A perceived advantage of screw-type foundations is the ability infer aspects of foundation performance from quantities measured or observed during installation, espec ially the installation torque. A particular concept widely used in practice is to correlate installation to rque to ultimate capacity. This notion has proven useful as a field verification technique despite the abs ence of validated models that relate key variables of interest, such as installation torque, axial (crow d) force, geometrical parameters, and soil strength. This paper considers pr evious work by the co-authors and collaborators on analytical, numerical, and physical modelling of screw piles to relate the quantities measured or controlled during installation (e.g., installation torque) to the ultimate capacity and soil s trength. Attention is given to saturated clay as a particular soil type amenable to simplified analysis. An analyt ical model for a single-helix pile is considered as a means of directly relating the ultimate capacity and undra ined shear strength to the installation torque, crowd force, plate pitch, plate d iameter, shaft diameter, insta llation depth, and surface roughness. The connection between the installation variables and ultimate capa city—and the sensitivity to crowd force in particular, a quantity that is typically not measured during fi eld installations—is also discussed. The theoretical predictions are compa red against data obtained from small-scale laboratory experiments that suggest the installation torque relates to the remolded strengt h of the soil. Keywords: screw piles, helical anc hors, installation, torque-ca pacity correlation, modeling, experiments INTRODUCTION Screw piles are deep foundations that are twisted into the grou nd through an applied torque. Advantages over driven piles or drilled foun dations include the relative s ilence of the installation, with low ground vibrations, and the possibility of being easily decommissioned by reversing the direction of twisting. Screw piles are now routinely encounter ed as a flexible, low-cost sol ution for numerous applications (Figs. 1 and 2), and they are also being cons idered for applications in offs hore energy production due to limitations being imposed with respect to decommissioning and underwater no ise. Also known as “screw anchors,” “helical piles”, or “helical anc hors,” screw piles consist of helices or helical plate elements attached to a central shaft. Figure 3a s hows the components of a single-helix pile and key variables. The diameters of the shaft and helix are denoted by d and D, respectively, and p is the pitch of the helix. Variable H denotes depth of the helical plate, and T and N denote the torque and axial (crowd) force applied during installation. In typical applications, the pile includes multiple helical plates, and the shaft is composed of segments th at allow for it to extend to la rge depths into the soil. Fig. 1. Selected applications for helical anchors: (a) underpin ning of shallow foundations; (b); ground anchorage; (c) tiebacks; (d) control of buoyancy for bur ied and underwater pipelines (Hambleton et al. 2014; reproduced with permission from the Aus tralian Geomechanics Society) Fig. 2. Installation of screw piles (helical anchors) to be used as tiebacks in a sl ope stabilization project A compelling concept utilized widely in practice is that the in stallation torque should, in principle, relate to the ultimate capacity of the pile . In other words, a larger ins tallation torque implies a larger capacity. This concept of “torque-capacity correlation” is embodied in the fol lowing formula (Hoyt and Clemence 1989): maxFK T [1] where Fmax is the ultimate axial capacity of the pile in tension or compr ession and K is the “capacity-to- torque ratio.” Perko (2009) ascertained the following empirical expression for K based on numerous field measurements: 0.921433Kd [2] Fig. 3. Schematic of a single-helix screw pile: (a) key variabl es; (b) stresses and resultant forces generated on the shaft and helica l plate during installation (Hambleton et al. 2014; reproduced with per mission from the Australian Geomechanics Society) In Eq. [2], K and d have units of m-1 and mm, respectively, such that Fmax and T in Eq. [1] have units of N and Nꞏm. Standard practice is t o assume that Eqs. [1] and [2] a pply to the ultimate capacity in both tension and compression, and this is supported by data showing that K is only slightly higher in compression compared to tension (Perko 2009). The equations above are assum ed to hold regardless of the soil type. A concept explored in this paper specifically is that the insta llation torque should relate to the strength of the soil. This concept has not received prior attention in larg e part due to the absence of theoretical or empirical models that involve soil strength as a variable, as e videnced by Eqs. [1] and [2]. Provided installation torque can be related to soil strength, a record o f installation torque with depth could potentially