INTERNATIONAL SOCIETY FOR SOIL MECHANICS AND GEOTECHNICAL ENGINEERING
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Estimation of vertical subgrade reaction modulus from CPT and comparison with SPT for a liquefiable site in Christchurch
N. Barounis1, CEng MICE MIPENZ and Brett Menefy2, CertETn, AIPENZ
1Opus International Consultants, 20 Moorhouse Avenue, Christchurch, New Zealand, email: [email protected] 2Opus International Consultants, 20 Moorhouse Avenue, Christchurch, New Zealand, email: [email protected]
ABSTRACT
A methodology introduced in 2013 (Barounis et al.) for estimating the coefficient of subgrade reaction for sands from Cone Penetration Test (CPT) data was applied for a liquefiable residential site in Christchurch. The data gathered from a site investigation comprising of four CPT’s and one borehole with Standard Penetration Test’s (SPT’s). The site consists of relatively uniform soil formations. The results from the CPT’s are compared with the SPT borehole results. The SPT results are analysed by using the methods proposed by Scott (1981) and Moayed and Janbaz (2011). The three methods are applied on different sizes of foundations: square footing, rectangular footing and strip footing. The results from the CPT methodology are presented and compared with the other two methods. The proposed method can be of use in foundation design after applying suitable conversion factors which are also presented.
Keywords: Subgrade reaction coefficient, CPT, foundation, sand, SPT
1 INTRODUCTION
The earthquake activity in the Canterbury area, New Zealand, between September 2010 and June 2011 resulted in extensive CPT investigations within the affected City of Christchurch. As Christchurch is currently under rebuild, there is a high demand both for strengthening of existing foundations and design of new foundations for schools, churches, residential, commercial and industrial properties in limited amount of time and budget (Opus International Consultants Ltd., 2010 – 2014). For these reasons, a rapid method for the estimation of the vertical subgrade reaction modulus k [N/m3] (others may use the terminology subgrade reaction coefficient) for sands from CPT data was introduced in 2013 by Barounis et al. The k obtained from CPT data will carry the symbol KCPT while the resulted subgrade reaction for a given foundation will carry the following symbols throughout this paper: KFCPT for CPT data KFSCOTT for SPT data KFM&J for SPT data This paper presents the results of the proposed method applied at a liquefiable site in Papanui, Christchurch. The CPT results are compared with SPT results executed within a borehole at the same site.
2 ADVANTAGES AND DISADVANTAGES OF THE PROPOSED METHOD
The proposed method offers the following advantages over plate loading testing (Barounis et al., 2013): 1. Inexpensive 2. Quicker 3. No requirement for kentledge or reaction loads 4. No dewatering of excavations 5. Independence from plate load size effects 6. Higher exerted pressure (up to 40MPa, nominal 100MPa) 7. All soil types can be tested 8. Testing at greater depths 9. Influence of stress field at depth is reflected in the measurement
10. Testing to soil failure 11. k versus depth is delineated 12. Statistical analysis on obtained values 13. A pair of (qc, δ) values for penetration between 1 and 2 centimetres gives 50 to 100 measurements per meter 14. KCPT can be correlated with consistency of clays, Dr of sands, SPT N and soil behaviour 15. Measured KCPT can be transformed to a reliable KFCPT 16. May prove useful for liquefaction potential assessment.
It also has the following disadvantages compared to plate loading testing and common laboratory tests (Barounis, 2013): 1. CPT measures properties at soil failure; 2. Plate load, unconfined and triaxial compression test and consolidation test measure properties within elastic range and/or at soil failure; 3. KCPT is considerably higher than Kplate due to the smaller probe diameter used; 4. Limited capacity to penetrate through hard soils or refuse on gravels may result in termination of the test with insufficient KCPT values.
