Friction to Unconfined Compression Strength Correlation for Evaluating Capacity of Weak Rock Foundation Sockets

Historically, deep foundations in weak rock have been designed as friction elements using frictional resistance (fs), calculated from the unconfined compressive strength (UCS) of rock. Most of the published correlations of fs to UCS were developed based on load tests on low-capacity piles in specific geological conditions, using UCS values not necessarily representative over the test depth. There is a large variation in foundation design depths calculated using these correlations. This paper presents a correlation between fs and UCS of weak rock, developed using data from 44 bidirectional load tests from high-capacity deep foundations in weak rocks. The dataset used in this study, is one of the largest used for weak rocks, with high test loads in the range of 100–320MN and the depth of foundations mostly in the range of 20–87 m below ground level. Bi-directional load test data from La Maison tower site is then simulated in Plaxis, and ultimate skin friction developed is compared against the skin friction calculated using the new corelation. The actual ground profile and foundation layout of La Maison tower is then modelled in Plaxis with the required foundation depth derived using the recommended corelation, to check serviceability limits. The resulting maximum settlements are found to be well within the acceptable limits. The correlation factor of 0.5 between fs and UCS is thus recommended for estimating rock socket friction for design of deep foundations in weak carbonate rock formations.


V s
Shear wave velocity of a layer obtained from dynamic tests f s The ultimate unit skin friction for the considered layer f b Ultimate unit end bearing for the considered layer α Coefficient relating ultimate skin friction to UCS of rock β b rock socket correction factor ϕ b side resistance factor

Introduction
Deep foundations in weak rock formations are typically designed as rock sockets and the design is a function of the loading magnitude, geometry, elastic properties, and the side resistance of the socket. End bearing may also contribute to the total resistance, when socketed lengths are relatively small. Until the early 1960's there was little research and few acceptable design methods for rock socketed piles (Tomlinson and Woodward 2007). However, in the next decade several investigations of the design of rock socketed bored piles (referred as piles in this paper) resulted in various improved design methods which considered the principles of applied mechanics and the rock socket properties, for example, Pells et al. (1980), Kulhawy and Phoon (1993). Many of these design methods predicted the bearing capacity of piles socketed in rock from unconfined compression strength (UCS) of intact rock. Kulhawy et al. (1993) reviewed these methods to predict rock socket friction (f s ) and highlighted a relative lack of sophistication in earlier empirical methods and also commented that in the load testbased methods, the UCS of rock used in developing these correlations was not the average UCS over test depth and might not represent the values at the test locations. Furthermore, many of these methods were developed mainly for small diameter shallow piles of 700-750 mm diameter, with low shaft frictional capacities mostly below 1-5 MPa and in specific geological conditions (Williams and Pells 1999;Alrifai 2007;Ibrahim et al. 2009;Latapie et al. 2018;Manoj et al. 2020). There is also a variation in the correlation coefficient α of 0.15−0.80 between the lower and upper bound relationships.
Based on a detailed literature survey and comparison of published case studies, mostly focused on the tall towers in the United Arab Emirates (UAE) where more than 20% of world's tall towers are being built, the methods used to estimate ultimate friction (f s ) for high-capacity deep foundations in the weak carbonate rocks, are assessed to be conservative, probably due to a lack of geology-specific methods for the region. (Manoj et al. 2020;Latapie et al. 2018;Alrifai 2007;Ibrahim et al. 2009).
This paper presents the results of a study based on 44 high-capacity load tests on barrettes and piles supporting tall towers in weak rock, with UCS in the range of 1.25-3 MPa as defined in EN ISO 14689 (1999). The load test results along with UCS within the test depth at these locations, are back-analysed to develop a relationship between f s and UCS of rock. The actual friction measured closest to the load cell locations are considered conservatively as ultimate values, while developing these correlations. The rock sockets are actually supported by the rock mass and not the intact rock and therefore using the frictional resistances measured from Bidirectional Static Load test is considered to take in to account the effect of discontinuities in rock and its stress state. Based on the study of high-capacity load tests on large diameter piles and barrettes, a new correlation to estimate ultimate skin friction from UCS in weak rock sockets is recommended in this paper. The correlation was then tested via a load test simulation by finite element modelling of the load test done at the La Maison tower location. Resulting ultimate friction from the simulation, is then compared, and confirmed with the calculated skin friction from the new correlation.
The foundation design of the supertall La Maison tower (Manoj et al. 2020) is then repeated with barrette and pile lengths calculated using rock socket friction calculated using the new correlation. The small-strain stiffness modulus E d obtained from down hole seismic tests is used to model ground stiffness behaviour in the model, as recommended by Poulos (2017). Model results show that when pile and barrette lengths are revised using the new correlation, group settlements are found to be within acceptable limits. The new correlation is recommended for use to estimate rock socket friction in weak carbonate rock formations and a design chart is proposed on this basis.