be interpreted to determine a soil strength profile in much the same way as a cone penetration test is used to infer soil strength from tip resistance. This paper considers the theoretical model proposed by Hambleto n et al. (2014) as a means of understanding the merits and limitations of torque-capacity correlation and, by relating the installation response to soil strength, the possibility of reg arding the installation process as a form of in situ testing. Attention is limited to the case of installation and u ltimate loading under undraine d conditions (e.g., saturated clay), and focus is exclusively on the single-he lix configuration shown in Figur e 3. The analysis highlights the fact that the capacity-to-torque ratio in Eq. [1] depends on not only the sha ft diameter but also the crowd force and undrained shear strength of the soil among other variables. ANALYTICAL MODEL FOR SCREW PILE INSTALLATION IN CLAY Hambleton et al. (2014) developed a theoretical formula that pr edicts the installation torque for a single- helix pile installed in undrained conditions (e.g., saturated c lay). As illustrated in Fig. 3b, the underlying analysis considers the total installation torque T as the torque mobilized along the shaft ( Ts) and at the helical plate ( Tp). Similarly, the axial (crowd) force N is the summation of resistance along the shaft ( Ns) and the plate ( Np). Upon assuming that the displacement rate Δ u and rotation rate Δ ω are determined by the helix pitch p (so- called neutral rotation with Δ ω/Δu = 2/p), Ts and Ns are determined by assuming that the shear stresses mobilized along the shaft are co-axial with the incremental axi al displacement and rotation of the pile, as shown in Fig. 3b. The shear str esses are assumed to be uniform along the shaft and given by τ = αsu, where α is the so-called adhesion coefficient (0 ≤ α ≤ 1) and τ = (τω2 + τu2)1/2. The case α = 0 corresponds to a perfectly smooth (frictionless) shaft or no contact, and the ca se α = 1 corresponds to perfect adhesion b e t w e e n t h e s h a f t a n d t h e s o i l , s u c h t h a t t h e u n d r a i n e d s h e a r s trength su is fully mobilized along the interface. The torque and axial force at the plate, Tp and Np, are determined based on the following yield envelope, determined from a large number of finite element simulations fo r a single deeply embedded helical plate subjected to combined torque and axial force (Todeshkejoei et a l. 2014): ,max ,max1qr pp ppNT NT         [3] where 1 222 23 ,max ,max1.07, 5.16 8.02 10.82 1 1 0.74 0.33 ,pu p upqr D dp pNs D T s D D DD                 [4] The relationships given in Eq . [4] are valid for 0.16 ≤ p/D ≤ 0.48 and 0 ≤ d/D ≤ 0.4, and they are based on the assumptions of perfect adhesion between the shaft and soil, as well as plate thickness t = 0.05 D. In Eqs. [3] and [4], Np,max is the ultimately capacity of the plate under pure axial loadi ng (Tp = 0), which for all values of p/D and d/D remains close to the theoretical capacity of 12.42 suD2 for a deeply embedded circular plate (Martin and Randolph 2001). The final formula derived by Hambleton et al. (2014) can be exp ressed as 1 23 ,max22 2 22 2 22 2 ,max11s i g n 2qr uu u p ps d H s dHp s dHpTT N N N pd pd pd                  [5] where q, r, Np,max and Tp,max are given by Eq. [4]. Equation [5] is slightly adapted from th e original expression given by Hambleton et al. (2014) to allow for the case when cro wd N is insufficient to overcome the resistance along the shaft, such that the force generated on th e pile by the soil must be directed downward (Np < 0). In Eq. [5], the function sign( x) assumes values of sign( x) = 0 for x ≤ 0 and sign( x) = 1 for x > 0, and the function | x| gives the absolute value of x. Despite its apparent complexity, Eq. [5] provides a straightfor ward way of relating the torque T, crowd force N, undrained shear strength su, shaft roughness α, embedment depth H, and the parameters that define the pile configuration ( d, D, and p). The formula can be easily programmed into a spreadsheet, whi ch can then also be used to solve for any variable as a function of th e others. The Appendix shows an example completed with an Excel spreadsheet available for download on t he first author’s website: https://sites.northwestern.edu/hambleton/resources/ . Figure 4 plots the torque T computed using Eq. [5] for a typical set of parameters: d = 50 mm, D = 250 mm, p = 70 mm, H = 1.5 m, su = 40 kPa, and α = 1 (full shaft adhesion). The torque is plotted as a function of the crowd force N to highlight two particularly important features. First and fo remost, it can be observed that Eq. [5] directly provides a prediction of the pile’s axial capacity by consideri ng the particular case T = 0 and solving for the axial force N. This point corresponding to the maximum axial force is indica ted as “pile capacity” in Fig. 4. This value is somewhat larger than t he capacity of the plate alone due to resistance generated along the shaft, which is also responsible for revers ing the