3 BACKGROUND THEORY
During cone penetration, δ, the soil is initially compressed and then sheared to failure at a stress equal to the measured value of qc. The rate of cone penetration of two centimetres per second classifies this type of testing as strain controlled undrained in-situ testing, similarly to the laboratory triaxial UU test and unconfined compression test. For the case of cone penetration with δ=10 mm, each soil layer of thickness T can be perceived as a number of vertical springs 10 mm long connected in series like a chain (see Figure 2). Each soil spring is assumed having an ultimate vertical reaction coefficient value of KCPT, which is fully mobilized during cone penetration. The cone penetration test offers the ability to measure this ultimate reaction coefficient KCPT for the complete depth of the CPT profile as both qc and δ are measured. The mathematical definition for KCPT can be described by using a qc versus δ graph shown in Figure 1. The slope of the straight line connecting the origin of the axes and the value of qc is KCPT, defined as 3 qc/δ and carries units of N/m . This resembles elasto-plastic soil behaviour when loaded. At qc the soil fails, as this is proved during testing. At this failure point the soil is considered as behaving as a spring which has reached its ultimate stress limit. The duration of testing for 1cm of soil is between 0.5 to 1 seconds. A well maintained and calibrated CPT probe can let us assume with a lot of confidence that for each centimetre tested a straight line can be always drawn as shown in Figure 1. 50 q 45 c 40
35 30 25 (MPa) c
q 20 15 10 5 0 0246810 δ (mm)
Figure 1. Definition of KCPT by using a qc/δ graph for δ = 10 mm
Figure 2. Delineation of K from CPT with depth
For foundation design the KCPT value needs to be scaled before it is used as the foundation size is several orders of magnitude greater than the diameter of the CPT probe used. The applicable scaling factor is discussed in the next paragraph.
4 ESTIMATION PROCEDURE FOR KCPT AND KFCPT
The KCPT and KFCPT can be estimated in five steps: Step 1: Calculation of KCPT KCPT = qc/δ (1) 3 where, KCPT = coefficient of subgrade reaction from CPT [N/m ] qc = tip cone resistance measured at any depth [MPa] δ = cone penetration applied [mm] For δ = 10 mm and qc is in MPa then, 3 KCPT = 100qc [MN/m ] (2)
Step 2: Transformation of KCPT to a reference 300 mm load plate value KCPT(0.3) KCPT(0.3) = KCPT x (DCPT/300) (3) where, KCPT(0.3) = coefficient of subgrade reaction for a 300 mm load plate based on CPT measurements DCPT = the diameter of the cone used [mm] 300 = the reference plate diameter [mm] KCPT = the subgrade reaction coefficient calculated according to step 1 depending on the 3 penetration increment δ used [N/m ]. For DCPT = 35.7 mm, KCPT (0.3) is approximately 12% of KCPT (scaling factor of 0.119).
Step 3: Conversion of KCPT(0.3) to KFCPT
KFCPT = KCPT(0.3) x ) (4) where, m = L/B (Bowles, 1997), applicable to strip, pad or . raft foundations on medium dense sand. . For the same types of foundations on sands of any relative density:
KFCPT = KCPT(0.3) x ( ) (5) where, B1 = 0.3 m (reference plate width) and B = actual foundation width [m]. Step 4: Divide the estimated KFCPT by a conversion factor, CF to obtain the value for foundation design: KDESIGN = KFCPT/CF (6) The recommended CF values for sands is discussed in paragraph six.
5 APPLICATION OF THE METHOD AT A SITE IN CHRISTCHURCH
5.1 Geotechnical site investigations The method was applied at a site on Paparoa Street, Christchurch at an existing residential building that suffered structural damage due to the recent Canterbury earthquakes. The property is situated 3.7km northwest of Christchurch CBD. The geotechnical site investigations undertaken in 2014 included: A sonic drilled borehole to a depth of 15m; SPT was undertaken at 1.5m depth intervals Four CPT’s with pore pressure measurements to effective tip refusal (CPT01 is shown in Figure 2, qc and KCPT versus depth are shown). The conducted site investigations and testing is shown in Table 1.
Table 1: Conducted site investigations and testing Investigation depth below Site investigation Testing ground level (m) SPT with hammer efficiency Borehole 01 (BH01) 15.0 Er = 90.7%1 CPT 1 (1.5m away from BH01) 9.48
CPT 2 (20m away from BH01) 9.32 Pore pressure CPT 3 (35m away from BH01) 9.58 measurements CPT 4 (45m away from BH01) 9.30 1 Hammer efficiency determined from calibration certificate of the SPT hammer used.
