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Technical paper: Improved estimation of ground stiffness for railway projects using continuous surface wave testing

Mark Deighton, TSP Projects and John Rigby-Jones, Ground Stiffness Surveys

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1.0 Introduction

As geotechnical engineers we have become adept at maintaining a safe distance from ultimate limit states, which are generally controlled by soil strength. However, as serviceability requirements have become more demanding and construction adjacent to existing structures more commonplace, the focus in design has increasingly shifted to the movements which take place far from soil yield and possible failure. The realistic prediction of these ground movements, key to the production of economical design, requires a sound knowledge of ground stiffness and its stress strain behaviour.

Undertaking any work on the UK railway network is challenging due to the conflicting requirements to undertake work safely while minimising disruption to the running of trains. As a result of these constraints ground investigation is often severely constrained in quality and quantity.

While the simple and traditional investigation techniques typically employed generally permit the ground profile and strength to be estimated with reasonable accuracy, direct assessment of ground stiffness is rarely attempted due to the numerous difficulties accessing the railway with suitable in-situ testing or high quality sampling equipment poses. As a result, ground stiffness values are often determined from simple empirical relationships with either standard penetration test (SPT) N values or basic in-situ measurement of undrained strength. This approach can lead to conservatism and result in uneconomic design.

The importance of obtaining good ground stiffness data to producing economical designs was recognised at an early stage in a recent railway scheme in London. Consequently an improved methodology of obtaining accurate ground stiffness profiles was sought through the use of continuous surface wave (CSW) profiling. This non-intrusive, portable and economical technique has been used successfully by TSP on numerous recent ground investigations. It allowed ground stiffness profiles to be obtained close to the numerous proposed overhead line equipment (OLE) structures while minimising the need for possession working.

This paper describes the practicalities of using the CSW technique at the London site and compares the results with empirically derived values along with ground truth data obtained from boreholes within 5m. The benefits of using more accurate stiffness values in the design of typical railway foundations is examined through foundation analyses for two test locations with differing ground conditions.

2.0 The project

The project is concerned with the upgrade and modification to the existing OLE infrastructure in west London between Hayes and Harlington Station to the west and Acton Mainline Station to the east. TSP was employed as lead designer for the OLE foundations by the principal contractor. The proposed new OLE structures were combinations of portal, single and twin track cantilevers. These types of structures are associated with relatively high lateral loads and connection moments compared to their vertical loads and as such the near surface lateral resistance of the ground is important in determining lateral pile movement. Therefore, accurate assessment of near surface ground stiffness is key to minimising pile length and section.

TSP’s early review concluded that the expected geological sequence across the site comprised made ground associated with the railway trackbed and formation, overlying Langley Silt, over the Lynch Hill Gravel with the bedrock geology comprising the London Clay Formation. The key geotechnical risks posed to foundation design associated with this ground profile were assessed as:

  • Unacceptable settlement of shallow foundations where founded on compressible, low strength Langley Silt requiring the use of piled foundations
  • Difficulty in accurately assessing near surface ground stiffness, required to permit economical design of piles with significant lateral loading
  • Difficulty in assessing pile driving conditions through the potentially thick and dense Lynch Hill Gravel river terrace deposit and very stiff London Clay

While the London Basin is well understood in terms of geological setting, TSP’s initial studies identified that there was insufficient published and site specific data to satisfactorily control the above risks and permit economical foundation design. TSP therefore specified additional ground investigation aimed at both proving the stratigraphy across the site and characterising the key geotechnical parameters required for design.

Having previously used CSW testing on a number of schemes TSP proposed this technique to the client as providing a number of benefits. Firstly, the technique would provide the ground stiffness parameters required for economical OLE foundation design and secondly it would complement intrusive investigations in providing an indication of stratigraphy based upon changes in stiffness between the soft Langley Silt, dense Lynch Hill Gravel and stiff London Clay. Finally, as the technique is rapid and portable the investigation coverage could be greatly increased and extended to areas where other investigation techniques were impractical. Other seismic surface wave techniques were not considered due to the confined space available for testing. TSP devised the ground investigation strategy and employed Ground Stiffness Surveys (GSS) to undertake the CSW testing works.