direction of the axial force on the plate (Np < 0) at low values of the crowd force, as indicated in the plo t. The second important feature to recognize is that the installation torque T is a function of the crowd force N, a fact that is notable due to the absence of any consideration for the crow d force in empirical torque-ca pacity correlations suc h as Eqs. [1] and [2]. Indeed, guidance pertaining to how much crowd force should be a pplied during installation is limited (Perko 2009), and unlike installation torque, crowd force is typically not measured during construction. Figure 4 includes the value of tor que obtained from the empiric al torque-capacity correlation given by Perko (2009) and encapsulated in Eqs. [1] and [2], assuming F max is given by the plate capacity Np,max. This value of 638 Nꞏm determined using the empirical formulas agrees surprisingly well with the value of 611 Nꞏm predicted for zero crowd force using Eq. [5]. However, the discrepancy between the constant value obtained using the empirical formula and the values obtained us ing the theoretical model grows as the crowd force increases. RELATIONSHIP BETWEEN TORQU E AND ULTIMATE CAPACITY The analytical model presented in the previous section suggests that the installation torque is indeed directly related to ultimate capacity. However, the model also suggests that the capacity-to-torque ratio K commonly used in torque-capacity correlation is not in fact a constant t hat depends only on the shaft diameter but rather a function that depends on crowd force, soil strength, s haft roughness, embedment depth, and other parameters defining the pile configuration. The simplest means of obtaining a theoretical prediction of K is to assume, as commonly done in practice, that the ultimate capa city of the pile Fmax is identical to the plate capacity, which is given in Eq. [5] by the variable Np,max. Upon equating Fmax = Np,max, Eq. [5] can be used to compute the capacity-to-torque ratio K directly. Fig. 4. Predictions of installation torque T from Eq. [5], plotted against axial (crowd) force N, for assumed parameters d = 50 mm, D = 250 mm, p = 70 mm, H = 1.5 m, su = 40 kPa, and α = 1 (rough shaft) Figure 5 shows theoretically predicted values of the capacity-t o-torque ratio K in comparison to the empirical values obtained using Eq. [2]. The theoretical predic tions, totaling roughly 100 in Fig. 5, are obtained using Eq. [5] with randomized parameters that fall in to the following ranges: 50 mm ≤ d ≤ 400 mm, 250 mm ≤ D ≤ 750 mm, 30 mm ≤ p ≤ 140 mm, 1 m ≤ H ≤ 4 m, and 10 kPa ≤ su ≤ 100 kPa. The adhesion coefficient α was set to α = 1 for all calculations. The figure shows that the theory ten ds to follow the empirical relationship overall but that significant deviati ons are present as a result of variations in the capacity-to-torque ration produced by changes in individual par ameters. It must be emphasized that these deviations are not random but rat her variations that are predic ted by the theoretical model of Eq. [5]. This scatter is rather remarkable in comparison to the deviations ev ident in the data compiled by Perko (2009) and reproduced in Fig. 5, which has been heretofore tacitly att ributed to random error and unattributed to the effects of any particular parameters. RELATIONSHIP BETWEEN TOR QUE AND SOIL STRENGTH An overlooked feature of screw piles is the possibility of infe rring soil strength from the measured response during installation. This is directly reflected in Eq. [5], whi ch in principle can be solved to determine the undrained shear strength su as a function of all other variables. While the equation does not lend itself being solved with respect to su explicitly, su can be computed numerically. A spreadsheet for computing su, when all other quantities are known, can be downloaded from the firs t author’s website: https://sites.northwestern.edu/hambleton/resources/ (see also Appendix). Fig. 5. Relationship between the capacity-torque ratio K and the shaft diameter d as predicted by the theoretical model of Eq. [5] for randomized inputs compared against the values obtained using th e empirical formula of Eq. (2) (Perko 2009) Data obtained by Todeshkejoei (2019) from small-scale laborator y tests is used to illustrate how soil strength can be assessed from measured torque and axial (crowd) force. Todeshkejoei’s tests were completed on kaolin samples usi ng a model screw pile with shaft diameter d = 10 mm, plate diameter D = 40 mm, and pitch p = 8.5 mm. Piles were tested in various configurations and unde r a range of loading protocols, but here only the data corresponding to neutral inst allation of a single-helix pile is considered. While the pile was instrumented with strain gauges to measure t orque and axial force at various locations along the shaft, only the measure ments corresponding to the top of the shaft, which correspond to the total installation torque and total axial (crowd) force, as might be measured during a field installation, are presented and discussed