u n 1 kN 66.3 = (3x0.305)] [(8x0.305) 49.5 2x100 10)2.54 + (12 = Q_f

Deep anchor in Clay Assume ca = 0.9c = 0.9(48.0) = 43.2 kN/m2. FS = 3.0 Qall = Qu/FS = 235.3/3 = 78 kN c H D + c ) H -H ( 2 D + D + ) H + c )(9 D ( 4 = Q a 1 s u 1 n n 1 1 u 2 1 u kN 47.4 = 12.63 + 0.64 + 34.17 = Q 2 6x.305x43. 12 2x.305 + .0 6)(.305)48 -(11 12x2x100 10).305 + (12 + 05)] 19.5x(6x.3 + )[9x48.0 ) [(1x.305 4 = Q u 2 u

Bearing Capacity of a Helical Pile in Com-pression

Anchor in Sand (Figure EX-5)

c = 0 γ = 105 pcf Φ = 35 deg 49) (equation 1) -N q( + cN = qult c q 1)] -N ( q + N c A = Q i i ci i qi n i ult

[

Anchor in Clay (Figure EX-6) c = 1000 psf γ = 124 pcf Φ = 0 deg Nq= = 1 (Figure 11) kips 35.2 = 3 105 = FS Q = Q kips 105 = lbs 105,487 = 28,367 + 39,867 + 24,035 + 13,219 = 0)](110) (0.307)(84 + 5)(110) (0.545)(66 + 0)(90) (0.545)(49 + 15)(77) [(0.545)(3 = N q A = ] N q + N c A = Q ult allow qi i i 4 1 i q i i c i i n i ult

[

[

16 = 4 N 7) = 9.6( = D H 8.0 = H 12 10 = D 15 = 3 N 6.34 = D H 6.34 = H 12 12 = D 14 = 2 N 4.67 = D H 4.67 = H 12 12 = D 10 = 1 N 3.0 = D H 3 = H 12 12 = D c 4 4 4 4 c 3 3 3 3 c 2 2 2 2 c 1 1 1 1 max sf 0.545 = 4 ) (10/12 = 4 D = A sf 0.785 = 4 ) (12/12 = 4 D = A sf 0.785 = 4 ) (12/12 = 4 D = A sf 0.785 = 4 ) (12/12 = 4 D = A 2 2 4 4 2 2 3 3 2 2 2 2 2 2 1 1 kips 13.1 = 3 39.3 = FS Q = Q kips 39.3 = lbs 39,335 = 8720 + 11,775 + 10,990 + 7850 = )(16) 0.545(1000 + )(15) 0.785(1000 + )(14) 0.785(1000 + )(10) 0.785(1000 = Q ult allow ult

Lateral Capacity of a laterally Loaded Helical Pile in Medium Clay Assume the situation is as shown in Figure EX-7. Also assume:

Load = 40 kN

c = 1000 psf = 48 kPa Shaft Properties:

L = 8 ft = 2.4 m

2 inch square outside dimension wall thickness = 05 inch

Check to see if buckling will be a concern. From Table 4, soil is a medium clay.

Using Figure 13, situation plots significantly below is medium clay line, therefore, buckling is not a concern.

Lateral Capacity of a Laterally Loaded Helical Pile in Soft Clay

Assume the situation is as shown in Figure EX-7. Also assume:

Load = 40 kN c = 400 psf = 19 kPa Shaft Properties:

L = 8 ft = 2.4 m

Check to see if buckling will be a concern. From Table 4, soil is a soft clay.

Using Figure 13, situation plots near the soft clay line, therefore, buckling is a concern.

Helical shaft properties:

Ep = 30 106 psi = 20.7 107 kPa

I = π(do4 -di4)/64 = 4.8 10-7 m4

From Table 5 assume nh = 500 kN/m4

Assume u* = 15 mm = yield deflection

Using equation 6 from Table 6

Using equation 6 from Table 7

mm 69 = m -0.069 = u 0.83 + u 0.19u/ u u/ = P P * * c f o 6) (Table 0.519 = ) 10 )(4.8x 10 7x 0.032/(20. * 500 = I E / d * n =₅ 5 7 -7 p p o h kN 0.331 = u I E 0.9279 1 = Pcf p p 3 *

Using Equation 6 from Table 7 m -kN 359 = M M M 1.09 = P P c f 0.72 c f o max max

Lateral Capacity of a Laterally Loaded Helical Pile in Overconsolidated Clay Assume the situation is as shown in Figure EX-7. Also assume:

Load = 40 kN

c = 2000 psf = 96 kPa Shaft Properties:

L = 8 ft = 2.4 m

2 inch square outside dimension wall thickness = 0.5 inch

Check to see if buckling will be a concern. From Table 4, soil is a stiff clay.

Using Figure 14, situation plots to the right of the stiff clay line, therefore, buckling is not a concern.

Helical shaft properties:

Ep = 30 106 psi = 20.7 107 kPa I = π(do4 -di4)/64 = 4.8 10-7 m4 m -kN 0.519 = P 0.9271 = M c f c max

Assume u* = 15 mm = yield deflection

Using equation 2 from Table 6

Using equation 2 from Table 7

mm 3.064 = u 0.87 + u 0.15u/ u u/ = M M * * c o

Determine the maximum moment. Using Equation 2 from Table 6

Since Mcmax <Mo, part of soil is yielding.