Figure 3: CPT01 and KCPT profiles versus depth
5.2 Ground conditions
The published geology map of the area (Brown and Weeber, 1992) indicates the site is predominantly underlain with alluvial sand and silt overbank deposits (Yaldhurst Member of the Springston Formation). The typical ground profile of the site has been inferred based on the site investigations, and is shown in Table 2. Generally the site is underlain by very uniform stratigraphy in terms of soil formation and thickness. The variation of qc, soil behaviour type (SBT), depth and thickness between the four CPT’s undertaken is very small for the same layer. The results from the borehole correlate sufficiently with the CPT results and this allows to build a three dimensional ground model for the site with great confidence. The SPT ‘N’ values have been corrected as per the Ministry of Business, Innovation and Employment (MBIE) Guidance for Repairing and building houses affected by the Canterbury earthquakes, Appendix C3 (2012). The groundwater level was encountered from between 1.0m and 1.4m below ground level. Table 2: Typical ground profile of the site Layer Depth (m) Thickness Average CPT Average Soil description number From To (m) qc (MPa) SPT N60 Silty Sand (very loose I 0.0 1.7 – 1.9 1.7 – 1.9 to loose) and Sandy 3.6 3 Silt (soft to firm) Clay and Silty Clay II 1.7 – 1.9 2.4 – 2.5 0.6 – 0.7 0.9 - (soft to firm) Silty Sand (loose) and III 2.4 – 2.5 3.1 – 3.6 0.6 – 0.9 1.9 4 Sandy Silt (soft) Clay and Silty Clay IV 3.1 – 3.6 6.0 – 7.2 2.5 – 4.1 with organics (soft to 0.5 4 firm) Silty Sand (loose) and V 6.0 – 7.2 6.6 – 7.8 0.5 – 1.3 1.5 4 Sandy Silt (soft) Clay and Silty Clay VI 6.6 – 7.8 8.6 – 8.8 1.5-2.0 1.0 - (soft to firm) Sandy fine to coarse VII 8.6-8.8 - – Gravel (dense to very - 63 dense)
5.3 Assessed foundation options A number of foundation options have been considered if a rebuild is proposed on the site. For demonstrating the proposed method, the following foundation sizes are assessed: L = 1 m, B = 1 m, Df = 1 m, square foundation L = 2 m, B = 1 m, Df = 1 m, rectangular foundation L = 5 m, B = 1 m, Df = 1 m, strip foundation where, L=foundation length, B=foundation breadth and Df = foundation depth.
The KFCPT results are dependent on the value of qc adopted. For this site an average value qcav is adopted for a depth of 2B below foundation level (i.e. 2 m below the foundation, between 1 m and 3 m depth below ground level). For determining qcav between these depths, values of qc corresponding only to sandy soils have been considered. A similar technique was applied for the average of SPT values N60av. The values for qcav and N60av are shown in Table 3. The values for KCPT and KCPT(0.3) are shown as well, with the latter to be equal approximately to 12% of the former as per equation 3 above.
Table 3: Adopted values for qc and N60 for each CPT for sandy soils only for a depth of 2B below foundation
Range of CPT Average CPT 3 KCPT(0.3) Average SPT CPT KCPT [MN/m ] 3 qc (MPa) qcav (MPa) [MN/m ] N60av 1 1.94 to 3.24 2.89 289 34.4 3.95 2 1.02 to 4.34 2.82 282 33.6 3.95 3 1.45 to 4.50 3.42 342 40.7 3.95 2 1.27 to 3.05 2.40 240 28.6 3.95
6 RESULTS AND DISCUSSION
The results from the application of the proposed method are shown in Table 4. As the SPT and plate load tests load the tested soils within their elastic range, it is expected that they produce lower subgrade reaction values than the CPT. The plate load test is usually terminated when the tested soil exhibits 25 mm of measured settlement. Results from the methods by Scott (1981) and Moayed and Janbaz (2011), which are correlated with plate load test results, are also shown in Table 4. By comparing the results from all three methods, it is evident that the proposed method overestimates the subgrade reaction values as it is expected.