Basic Design Approach
Rock socketed piles typically transfer applied load to the supporting ground in side shear, end bearing or by a combination of both. The initial transfer of shaft load through shear stresses on the interface is largely an elastic process and the socket roughness will also play a role in the shear load transfer of rock socketed piles (Poulos and Davids 2005;Poulos 2010, Katzenbach andChoudhury, 2013). The typical load settlement behavior from a pile load test is shown in Fig. 1. The ultimate capacity, Q, of axially loaded pile can thus be expressed as the sum of base capacity Q b , and the shaft capacity Q s . Thus: (1) Q = Q b + Q s and where A b is area of the pile base, f b is unit ultimate end-bearing pressure, A s is area of the pile shaft in rock socket and f s is average unit ultimate frictional resistance of the rock socket.
As the pile is loaded in compression, the movement required to mobilize maximum shaft friction is typically only about 0.3% to 1% of the diameter of pile, whereas the base resistance of the pile needs a downward movement typically in the range of 10 to 20% of base diameter, for its full mobilization at point D in Fig. 1, when the pile will plunge downwards (Tomlinson and Woodward 2007). Moreover, when the depth to diameter (D/B) ratio increases to the range of 8 or higher the mobilised toe resistance will be negligible and most of the load will be carried in shaft resistance (Rezazadeh and Eslami 2017). The high-capacity piles and barrettes socketed in weak rocks, carry the applied load mainly by socket friction and only limited load will be transferred to the base, as evidenced by many reported load tests (Emrem et.al, 2008) including the ones considered in this study. Due to this fact, and also due to bottom cleaning issues as well as the risk of cavities, the piles, and barrettes in weak carbonate rocks for tall tower structures in the UAE are mostly designed as friction elements, ignoring any toe resistance.
From a practical design viewpoint, the ultimate capacity, Q, of an axially loaded pile is thus approximated as equal to the shaft capacity Q s , i.e.
The design approaches currently adopted for most of the tall tower designs in UAE are reviewed below.

Design Correlations and Current Design Practice in UAE
The typical local geology in the middle east region consists of a surficial layer of sand underlain by rock units that are weak, and mostly fit into the description of an Intermediate Geo-material (IGM), which is the material having compressibility and strength in between soil and hard rock as defined in AASHTO (2017). Very weak reddish-brown fine to medium grained Sandstone or Calcarenite and the Sandstone bed overlies weak, Conglomeratic Calcisiltite / Calcisiltite interbedded with Weak, Conglomerate which is followed by Siltstone, Claystone and Mudstone units in deeper layers. Piles and barrettes in the weak IGM (Intermediate Geo Material) and carbonate rocks in UAE are designed typically as friction piles and the end bearing strength is generally ignored in the design due to pile bottom cleaning issues and due to the risk of cavities. Some of the recently published and other commonly adopted correlations for the pile and barrette designs in the UAE are provided in Table 1.
A review of design of tall towers in UAE reveals that large diameter piles or barrettes of most of these towers are designed using the following equation for ultimate skin friction by Horvath et al. (1983), which has actually been developed using load test data from short piles in shale and mudstone: In order to demonstrate the variability in these existing design methods and the existing data gap, a design has been performed using the commonly used equations selected from those presented in Table 1, using the subsurface profile from La Maison tower in Business Bay in Dubai (Manoj et al. 2020). The results, presented in Fig. 2 show that for barrette of 1.2 × 2.8 m size, the required design depth to generate 40 MN design capacity will vary between 10 to 62 m below cut off level of -20 m RL, following these various design methods, demonstrating a remarkable variation in the estimated design requirements. Figure 2 justifies the need to develop a more efficient and optimized design method for high-capacity piles and barrettes, especially for the geological conditions of weathered weak rocks and IGM materials such as the carbonate rocks in the UAE.