3.0 CSW ground stiffness profiling

The potential for determining ground stiffness through the measurement of seismic wave velocity is not new, with the relationship between shear wave velocity and shear stiffness as a function of soil density described by Love (1927) in the early part of the 20th Century. However, it was the arrival of computer based processing power combined with the increasing awareness of non-linear stiffness in the early 1990s which created the demand for commercial seismic stiffness profiling systems.

The use of surface waves (as opposed to body waves) for ground stiffness measurement is particularly attractive for two reasons. Firstly, approximately two thirds of the energy imparted at the ground surface produces one of the two types of surface wave known as Rayleigh waves. This means that seismic sources can be relatively small and therefore portable. Secondly, Rayleigh waves are dispersive in nature, meaning that longer wavelengths penetrate to greater depth. This permits a stiffness versus depth profile to be developed for measurements made across a range of frequencies and, therefore, wavelengths. Once measured the Rayleigh Wave velocity is simply converted to shear wave velocity through a function with Poisson’s ratio and hence to shear stiffness. A detailed description of the CSW ground stiffness profiling technique is provided by Heymann (2007).

The importance of adjusting design stiffness for strain to account for the non-linear stiffness behaviour of soils and weak rocks is now widely appreciated. Fortunately the stiffness degradation – or softening – curve for a wide range of geomaterials is remarkably uniform (Clayton and Heymann, 2001) permitting straightforward adjustment for strain level (see figure 1). However, traditionally employed methods of stiffness measurement either do not directly measure stiffness (ie empirical relationships with SPT N value) or measure stiffness across a range of strains (ie plate load test and oedometer) making subsequent strain adjustment for operational levels difficult. As a seismic test CSW derived ground stiffness values are measured in the small strain linear part of the stiffness degradation curve and therefore application of softening functions is straightforward.

Early attempts at commercial CSW testing systems were sensitive to the effects of background noise and provided limited depth of investigation. Furthermore the simplistic inversion methods used were unable to deal with complex and inversely dispersive profiles. However, these issues have all largely been addressed with the advent of high power, low tuned, seismic sources combined with advanced data acquisition and inversion techniques. This has resulted in the advent of the modern CSW testing system which has a number of attractive features:

  • Provides accurate small strain shear stiffness values (Go) which are readily softened to operational strain levels and converted to Young’s Modulus values
  • Provides stiffness profiles to typical depths of 6-10m
  • Is portable permitting investigation at remote and confined sites
  • Is non-intrusive minimising the risks associated with buried services or ground contamination

While the application of the CSW technique to the measurement of small strain ground stiffness is well understood (Clayton, 2011) its use in the UK lags behind many other countries. This is despite the comparable cost of CSW testing to established simple stiffness measurement techniques (ie plate load test) and demonstration that the data obtained is equally applicable to routine analysis techniques as well as complex numerical modelling (Heymann et al, 2008). This is possibly in part due to the UK geotechnical industry’s reluctance for change and longstanding familiarity with the SPT N value.

Csw figure 1

Csw figure 1

4.0 Fieldwork

Railway sites typically provide a number of challenges to ground investigation, at the London site these included (see photo 1):

  • Difficult access to many OLE locations requiring access both along the track and through operational stations, potentially requiring extensive night time possession working
  • Short and limited possession availability
  • Typically narrow linear test locations with difficult topography limiting options for orientation of the test set up
  • Limited options to avoid testing on ballast in areas of dense services and buried obstructions

In light of the above constraints it was appreciated early on in the project that careful planning was required to maximise the quantity and quality of CSW data which could be obtained within the allocated budget. A key element of this planning was a joint site reconnaissance visit between TSP, GSS and the principal contractor, carried out at the onset of the project and covering all proposed OLE foundation locations. This inspection was invaluable allowing survey locations to be optimised in terms of practicality of access and quality of data while ensuring a safe system of working was possible. As a result of this inspection the site was divided into five geographical study locations, for each of which a detailed access and completion strategy was produced which minimised the requirement for line blocks and night time possession working thereby avoiding disruption to rail services and significantly reducing the cost and programme of the works. In order to provide ground truth for comparison with CSW testing two shell and auger boreholes were also drilled within 5m of selected CSW test locations where access for drill rigs were possible.