Using Equation 2 from Table 7

M M 1.00 = M M c 1.0 c o max max 6) (Table m 1.304 = ) 10 )(4.8x 10 .7x 0.057/4(20 * 20000 = I E /4 d * k =₄ 4 7 -7 -1 p p o h m -kN 5.1 = u I E 2 = Mc p p 2 * m -kN 5.1 = M = Mcmax c

1. Stephenson, R.W., ADesign and Applications of Helical Earth Anchors,@ (1988), unpublished notes of a seminar for geotechnical engineering graduate students, University of Missouri-Rolla, Oct. 20, 1988.

1. Clemence, S.P., Thorsten, R.E., and Edwards, B., AHelical Anchors: Overview of Application and Design@ (1990), Foundation Drilling, Dec./Jan. 1990, P.P. 8-12.

1. Das, Braja M. Earth Anchors, Developments in Geotechnical Engineering, Series No. 50, Elsevier, NY 1990.

1. Udwari, J.J., Rodgers, T.E., and Singh, H., "A Rational Approach to the Design of High Capacity ;Multi-helix Screw Anchors," Proceedings, Seventh IEEE/PES Transmission and Distribution Conference and Exposition, April 1-6, 1979, pp. 606-609.

1. Lutenegger, A.J., Smith, B.L., and Kabir, M.G., "Use of In Situ Tests to Predict Uplift Performance of Multihelix Anchors," Special Topics in Foundations, ASCE, pp. 93-108.

1. A.B. Chance Co. Encyclopedia of Anchoring, The A.B. chance Co., 1977.

1. Hoyt, R.M., and S.P. Clemence (1989), "Uplift Capacity of Helical Anchors in Sand," Proceedings of the XII International Conference on Soil Mechanics and Foundation Engineering, Rio De Janeiro, Aug, 1989, pp 1019-1022.

1. Kulhawy, F.H., "Uplift Behavior of Shallow Soil Anchors - An Overview", Uplift Behavior of Anchor Foundations in Soil, ASCE, New York, pp. 1-25, 1985.

1. Clemence, Samuel P., "The Uplift and Bearing Capacity of Helix Anchors in Soil," Contract Report TT112-1, 3 Volumes, Niagara Mohawk Power Corporation, Syracuse, New York (1984).

1. Mitsch, M.P., and Clemence, S.P., AThe Uplift Capacity of Helical Anchors in Sand,@ Uplift Behavior of Anchor Foundations in Soil, ASCE, New York, pp. 26-47 (1985). 1. Mooney, J.S., Adamczak, S., and Clemence, S.P., "Uplift Capacity of Helical Anchors in

Clay and Silt," Uplift Behavior of Anchor Foundations in Soil, ASCE, pp. 48-72 (1985).

1. Carville, Chester, A., P.E., and Walton, Robert W. , AFoundation Repair Using Helical Screw Anchors,@ Foundation Upgrading and Repair for Infrastructure Improvement,@ Geotechnical Special Publication, N. 50, American Society of Civil Engineering, New York, 1995.

1. Meyerhof, G.G., ABearing Capacity and Settlement of Pile foundations,@ Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 102, No. GT3, pp. 197-228, 1976. 1. Hansen, Brinch, J., AThe Ultimate Resistance of Rigid Foundation Piles Against Transveral

Forces,@ Bulletin-12, Danish Geotechnical Institute, Copenhagen, 1951.

1. Meyerhof, G.G. and Ranjan, Gopal, AThe Bearing Capacity of Rigid Piles Under Inclined Load in Sand, Part I: Vertical Piles,@ Canadian Geotechnical Journal, Vol. 9, 1972,. 1. Reese, L.C., and Matlock, H., ANon-dimensional Solution for Laterally Loaded Piles with

Soil Modulus Assumed Proportional to Depth,@ Proceedings of the Eighth Texas Conference on Soil Mechanics and Foundation Engineering, Austin TX, 1965.

1. Davisson, M.T. and Gill, H.L., Laterally Loaded Piles in layered Soil System,@, Journal of the Soil Mechanics and Foundation Division, Vol. 89, No. SM3, American Society of Civil Engineers, 1963.

1. Stephenson, Richard W., and Puri, Vijay, AUltimate Capacity of A.B. Chance Helical Anchors,@ Unpublished report, prepared for the A.B. Chance Co., Centralia MO, 1981. 1. Hoyt, Robert, Seider, Gary, Reese, Lymon C., and Wang, Shin-Tower, ABuckling of Helical

Anchors Used for Underpinning,@ Foundation Upgrading and Repair for Infrastructure Improvement,@ Geotechnical Special Publication, N. 50, American Society of Civil Engineering, New York, 1995.

1. Sowers, G.B. and Sowers, G.F., Introductory Soil Mechanics and Foundations, Third Edition, Macmillan Publishing Co., New York, NY, 1970.

1. Hsiuing, Yun-mei and Chen, Ya-ling, ASimplified Method for Analyzing laterally Loaded single Piles in Clay,@ Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123, No. 11, November, 1997.

1. Poulos, H.G., and Davis, E.HH., Pile Foundaton Analysis and Design, John Wiley & sons, Inc., New York, 1971.