Load Cell Tests
The bi-directional load cell test, (Osterberg 1989) is the method often adopted for static load testing for high-capacity piles and barrettes, which overcomes the limitation of the conventional top-loading test where the load capacity is generally limited to about 10 to 40MN. The test separates the resistance and displacement data for each component of the pile (England 2003(England , 2010Tan and Fellenius 2012).
The uni-directional load for a given internal pressure is determined using the load cell's calibration coefficient. Typically, the load cell location is close to the base of the pile as shown in Fig. 3 and determination of side shear and end bearing resistance is straightforward. The loading is continued until either ultimate upward or downward capacity is reached, or until the maximum load cell stroke or load capacity is reached. Distribution of load throughout the foundation length is obtained by use of strain gages within the foundation. Analysis of the test results enables the design engineer to conveniently interpret the friction and end bearing strengths developed.
With design validation and value engineering from load cell test data, it is possible to achieve a significant improvement in the outcomes of the design methods, thereby achieving more efficiency and cost savings. There are several case studies where results of static load test on piles and barrettes in the UAE are presented (Ibrahim et al 2009, Alrifai, 2007, Poulos and Davids 2005. Value engineering and back analysis to revise the design lengths have been attempted, in few cases for high-capacity load cell tests on barrettes and large diameter piles (Haberfield 2013;Pereira et al 2017).
The results from 44 O-cell tests of large diameter piles and barrettes, are used in this paper along with UCS results from the same depth zones, to back analyse and calibrate the data and arrive at an appropriate correlation between rock socket friction and UCS.

The Study Region
The data set collected for this study are all from tall and supertall tower foundation locations. A large number of tall buildings constructed and proposed in recent decades have been in the Middle East region, which justifies the study region selection. The tall and super tall towers in Dubai are mostly clustered along Shaikh Zayed Road and within the Dubai Marina and Business Bay areas, from where the dataset shown in Fig. 4 has been collected.
Tables 2 and 3 provide details of the 44 load tests collected from 18 locations, of which 10 are on barrettes and the remaining tests are on large diameter piles.

Typical Subsurface Conditions in Study Area
The regional geology of Dubai typically consists of surficial loose to medium dense light brown to light grey/grey slightly gravelly, silty sand which is mostly aeolian sand that extends to approximately 17 m to 20 m below natural ground level, with the presence of Sabkha at shallow depths. Sabkha is a Interpreted from load tests for weathered and soft rocks general term used to refer to any salt flat, and the coastal Sabkha around Dubai are typically flat topographic areas of hyper-saline environments (Glennie 1996;Goodall 1995;Kirkham 1998;Macklin et al 2010). The underlying tertiary formation discharges brine into the Sabkha which forms an evaporated crust on the surface due to large evaporation losses when subjected to high temperature. This layer has no significance in the design of deep foundations of tall towers where the cut off level is below this layer, as shown in Fig. 5.

Selection of UCS Values in the Dataset
In order to obtain representative UCS values close to load test locations, the boreholes nearest to the load   pile location were analysed. The test results and rock parameters from the study area are presented in the following sections. A statistical analysis of the range of strength parameters within the study area is presented in Figs. 7a and 7b. Since most of the tall tower locations have several basements, the cut off levels of piles and barrettes are typically below the overburden soils. The piles and barrettes have been designed based on frictional resistance within the rock socket. The depth zone is selected accordingly. Both UCS and PLT test results from all the 18 locations have been collected and studied.
The UCS measurements across all 18 project sites where the 44 load tests are conducted, have been analysed statistically and average rock strength parameters are presented in Figs 7a and b. The rock is weak to very weak with average UCS values in the range of 1 to 3 MPa. An average UCS profile from another similar study reported by Latapie and Lochaden (2016) and Latapie et al (2018) for the same area also supports the conclusion that the vast majority of UCS values are in a similar range, 1.5-3 MPa, to that shown in Fig. 7a and b.

