HELICAL FOUNDATIONS AND TIE BACKS. State of the Art. Richard W. Stephenson. Professor of Civil Engineering. University of Missouri-Rolla

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1 ELICAL FOUNATIONS AN TIE BACKS State of the Art Richard W. Stephenson Professor of Civil Engineering University of Missouri-Rolla Rolla, Missouri 6509 June 6, 997 November, 003 (0:AM)

2 INTROUCTION...3 ISTORY...3 Modern Usage... ELICAL PILE ESIGN...7 Prototype...8 Theoretical...8 Semi -empirical...8 Empirical...9 UPLIFT CAPACITY OF ELICAL PILES...9 General...9 Semi-Empirical elical Pile Capacity...0 Individual Plate Capacity Method...0 Kulhawy Method... Clemence Method...6 Uplift capacity of shallow anchors in sand...6 Uplift capacity of deep anchors in sand...5 Uplift capacity of helical anchors in clay...8 Empirical Method....3 BEARING CAPACITY OF ELICAL PILES...33 Bearing Capacity esign of elical Piles...3 LATERAL CAPACITY OF ELICAL PILES...36 Analysis Based on Limiting Equilibrium or Plasticity Theory...36 Analysis Based on Elastic Theory...37 Analysis Based on Nonlinear Theory...37 Simplified Method for Nonlinear Analysis of elical Piles in Clay...39 BIBLIOGRAPY...6 EXAMPLE PROBLEMS...8 Uplift Capacity...8 Shallow Anchor in Sand...8 eep Anchor in Sand...9 Shallow anchor in Clay...50 eep anchor in Clay...5 Anchor in Sand...5 Anchor in Clay...53 Lateral Capacity of a laterally Loaded elical Pile in Medium Clay...53 Lateral Capacity of a Laterally Loaded elical Pile in Soft Clay...5

3 ELICAL FOUNATIONS AN ANCORS STATE OF TE ART 6/6/997 R.W. Stephenson, P.E., Ph.. INTROUCTION elical 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 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 ISTORY elical foundations have evolved from early foundations known as screw piles or screw The earliest reported screw pile was a timber fitted with an iron screw propeller that was twisted into the ground( ). 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 They were then immediately withdrawn and the hole formed was filled with a crude form of concrete and served as foundations for small structures.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 8th century for support of waterfront and in soft soil conditions for bridge structures as early as the 9th century. Power installed foundations were developed in England in the early 800's by Alexander Mitchell. In 833, Mitchell began constructing a series of lighthouses in the English tidal basin founded on his new screw ( The first commercially feasible helical anchor was developed in the early 900'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( ). Modern Usage Modern helical anchors are earth anchors constructed of helical shaped circular steel plates welded to a steel shaft (Figure ). 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. 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. elical 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 3

4 Figure : Modern elical Pile

5 Figure : Installation of elical Pile multi-helix anchors develop capacities of up to 00,000 lbs. (50 kn). In the past 0 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, tie downs 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 behavior of helical anchors. Since about 975, a number of researchers have studied 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( ). owever, studies in the lateral and bearing (compression) load performance are reported as well. 5

6 ELICAL PILE ESIGN 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. owever, 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 semiempirical 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 ( )( )( )( ). 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 been carried out on the performance of helical piles under lateral loading. owever, significant 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. 6