CSW testing was undertaken using the GSS 1.1kW 80kg mechanical “shaker” operating between 10-90Hz and powered by a portable generator. Where vehicle access was available testing was undertaken with the generator and data acquisition equipment remaining in the GSS test vehicle. However many test locations were remote from vehicle access points requiring equipment to either be transported along the track using a rail trolley (see photo 3) or through operational stations using three wheelbarrows.

The portable nature of the CSW equipment combined with the careful pre-start planning allowed the significant site and access restrictions to be overcome while permitting safe working and an average of four tests per shift to be completed.

Csw photo 1

Photo 1 - Typical site view of the narrow railway corridor in urban London

Data acquisition was undertaken using an array of five vertically polarised geophones at 0.75m spacing logged using a portable field computer. The typical field setup is illustrated in photo 2. The field testing protocol included a number of features and checks to optimise data quality and provide data redundancy as follows:

  • Recording of GPS coordinates and railway mileage/offset of each test to ensure accurate location
  • Check for constant velocity across the geophone array with adjustment of array orientation or relocation of the test where lateral changes in stiffness indicated
  • Real time review of individual geophone signal strengths to ensure adequate signal to noise ratio with adjustment of geophone offset from seismic source as necessary
  • Basic real time data inversion to confirm data quality suitable for advanced inversion
  • Both discrete frequency and frequency sweep data capture
  • Annotation to each test file of any changes to the standard test procedure or unusual conditions encountered

As is typically found at railway sites, even in urban settings, background noise levels between trains were low. However the busy nature of the line, especially at the test locations closest to London, meant that gaps between trains were brief, significantly increasing the time taken to complete data acquisition. Where testing on ballast was unavoidable signal strengths were found to be reduced requiring the offset distance of the seismic source from the first geophone to be reduced. It was also observed that testing on ballast could cause a resonant response at high frequencies with the signal strength of higher modes exceeding that of the test frequency. However by observing and recording this phenomenon in the field it was subsequently possible to ensure inversion identified the correct geophone response data. Additional assurance was also provided through the dispersion curve data obtained from the frequency sweep data capture.

Field dispersion curves recording the variation in Rayleigh Wave velocity with wavelength must be subject to numerical inversion in order to obtain the ground stiffness profile. The inversion process assumes a transversely (cross) isotropic material and hence the importance of the field checks made to ensure as far as possible testing is not carried out over shallow lateral changes in stiffness which might be provided by buried foundations or services.

Inversion was undertaken using an iterative forward modelling process searching for the best fit dispersion curve to field data. The inversion undertaken for normally dispersive data was based upon an advanced multi modal inversion of data (Wathelett et al, 2004). Where appropriate an inversely dispersive inversion was undertaken (Leong and Aung, 2013). A Poisson’s ratio of 0.26 was used in calculating the shear wave velocity and a typical lower bound soil density of 1.80Mg/m3 was assumed in the calculation of shear modulus (conservative). It is noted that, while there may be some uncertainty over the exact values of Poisson’s ratio and soil density used, due to the numerical form of the equations and the relatively small possible range of values compared to variations in shear wave velocity, calculated values of shear modulus are relatively insensitive to errors in assessment of Poisson’s ratio and soil density.

All the testing equipment and software used for the project was designed and developed by GSS in conjunction with University of Pretoria professor Gerhard Heymann.

Csw photo 2

Photo 2 - Typical testing set up

Csw photo 3

Photo 3 - Equipment transportation via rail trolley

5.0 Review of CSW results

Two study sites have been selected due to the proximity of the CSW tests to boreholes with clearly defined stiffness boundaries presented by their profiles of soft organic clay overlying medium dense sand and gravels overlying stiff overconsolidated clay. These features made them ideal for comparison of the CSW ground stiffness profiles with both the stratigraphy recorded in boreholes and the ground stiffness values derived using empirical relationships with in situ testing.