Load Cell Test Data and Back Analysis
Only skin friction measurements from load cell test data have been used in this study. The load cell and corresponding ground parameter data have been collected from load test and foundation contractors as well as from the Dubai creative cluster authority for research purposes, and the project names are therefore confidential. All the locations are within the Dubai region around Dubai Marina to Bur Dubai, as shown in Fig. 4.
The load test data from all 44 tests conducted at 18 locations, and the geotechnical information collected at these locations, are presented in following sections along with results of back-analysis. Out of the 44 tests, 10 are load cell test data on barrettes, and the remaining 34 are for large diameter piles. Since the piles are designed as friction piles, the load cell during load test have been placed near the toe of the pile and measure predominantly the mobilized friction, which has been used in the analysis presented in this paper. At locations away from the load cell, the friction is only partly mobilized, and these data are excluded from the study. Strain gauges near the load cell only were considered in the study, together with UCS values at the corresponding depths.
The load distribution curves were plotted from the measured changes in strain gauge readings and estimated barrette properties based on cross-sectional area calculated from the average diameter from caliper report and modulus of elasticity.
Load transfer (P) at each strain gauge level was calculated as follows: where, Δ = change in strain gauge readings. AE P = equivalent axial barrette stiffness.
Modulus of Elasticity for a concrete cube (E c ) was calculated as 4700 x √ f ck , where f ck is compressive strength of the concrete (Cobb 2009) based on the results of concrete cylinder compressive strength tests at 14 days, conducted at the site. The average unit side shear between any two strain gauge levels of the barrette was calculated as the change in load divided by the surface area between the two strain gauge levels.
None of the load tests have been taken close to overall failure, and the friction close to ultimate values has only been fully mobilized close to the load cell locations and are included in the study. The results of the analysis are presented below, with the results from load tests on barrettes being analysed first and presented in Sect. 5.1. Since the data set (4) P = Δ × AE P for barrettes is relatively sparse, data from tests on large diameter piles are also included and results of analysis for both barrettes and piles are presented in Sect. 5.2.

UCS to Ultimate Skin Friction Correlation for Barrettes
Data from strain gauges closest to the load cell only were considered in the study and the representative values of UCS at each test depth zone corresponding to those respective strain gauges were collected. UCS values and the corresponding mobilized skin friction were plotted for all the ten sets of available barrette test results, and the results are presented in Fig. 8a. Lower bound and upper bound relationship were obtained based on the data plotted. An average UCSskin friction relationship for barrettes was derived as where, f s = maximum mobilised skin friction, MPa, UCS = Unconfined compressive strength of rock, MPa.
The above Eq. 5 is recommended for estimating the ultimate friction for barrettes in weak rock, when it is possible to verify the static capacity by testing preliminary test barrettes using bidirectional static loadcell tests (BDSLT)..

UCS to Ultimate Skin Friction Correlation for all
Barrettes and Piles and Regression Analysis UCS values and corresponding mobilized skin friction were plotted for all the 44 sets of test results available, for both barrettes and piles, and the results are presented in Fig. 8b. For finding the relation between mobilised skin friction and UCS, a linear regression was used for the collected data. Linear regression is a frequently used and well-accepted technique to investigate the potential relationship between a variable of interest and one or more variables. For this study, an opensource tool 'RStudio' was used, which is based on programming language R, a software environment and graphics supported by the R Foundation for statistical computing. The regression analysis shows a coefficient of 0.52 between mobilised friction and square root of UCS as the best fit with a minimal residual standard error 0.2924 and multiple R-squared of 0.8791. Hence it is suggested that the following average equation as shown in Fig. 8b can be adopted as the relationship between mobilised skin friction and UCS, for all deep foundation elements.
Equation 6 is recommended for use to calculate ultimate skin friction developed when large diameter piles or barrettes are socketed into weak carbonate rock with UCS ranging from 0.6 to 3 MPa. It is recommended that the barrette and large diameter pile foundations for tall towers in carbonate rocks be designed using this relationship after verifying the capacity in preliminary tests. The test load for bidirectional load cell testing should then be estimated using ultimate friction predicted by this method and the design capacity should be verified for the site conditions.