here. The clay samples were prepared by mixing kaolin with a high water content to form a slurry, and then consolidating the mixture in a press . The reader is referred to the thesis by Todeshkejoei (2019) for additional details. Figure 6 shows the data collected by Todeshkejoei (2019) for th e two tests completed by installing the pile through “neutral rotation,” such that the advance rate of the p ile per revolution is equal to the pitch (Δ ω/Δu = 2/p). It should be emphasized that the smooth curves plotted in Fi g. 6 were obtained by digitizing and replotting the data from Todeshkejoei’s thesis, which results e ffectively in some filtering that does not in any substantive way obfuscate the trends in the original data. The curves were slightly adjusted, using some degree of judgement, such that all curves originate from the or igin. The two tests plotted in Fig. 6 correspond to the same test completed at different locations ac ross the clay sample, indicating a high degree of repeatability. Fig. 6. Axial (crowd) force and torque measured by Todeshkejoei (2019) for a single-helix pile installed in clay Figure 7 shows the values of undrained shear strength su back-calculated from the data plotted in Fig. 6 using Eq. [5]. Only the data for “Test 1” is considered in the back-calculation. An adhesion coefficient of α = 1 is assumed, but all other parameters are measured or other wise known quantities. Figure 7 also shows the intact strength measured us ing a T-bar, as well as the remo lded strength obtained by dividing the intact strength by the measured sensitivity of su,intact /su,remolded = 3 (Todeshkejoei 2019). It can be observed that the back-calculated values of the undrained shear strength deviate from the remolded strength at small embedment depth but match the remolded strength closely as the embedment depth increases. The source of the discrepancy at small embedment depth is unknown but not unexpected given the complex deformation induced as the screw pile first comes into contact with the soil. Similarly, the strong correlation between the measured installation response and the remolded str ength is as one might expect, given the large shear deformations produced as the screw pile is twisted into the ground. CONCLUDING REMARKS The analysis considered in this paper casts new light on the co ncept of torque-capacity correlation and provides some evidence to suggest that soil strength can be inf erred by measuring the installation response of screw piles in much the same way that strength is inferred f rom other types of in situ tests (e.g., cone penetration or T-bar). The paper shows that the theoretical rel ationship derived by Hambleton et al. (2014) for a single-helix pile in clay can be used as the basis for co mputing capacity-to-torque ratios that include dependence on key parameters suc h as crowd force, soil strength , shaft roughness, embedment depth, shaft diameter, plate diameter, and helix pitch. Moreover, the analys is reveals that the capacity-to-torque ratio should not be considered a consta nt but rather a function of th e numerous parameters involved. The analysis presented in this paper considering experimental data from smal l-scale testing on saturated clay further suggests that one can potentially infer the remolded strength o f fine-grained soil from measured installation torque and axial (crowd) force. These conclusions require valid ation from carefully completed full-scale testing. Fig. 7. Comparison of back-calculated and measured strengths fr om installation data collected by Todeshkejoei (2019) for a single-helix pile instal led in clay (“Test 1” only) This paper considers only a limited subset of the possible conf igurations and soil types encountered in applications. In addition to va lidating and refining the model described in this paper, extensions to multi- helix systems and other soils types, particularly sand, represe nts areas of future work. APPENDIX: SPREADSHEETS Spreadsheets for computing torque and shear strength using the theory described in this paper can be downloaded on the first author’s website: https://sites.northwestern.edu/hambleton/resources/ . Figure 8 shows an example calculati on of installation torque. ACKNOWLEDGEMENTS The content of this paper was first presented at the 1st Intern ational Symposium on Screw Piles for Energy Applications in Dundee, Scotland on May 27-28, 2019, the procee dings of which include an extended abstract that reproduces a small portion of this work (Hambleto n and Stanier 2019). This work could not have been completed without enab ling financial support from the Australian Research Council (ARC) and the National Science Foundation (NSF), in particular through AR C award numbers CE110001009 and DE160100328 and NSF award number CMMI 1846817. Fig. 8. Spreadsheet for computing installation torque T for specified values of undrained shear strength su, adhesion factor α, helix diameter D, helix pitch p, shaft diameter d, embedment depth H, and axial (crowd) force N based on Eq. [5]