7 UPLIFT CAPACITY OF ELICAL 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 nonhomogeneities, groundwater levels, soil plasticity and volume change potential as well as installation procedures and equipment. Semi-Empirical elical 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: u n () U i i where n is the number of helices and ui is the ultimate uplift capacity of the individual helix. ui can be computed from bearing capacity theory as: where: q u i u i q i diameter of helix (3) i epth from ground surface to helix γ effective unit weight of soil above helix 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. N c *, N γ * and N q * are bearing capacity factors on cohesion, friction and surcharge respectively. For cohesive (clay) soils, N c * is normally taken as 9.0 for / > 3. For / 3, N c * is normally taken as 5.7. N γ * and N q * are taken as 0 and respectively. For helical foundations embedded in cohesionless (sand) soils, c is zero and N γ * and N q * vary as a function of the coefficient of friction (Φ) of the sand. Meyerhofs values of N γ * and N q * are often used and are presented as Table, below. Kulhawy Method. Kulhawy ( ) described a method of analysis of the uplift capacity of helical anchors by describing their behavior as intermediate between the grouted and spread anchors (Figure 3). 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 shearing resistance along the interface is said to be controlled by the friction angle and state of stress 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: u i xa * * cn c + iγ N γ + γ A area of helix 7 i N * q ()

8 u p+ f +W f () u Ultimate uplift capacity p Top plate (cone breakout) capacity f Cylinder friction capacity W f Weight of helical pile (often neglected) For cohesionless (sand) soils, Kulhawy recommended the following equations: Table Meyerhof s Bearing Capacity Factors Φ (deg) N c * N q * N γ *

9 where: ( max ) A f ( q N q ζ ζ ζ )+W f + (5) p p (max) Top plate capacity limit A f Area of top helix q effective surcharge γ W f Effective weight of helical pile alone tu Tip capacity in uplift (usually neglected) q qr qs qd tu Figure 3: Force model for helix 9

10 The N q term is a bearing capacity factor given by: π φ N e φ _ q tan 5 + (6) log I r 0 ζ qr exp ( - 3.8) tanφ +(3.07 sinφ ).0 + sinφ (7) G E I r (8) q tanφ (+ ν ) i qi tanφ The ζ terms are modification factors for soil rigidity (ζ qr ), anchor shape (ζ qs ), and anchor depth (ζ qd ) as given below. ζ + tanφ qs (9a) ζ qs + tanφ (9b) - ζ qd + tanφ(- sinφ ) tan (9c) with the tan - term in radians. G soil shear modulus E soil elastic modulus The cylinder friction capacity, f, is computed from the following equation: where: f k k o P(z) σ v k P(z) σ v k u o (z)( tanδ )(z)dz δ (z) tan φ(z) φ P helix perimeter σ v effective vertical stress k coefficient of horizontal earth pressure δ effective interface friction angle k o Coefficient of earth pressure at rest φ Effective stress soil friction angle δ/ φ 0.9 k/k o 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: β r f(reduced) () f β 0 0 (0)

11 δ β β β tan k 3 + o o o r () Clemence Method. A significant series of studies on helical anchor uplift capacity was done by Clemence ( ), and later summarized in Mitsch and Clemence ( ) and Mooney, Adamczak, and Clemence ( ). 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: + f p u (3) Uplift capacity of shallow anchors in sand (Figure ): +W 3 + k s 3 u u φ φ φ γ π tan cos tan () The weight of the soil, W s can be expressed as: + ) +( + )+ ( 3 W s φ φ π γ tan tan (5) as non-dimensionalized these equations into: A F p q γ (6) ) ( k A F u p q φ φ φ γ tan cos tan (7) Similarly: A W F s q φ φ γ tan tan (8)

12 Figure : Idealized failure surface in sand for shallow anchor condition

13 Let Combining: F q p γ A R φ 0.5 φ R k u( tanφ ) cos tan R R φ φ tan +8R tan (9) (0) F q is called the breakout factor by as. To determine F q the value of k u must be determined. Mitsch and Clemence() showed that this value varies with the soil friction angle, Φ. Their values can be expressed as: ku 0.6 +m () The variation of m is given below. Table Variation of m Soil friction angle, Φ (degrees) m The magnitude of k u increases with / up to a maximum value and remains constant after that. This maximum value is attained at ( / ) cr R cr. The variation of k u with / and Φ are plotted in Figure 5. Substituting the appropriate value of k u and R into the previous equation, the variation of the breakout factor is shown in Figure 6 and Table 3. Now, 3