For comparative purposes the CSW small strain shear modulus profiles were softened to a strain of 0.1% using equation 1. An operational strain of 0.1% was selected as it represents a relatively conservative estimate of typical strains around foundations.

Csw equation 1

Young’s modulus values were then calculated using equation 2 and an assumed Poisson’s ratio of 0.26

Csw equation 2

Empirical relationships are frequently used to assess ground stiffness due to the practical and technical difficulties in undertaking direct field or laboratory measurement of stiffness. Commonly used empirical relationships relate Cone Penetration test (CPT) cone resistance (qc) or SPT N value to the stiffness of coarse granular soils and undrained shear strength to the stiffness of fine grained cohesive soils. However, these relationships are limited in their reliability as the relationship between the measured properties and stiffness are complex. Consequently, TSP Engineers are forced to take a conservative approach, often using lower bound values to generate conservative stiffness values for design. There are a number of empirical relationships with stiffness in published literature, for the purposes of this paper the relationships commonly used by TSP in routine design have been employed as described below.

In the absence of laboratory testing, the stiffness of fine grained cohesive soils has been related to insitu measurements of undrained shear strength. These were cross checked against SPT N60 values and converted to undrained Young’s modulus values, using equation 3, where m is related to the operational strain level. A strain level of 0.1% (m=800) was used, consistent with typical strain levels beneath foundations and as used for softening CSW small strain stiffness values (Burland et al, 1979). Drained Young’s modulus values were then calculated using equation 4, assuming a Poisson’s ratio of 0.26.

Csw equation 3

Csw equation 4

The stiffness of coarse, granular soils was related to SPT N60 values using Table 11 of CIRIA Report 143 (Clayton, 1995) with interpolation of intermediate values.

Drained Young’s moduli were derived using the above empirical correlations for each of the strata at the two study sites and are summarised in tables 1 and 2 along with the E0.1% values determined from CSW testing. The Cu values used in the correlations were direct measurements taken in the field using a hand vane or hand penetrometer, with an average of three measurements being used in equation 3.

5.1 Case study site 1

The shallow geology at the first study site is dominated by fluvial deposits up to 7m thick, associated with the depositional environment of the River Thames. The soil profile determined from borehole investigation is presented in figure 2 and shows a thin layer of Made Ground underlain by soft to firm organic clay (Langley Silt) to a depth of 3.10m below ground level. This is in turn underlain by the Lynch Hill Gravel, a river terrace deposit with a gravel dominated upper sub-horizon and sand dominated lower sub-horizon. The bedrock geology comprises the London Clay Formation.

It can be seen from figure 2 that the CSW testing identified a moderate stiffness surface layer (E’0.1%=78-91MPa) overlying a lower high stiffness layer below 3.3m (E’0.1%=219-262MPa). The depth of sharp increase in stiffness corresponds closely to the base of the Langley Silt deposit (3.1m bgl). The CSW profile did not penetrate the base of the Lynch Hill Gravel deposit due to the high stiffness of this deposit compared to the underlying London Clay resulting in the seismic energy being largely contained in this stiff layer.

Table 1 indicates that the stiffness for the Langley Silt estimated using empirical relationships to be 35% of that measured using the CSW technique and may reflect the difficulty in selection of an appropriate empirical stiffness relationship for intermediate soils. Empirically derived stiffness values for the Lynch Hill Gravel gave comparable results, being within only 13% lower than the CSW measured values.

Csw figure 2

StratumBase depth (m)Emp. E’0.1% (Mpa)CSW E’0.1% (MPa)Emp E/CSW E’0.1% (%)






Langley Silt





Lynch Hill Gravel





London Clay





Table 1 - study site 1 - Comparison of CSW stiffness values with empirically derived values
* Values determined from nearby CSW tests
1 Conservative assumption based upon experience of the deposit (reworked natural clay)
2 Based on a measured average cu from hand shear vane of 45kPa
3 Based on a measured average N60 value of 38.5 and CIRIA143 Table 11 interpolated mean E’/N factor of 5
4 Based on a measured average cu from hand penetrometer of 144kPa

5.2 Case study site 2

The geological sequence is somewhat simpler at the second study site owing to the absence of any fluvial deposits. As can be seen from figure 3, made ground is directly underlain by the London Clay Formation.