Simulation of Barrette Load Test at La Maison Tower
Finite element modelling to simulate the actual load test of the Barrette from the La Maison tower location was done by first modelling a single 1.2mx2.8 m size barrette and 43.5 m length, in Plaxis3D. The soil and barrette were modelled as volumetric elements in a Mohr Coulomb constitutive model. The boundary conditions of the soil profile at the vertical faces are defined in such a way that only vertical displacements are permitted. The bottom of the soil profile is restrained from movement. The load cell was modelled as a gap and restraints were provided to avoid movement in the X and Y directions for the gap. The vertical faces of the gap created to simulate O-cell were restrained from horizontal movement by utilizing surface displacement options. Interface elements were placed along the pile to model the interaction between the barrette and the adjoining soil. A rigid interface R inter of 1 was defined to consider the interaction between barrette and rock. The interface factor R inter (6) Mobilised ultimate skin friction f s = 0.52(UCS) 0.5 Fig. 8 a UCS versus mobilised skin friction for barrettes. b. UCS versus mobilised skin friction for barrettes and piles ◂ represents the interface between two different materials, to consider the soil structure interaction and it is defined using the standard stiffness approach available in Plaxis. An initial stage was defined to initialise the stress in the model using K o procedure. The volumetric barrette was then activated, and corresponding interface was also activated. Restraints for the horizontal direction for the loadcell modelled as gap was also activated at this stage before activating the loading as uniform pressure. Schematic diagram of the test simulation in the model is presented in Fig. 9 below. The elevation considered in the model for loadcell and soil layers were as per actual conditions at the site. The design parameters used in the model are presented in Table 4.
Elastic modulus for concrete was taken 42.56 kN/ mm2 based on the concrete cube test result from site.  The concrete grade was C80 and cube test strength was 81 MPa. The generated soil profile, pile element and the soil interface, distributed load and generated mesh are shown in Fig. 10.
Loading was simulated by applying an equivalent surface pressure at the top and bottom of the load cell. Then with the calibrated model, a prescribed displacement of 200mm, estimated as 10% of the  Calibrated ultimate skin friction from load test simulation compared with the predicted friction from recommended equation equivalent barrette diameter, which is assumed to be the settlement at ultimate load (Tomlinson and Woodward 2007), was applied to the calibrated O-cell model to check for the ultimate skin resistance. . The interface friction generated in this model, which is the ultimate friction at the prescribed settlement, was then compared to the skin friction estimated using the proposed equation 6, as presented in Figure 11.
It can be observed from the test simulation that the ultimate friction developed based on the back analysis using the criteria of 200 mm (10% of equivalent pile diameter) is much higher than that estimated using the recommended correlation factor of 0.52 in Eq. 6. The correlation factor of 0.52 is therefore considered both reasonable and conservative for the purposes of barrette or pile design.

Design Flow Chart
A flow chart for design of piles and barrettes in weak carbonate rock deposits similar to those found in the Middle East region, is presented in Fig. 12.
While developing this correlation, only the data close to the load cell where maximum friction is developed, has been used. Even though the tests are not taken to failure, the friction values are assumed to be ultimate values while developing the correlation, and therefore the developed equation is considered to be conservative.

Conclusions and Recommendations
The following recommendations are made in this paper. • Equation 6, f s = 0.52(UCS) 0.5 be used for estimating ultimate skin friction in weak rock sockets. • For major projects, preliminary pile load testing should be conducted by a bi-directional load cell to validate the load capacity initially estimated by above equation. • The load test results should be calibrated by back analysis to match the results obtained from the equation above. • For slightly higher values of UCS in the weak carbonate rocks, the same Eq. 6 may be used if the design will be verified by load cell testing. • In the less desirable case in which there is no testing planned, the lower bound relationship of f s = 0.4(UCS) 0.5 may be used.
A flow chart for the design of piles and barrettes in weak rock, similar to the ones found in the Middle East region, is presented in Fig. 12. Use of the suggested approach should also assist in a reduction of the carbon footprint associated with foundation construction in such ground conditions. Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. The authors have no relevant financial or non-financial interests to disclose. The datasets generated during and/or analysed during the current study are not publicly available due to confidential nature of data but may be available from the corresponding author on reasonable request.

Data Availability
Enquiries about data availability should be directed to the authors. The datasets generated during and/ or analysed during the current study are not publicly available due to confidential nature of data but may be available from the corresponding author on reasonable request.

Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.