14 Figure 5: Variation of k u with / π p F qγ A F qγ () The frictional resistance that occurs at the interface of the cylinder is given as: π aγ ( n - )k utanφ (3) f a average helix diameter. Therefore the ultimate uplift capacity for a shallow anchor in sand is: π π + γ + n u F q ( γ )( n - )k u tanφ ()

15 Table 3: Variation of Breakout Factor F q for Shallow Anchor Condition F q R / Φ 5 Φ30 Φ35 Φ0 Φ

16 Φ 5 deg 00 Φ 0 deg Φ 35 deg F q Φ 30 deg Φ 5 deg / Figure 6: Variation of breakout factor with / for shallow condition Uplift capacity of deep anchors in sand: + + u p f s p f s bearing capacity of the top helix frictional resistance of the cone between the helices shaft friction resistance 0 where F * q π * p F q γ deep anchor breakout factor (5) (6) The magnitude of the F q F q * is determined by setting R R cr and k u k u(max) in equation 0. F q * has been plotted in Figure 8. The frictional resistance f is computed using: 6

17 π u a γ ( n - )k u max tanφ (7) + where n a The two equations can be combined to yield the net ultimate uplift capacity for deep anchors in sand: π * π + γ + n u F q γ ( n - )k u max tanφ (8) 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 It is recommended that the optimum spacing of the helices be about 3 apart. A factor of safety of.5 or more should be applied to the ultimate uplift capacity to determine the allowable or working uplift capacity. 7

18 Figure 7: Failure surface for deep helical pile in sand 8

19 eep Anchor Breakout Factor, F q * Soil Friction Angle (deg) Figure 8: Variation of deep anchor breakout factor with soil friction angle 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: s u c u (9) Uplift capacity of shallow helical anchors in clay. For shallow anchors ( / ) ( / ) cr ), the failure surface at ultimate load extends from the top helix to the ground surface (Figure 9 ). If the / ratio is relatively large then the failure zone will not extend to the ground surface and the deep anchor situation controls. For shallow anchors: u p+ f (30) where: p bearing capacity of the top helix f bearing due to friction along enclosed cylinder between helices. p A c F c + W s A( cu F c + γ ) (3) Where A area of the top helix F c breakout factor 9

20 . u Φ/ W s Φ/ p n f Figure 9 Failure mode for shallow helical pile in clay γ unit weight of soil above top helix distance between the ground surface and the top helix F c is related to the bearing capacity factor N c in that it increases with depth of embedment up to a maximum of 9 at the critical R cr ( / ) cr value that depends on the undrained cohesion, c u (kn/m ) as in: R cr cr 0.07 cu+.5 7 (3) 0

21 F c ( / )/( / ) cr Figure 0: Variation of F c with ( / )/( / ) cr The variation of the breakout factor F c is plotted as a function of ( / )/( / ) cr in Figure 0. The frictional resistance of the cylinder of soil between the helices can be computed from: + n f π cu ( n ) (33) Combining: π + n u ( cu F c + γ )+ π ( n - )cu (3) Uplift capacity of deep helical anchors in clay. For the deep anchor condition ( / )> ( / ) cr deep anchor criteria holds (Figure ). The capacity for this case is given below. + + (35) u p f s Where s resistance due to adhesion at the interface of the clay and the anchor shaft located above the top helix. π p ( )(9cu+ γ ) (36) + n f π cu ( n ) (37) s π s ca (38)

22 Where c a is the adhesion and varies from about 0.3c u for stiff clays to about c u for soft clays and s is the shaft diameter. Combining: c + )c - ( + )+ + )(9 c ( a s u n n u u π π γ π (39) Figure : eep helical pile in clay