Table 4: Results from the application of the proposed method and comparison with SPT methods KFCPT from KFM&J proposed K (MN/M3) (MN/M3) CPT Length Breadth Foundation FSCOTT method (Scott,1981) (Moayed and No. L (m) B (m) depth D (m) 3 2 f (MN/M ) Janbaz ,2011) Eq.4 Eq.5 (a) (b) (c) (d) 1 1 1 1 34.4 14.5 2 1 1 1 33.6 14.2 7.11 3.0 11.1 4.7 3 1 1 1 40.7 17.2 4 1 1 1 28.6 12.1 1 2 1 1 28.7 14.5 2 2 1 1 28.0 14.2 5.9 3.0 9.3 4.7 3 2 1 1 33.9 17.2 4 2 1 1 23.8 12.1 1 5 1 1 25.2 14.5 2 5 1 1 24.6 14.2 5.2 3.0 8.2 4.7 3 5 1 1 29.8 17.2 4 5 1 1 20.9 12.1 (a) Scott: KFSCOTT = 1.8 N60 x (m+0.5)/1.5m (b) Scott: KFSCOTT = 1.8 N60 x (B+B1)/2B (c) Moayed and Janbaz: KFM&J = 2.821 N60 x (m+0.5)/1.5m (d) Moayed and Janbaz: KFM&J = 2.821 N60 x (B+B1)/2B
For comparing the CPT results with the results of the other two methods, the ratio of KCPT(0.3)/K0.3(Scott) and KCPT(0.3)/K0.3(M&J) was estimated. These ratios simply indicate how many times greater the CPT results are than the corresponding results from the other two methods. The average values obtained from each CPT for these ratios are shown in Table 5.
Table 5: Results for the average ratios between CPT and SPT methods Average Average CPT No. KCPT(0.3)/K0.3(Scott) KCPT(0.3)/K0.3(M&J) 1 5.2 3.3 2 5.1 3.3 3 5.9 3.7 4 4.3 2.7 Average 5.1 3.3
From the results in Table 5 it is concluded that the proposed method produces 4.3 to 5.1 times higher K0.3 values than Scott’s method. This means that by dividing the KFCPT value by an average of 5.1, it becomes equal with KFSCOTT. Thus, the estimated KFCPT from step 3 in paragraph 4 has to be divided by a CF = 5.1 before using it for foundation design. It is also concluded that the proposed method produces 2.7 to 3.7 times higher K0.3 values than Moayed and Janbaz method. This means that by dividing the KFCPT value by an average of 3.3, it becomes equal with KFM&J. Thus, the estimated KFCPT from step 3 in paragraph 4 has to be divided by a CF = 3.3 before using it for foundation design.
7 CONCLUSION
A method has been developed for facilitating a rapid estimation for the subgrade reaction coefficient of sands from CPT. The method was developed for the needs of the Christchurch rebuild and has been applied with caution for buildings that suffered structural damage as well as for new buildings. The results from this method are considerably higher than the results from well-established methods which rely on correlations with SPT’s and with plate load tests. The values produced from CPT are comparable and can be of application in foundation design after applying a scale factor and a factor of safety. Depending on the method someone wishes to adopt (Scott or Moayed and Janbaz) a CF = 5.1 or CF = 3.3 should be applied, especially in the case that there are no available SPT data for use. The data were collected from a relatively uniform site in Christchurch consisting mainly of very loose to loose silty sands/sandy silts (N60 = 4). The method still needs to be proved that gives consistent values for the complete set of blows between 1 and 50. The proposed method can also be used for reducing site investigation costs and time consuming testing for structures of low to medium importance levels.
8 ACKNOWLEDGEMENTS
Opus International Consultants Ltd. and the authors of this paper would like to thank Mr John Ryan and Mrs Mia Ryan, the owners of the property in Christchurch cited in this paper, for their kind permission to let us use the data of their site for research purposes.
REFERENCES
Barounis, N., Saul, G. and Lally, D. (2013).”Estimation of vertical subgrade reaction coefficient from CPT investigations: applications in Christchurch”. Proceedings 19th NZGS Geotechnical Symposium, Queenstown. New Zealand Ministry of Business, Innovation and Employment (2012). “Guidance: Repairing and Rebuilding Houses Affected by the Canterbury Earthquakes”. Moayed, R. Z and Janbaz, M. (2011). “Subgrade reaction modulus of Tehran alluvium”. Proceedings of the Institution of Civil Engineers, Geotechnical Engineering 164, pages 283-288. Scott, R.F. (1981). “Foundation analysis”. Prentice Hall, Englewood Cliffs, NJ.