Reply to Discussion on“Empirical methods for determining shaft bearing capacity of semi-deep foundations socketed in rocks”

S.Rezazadeh,A.Eslami

Department of Civil and Environmental Engineering,Amirkabir University of Technology,Tehran,Iran

1.Introduction

One of the challenges for geotechnical engineers is to develop optimum foundation solution to deep foundations.Semi-deep foundations are another foundation category which is discriminated based on their performances in comparison to other foundations.The relatively new concept is becoming increasingly viable to support superstructures,especially in accessible depth,as an alternative for shallow and deep foundations.

Rock-socketed shafts are broadly utilized to carry huge loads in massive projects and high-rise buildings.Upon the evaluation of rock-socketed shaft applicability,some important factors,including the type and magnitude of the structural loads,and the factors related to rock mass characteristics,such as embedment depth into the rocks,rock type,and rock mass engineering properties(such as rock quality designation(RQD)and rock mass rating(RMR))should be taken into account(Turner,2006).

The bearing capacity of rock-socketed semi-deep foundations is roughly composed of two components similar to the axial bearing capacity of a deep foundation:(i)the toe bearing resistance,and(ii)the shaft friction resistance.In rock-socketed shaft,factors including the unconfined compressive strength(UCS)of rock,interface roughness,effective confining stress and the discontinuity of rock mass can affect the shaft bearing capacity(Zhang,2010).

Design approaches for determination of ultimate capacities in shear/base resistance are still based upon empirical regressions obtained from the back analysis of in situ rock-socketed shaft load tests(Serrano and Olalla,2004).In this research,the UCS of rock is used in order to study the shaft bearing capacity,since the compressive strength is a fundamental factor for recognition of intact rocks.

2.Background

A database was compiled based on numerous practical cases to analyze and evaluate the efficiency and accuracy of the equations presented by various researchers on shaft capacity of rock-socketed shafts and to propose proper equations.The database consists of 106 rock-socketed shafts which are categorized into three different series with the available UCS data of rock in addition to the records of static load test carried out in different countries which have been categorized according to the bearing rock type.

In order to understand the capability of different methods suggested by some researchers,a statistical work based on case studies has been performed.Comparing shaft resistance results obtained from the power equation to the measured ones in the graph of Horvath and Kenney(1979),the average value(AV)and standard deviation(SD)are equal to 0.92 and 0.45,respectively,which indicate a reasonable prediction in comparison to measured values.The methods of Williams et al.(1980)and Meigh and Wolski(1979)represent the same AV of 1.33,though a different dispersion of 0.63 and 0.69,respectively,which lead to overestimating the shaft capacity.Moreover,the AVs in the methods of Rosenberg and Journeaux(1976)and Rowe and Armitage(1984)are equal to 1.57 and 2.02,respectively,while the SDs are 0.77 and 0.98,respectively.In line with the conducted statistical studies,Horvath and Kenney(1979)’s method seems to be the most reliable approach in estimating the shaft bearing capacity.

In addition,new methods for individual types of rocks and a general expression without considering the bearing rock type have been proposed using the regression analyses of collected database,as summarized in Table 1.

As the rock-socketed shafts are located in the rock mass(not intact rock),the discontinuities of the rock mass should be considered to determine the shaft bearing capacity.The rock mass properties have not been specifically incorporated into the empirical relationships.Therefore,it is necessary to apply the parameters that represent the characteristics of the rock mass to acquire more realistic outcomes.

Accordingly,when including the rock mass properties in the empirical relationships,a reduction factor must be used for UCS as following:

Table 1Summary of proposed relationships for different types of rocks.

Amongst the suggested reduction factors forαE,accuracy of the following equations correlated to RMR and RQD given by Kulhawy(1978)and Zhang(2010),respectively,has been proved:

3.Verification and addition by Arioglu et al.(2018)

In order to increase the number of data set(n=178)for prediction of shaft resistancersand average UCS of intact rockσrc,the data cited in p.203-204 of Arioglu et al.(2007)were combined with the data set represented in Rezazadeh and Eslami(2017).The prediction capacity of the resulting equation obtained from the regression analysis was found to be in a good agreement with the observed data.The proposed empirical equation in this study comprises a wider range of UCS(0.15 MPa＜ σrc＜ 156 MPa)and various rock types.

The prediction of the resistance in the rock-socketed shafts is also investigated by Arioglu et al.(2018)with a different parameter named rock mass cuttability index(RMCI)instead of UCS.RMCI is a function of RQD and UCS which also has been used in the literature to predict the penetration rate/advanced rate of road headers and hydraulic breakers in mechanized tunneling machinery.The relationship between the shaft resistance(rs)and RMCI is investigated and a new empirical equation is also presented.The prediction capacity of the aforementioned equation is also found to be in a fair good agreement with the presented data in Rezazadeh and Eslami(2017).Since the RMCI is a promising parameter in prediction of shaft resistance,the researchers in the rock-socketed shaft design area should consider this parameter in the further investigations.

4.Conclusions

In the optimum design of semi-deep rock-socketed foundations,prediction of the shaft bearing capacity,rs,is critically important.For this purpose,a database of 106 full-scale load tests is compiled with UCS values of surrounding rocks,in which 34 tests with RQD,and 5 tests with RMR.The bearing rocks for semi-deep foundations include limestone,mudstone,siltstone,shale,granite,tuff,granodiorite,claystone,sandstone,phyllite,schist,and greywacke.

Methods for determining bearing capacity of rock-socketed shafts suggested by various researchers were reviewed and analyzed,and their validity was evaluated through the collected database.Various relationships were derived for individual type of rock in database and a general relation was proposed when the type of rock is unknown.Considering that in practice shafts are socketed into rock mass(not intact rock),a correction factor to incorporate the effects of discontinuities and rock mass properties should be applied to the UCS which is related to the RMR or RQD.

In the discussion raised by Arioglu et al.(2018),a new set of data(n=178)is compiled by adding a data set(n=72)collected by Arioglu et al.(2007)to the data set(n=106)presented in Rezazadeh and Eslami(2017).Another factor named RMCI has been correlated torstopredict the shaft resistance of rock-socketed piles.The prediction capacity of the RMCI versusrsequation is found to be in a promising good agreement with the presented data in Rezazadeh and Eslami(2017).

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