23 All ultimate uplift capacities should be divided by an appropriate factor of safety to set the allowable(working) factor of safety, i.e., u allow (0) FS 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: u K t xt () where: K t is the empirical factor relating installation torque and uplift capacity and T is the average installation torque. Currently, K t values are reported between 3 feet - for large (8 inch) extension shafts to around 0 feet - for all small (3 inch) shafts. 0 feet - is most widely used in the industry. BEARING CAPACITY OF ELICAL 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( ). Of particular importance is the general relationship between installation torque and helical pile capacity. It is possible to develop site-specific K t 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. elical 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 esign of elical Piles The bearing capacity of helical piles in compression is based upon the general bearing capacity equation: ' ' q cn + q(n - ) () ult Where: c soil cohesion q overburden pressure γ i γ effective unit weight i depth to helix c q 3

24 N c and N q are bearing capacity factors for circular plates at varying / values. Although there are some minor differences in these values depending upon the particular theory adopted, in general N c and N q are taken from Figure ( ). 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. n ult Ai ci N ' +q ( N ' -) (3) i [ i ] A i individual plate area c i cohesion of soil at and beneath helix I q i γ i i overburden pressure at helix i N ci Bearing capacity factor on cohesion for helix i (Figure ) N qi Bearing capacity factor on overburden for helix i (Figure ) c i q i 000 Nc* and Nq* 00 0 Nc / 7 7 Nq Soil Friction Angle (deg) Figure : N c * and N q * as a function of soil friction angle Φ

25 EXAMPLE PROBLEMS Uplift Capacity Shallow Anchor in Sand Given the situation shown in Figure EX-. Using equation : π π γ + n u F q + ( γ )( n - )k u max tanφ 36 R Interpolating from Table 3, F q k u.3 (Figure 5). u π x05 π (05)( 8 x - 3 ).3x tan 35 u 56+60,85 lbs FS.5 allow,85 7 lbs.5kips If the water surface were at the ground surface, then: γ γ γ -γ sat water pcf

26 π 0 u 30.06x55. u 590 lbs FS.5 allow 590/.5 36 lbs. kips π (55.)(8-3 ).3x tan 35 x eep Anchor in Sand Given the situation shown in Figure EX-. Using equation 8: k u max R (Figure 5) m cr For Φ 35, m 0.8 (Table ) cr cr 5 < R F * q 50 (Figure 8) π π + n u F qγ + ( γ )( n - )k umaxtanφ (equation 8 ) π 0 u 50x05 π (05)( x -6 ).5x tan 35

27 u lbs FS.5 allow 798/.5,67 lbs. kips If the water surface were at the ground surface, then: π 0 u 50x55. u 730 lbs FS.5 allow 730/ lbs 5.9 kips π (55.)( x -6 ).5x tan 35 Shallow anchor in Clay Figure EX-3 Shallow anchor in clay Given the situation shown in Figure EX-3. Using equation 30 A c F c +W s A( cu F c+ R p γ cr R R cr cr 0.07 cu+.5 7 cr 0.07(9) ) F c 9

28 in 30.5 cm π 30.5 p (9x9 +9.5) 33.6 kn 00 + n f π cu ( n ) (+0).5 f π 9.5 [(8x0.305) (3x0.305)] 66.3 kn x00 u kn

29 eep anchor in Clay u π ( )(9cu + γ Figure EX eep anchor in clay + )+ π n ( n - )cu + π s Assume c a 0.9c 0.9(8.0) 3. kn/m. π u [(x.305 ) )[9x x(6x.305)] (+0) π (- 6)(.305)8.0 xx00 x π 6x.305x kn FS 3.0 all u /FS 35.3/3 78 kn u c a (Equation39)

30 Bearing Capacity of a elical Pile in Compression Anchor in Sand (Figure EX-5) Figure 5 EX 5 Bearing capacity of helical pile in sand c 0 γ 05 pcf Φ 35 deg q cn c + q( N q - ) (equation ) ult A n Ai c N + q ( N ult [ i c i i q i i (0/ ) π π -)] 0.55 sf (0/ ) A π π 0.55 sf 3 (/ ) A3 π π 0.55 sf (0/ ) A π π sf

31 N q 77 N 7.6( max 7).8( max 7) q 90 q γ (05)(3) 35 psf q γ (05)(3+ 5/3) 90 psf q3 γ 3 3 (05)(3+0/3) 665 psf q γ (05)(3+5) 80 psf N N q 3 0 q 0 ult Ai [ ci N c i+qi N q i ] [(0.55)(35)(77)+(0.55)(90)(90)+(0.55)(665)(0)+(0.307)(80)](0) Anchor in Clay (Figure EX-6) n i 3,9+,035+39,867 +8,367 05,87 lbs 05 kips allow ult FS kips Ai q i N qi Figure 6 EX-6 Shallow anchor in clay

32 c 000 psf γ pcf Φ 0 deg N q (Figure ) * * q cn c + q( N q - ) (equation ) ult n ult Ai[ c i i N * ci + q ( N i * qi -)] N c N c 6.3 N c ( max 7) N c 6 (/ ) A π π sf (/ ) A π π sf 3 (/ ) A3 π π sf (0/ ) A π π 0.55 sf (000)()+0.785(000)(5) ,990+, ,335 lbs allow ult 0.785(000)(0) +0.55(000)(6) ult FS 39.3 kips kips

33 BIBLIOGRAPY. Wilson, Guthlac, The Bearing Capacity of Screw Piles and Screwcrete Cylinders, J. Inst of Civil Engineers, London, Vol 3, pp -93, Stephenson, R.W., esign and Applications of elical Earth Anchors, (988), unpublished notes of a seminar for geotechnical engineering graduate students, University of Missouri- Rolla, Oct. 0, Clemence, S.P., Thorsten, R.E., and Edwards, B., elical Anchors: Overview of Application and esign (990), Foundation rilling, ec./jan. 990, P.P as, Braja M. Earth Anchors, evelopments in Geotechnical Engineering, Series No. 50, Elsevier, NY Udwari, J.J., Rodgers, T.E., and Singh,., "A Rational Approach to the esign of igh Capacity ;Multi-helix Screw Anchors," Proceedings, Seventh IEEE/PES Transmission and istribution Conference and Exposition, April -6, 979, pp 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 A.B. Chance Co. Encyclopedia of Anchoring, The A.B. chance Co., oyt, R.M., and S.P. Clemence (989), "Uplift Capacity of elical Anchors in Sand," Proceedings of the XII International Conference on Soil Mechanics and Foundation Engineering, Rio e Janeiro, Aug, 989, pp Kulhawy, F.., "Uplift Behavior of Shallow Soil Anchors - An Overview", Uplift Behavior of Anchor Foundations in Soil, ASCE, New York, pp. -5, Clemence, Samuel P., "The Uplift and Bearing Capacity of elix Anchors in Soil," Contract Report TT-, 3 Volumes, Niagara Mohawk Power Corporation, Syracuse, New York (98).. Mitsch, M.P., and Clemence, S.P., The Uplift Capacity of elical Anchors in Sand, Uplift Behavior of Anchor Foundations in Soil, ASCE, New York, pp. 6-7 (985).. Mooney, J.S., Adamczak, S., and Clemence, S.P., "Uplift Capacity of elical Anchors in Clay and Silt," Uplift Behavior of Anchor Foundations in Soil, ASCE, pp. 8-7 (985).

34 3. Carville, Chester, A., P.E., and Walton, Robert W., Foundation Repair Using elical Screw Anchors, Foundation Upgrading and Repair for Infrastructure Geotechnical Special Publication, N. 50, American Society of Civil Engineering, New York, Meyerhof, G.G., Bearing Capacity and Settlement of Pile foundations, Journal of the Geotechnical Engineering ivision, American Society of Civil Engineers, Vol. 0, No. GT3, pp. 97-8, 976.

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