It can be seen from figure 3 that the CSW testing identified a 1.3m thick surface layer of reducing stiffness (E’0.1%=100-50MPa) overlying a thick layer of consistent stiffness (E’0.1%=50-58MPa) extending to the base of the CSW profile at 10m. The CSW profile corresponds well to the available ground truth, with the depth penetrated being typical for the 80kg seismic source where there are no sharp stiffness boundaries at depth.

Comparison with the empirically derived soil stiffness values in table 1 indicates that below a thin upper softened layer the stiffness for the London Clay estimated using empirical relationships was 32% higher than the CSW measured values. This good agreement supports the use of an m value of 800 in equation 3, a high value justifiable for the London Clay thanks to the many detailed studies available for this material, but which might be harder to justify for less well studied geomaterials.

Csw figure 3

StratumBase depth (m)Emp. E’0.1% (Mpa)CSW E’0.1% (MPa)Emp E/CSW E’0.1% (%)






Lynch Hill Gravel





London Clay 1





London Clay 2





London Clay 3





Table 2 – study site 2 - Comparison of CSW stiffness values with empirically derived values
1 Conservative assumption based upon experience of the deposit (reworked natural clay)
2 Based on a measured average cu from hand penetrometer of 50kPa
3 Based on a measured average N60 value of 9 and CIRIA143 Table 11 interpolated mean E’/N factor of 2.7
4 Based on a measured average cu from hand shear vane of 109kPa
5 Based on a measured average cu from hand shear vane of 117kPa

6.0 Analysis

In order to investigate the significance of using CSW derived stiffness data on subsequent design foundation calculations were undertaken for two theoretical, simple foundation types using both CSW and empirically derived stiffness data at the two study sites described above. Analysis was undertaken for the following two design cases:

  1. A square pad foundation founded at 1m depth
  2. A 0.6m diameter drive tubular steel pile

For routine analysis CSW small strain stiffness values may be adjusted for operational strain level in a single step prior to analysis, for more complex analysis small strain values may be iteratively softened using a step wise non-linear analysis (Archer and Heymann, 2015) or finite element software with inbuilt softening functions used. For the purposes of this paper it was elected to directly input E0.1% softened stiffness values rather than undertake more complex methods as this represents the methodology presently used for routine analysis.

Analysis was undertaken using Fine GEO5 Spread Footing and Piles software with the only changes between comparative analyses being soil stiffness values. GEO5 spread footing undertakes a simple layered elastic analysis of settlement with Boussinesq theory used to determine soil stresses. GEO5 piles determines lateral pile behaviour through a finite element modelling of the pile as a beam on an elastic Winkler foundation. A summary of the analyses undertaken are provided in tables 3 and 4.

From table 3 it can be seen that the settlements calculated using the empirically derived values at study site 1 are approximately 80% greater than those calculated using CSW derived stiffness values. The required pad dimensions are also approximately halved. At study site 2 the calculated differences are lower due to the closer agreement in empirical and CSW stiffness values with the pad settlements being 35% greater and pad dimensions 50% greater when calculated using the empirically derived stiffness values.



Emp. E’0.1%

CSW E’0.1%

Emp E0.1%/ CSW E’0.1% (%)

Emp. E’0.1%

CSW E’0.1%

Emp E0.1% /CSW E’0.1% (%)

Settlement of 2.5m square pad under 250kPa (mm)







Square pad dimension for 5mm settlement (m)







Table 3 Summary of spread footing analyses

From table 4 it can be seen that the pile head displacements calculated using the empirically derived values at both study sites are between two to three times greater than those calculated using CSW derived stiffness values. This emphasises the importance of accurate shallow stiffness assessment in determining pile head displacements. The effect of stiffness profiles on structural forces can be seen to be lower and less critical.


Emp. E’0.1%

CSW E’0.1%

Emp E0.1%/ CSW E’0.1% (%)

Emp. E’0.1%

CSW E’0.1%

Emp E0.1% /CSW E’0.1% (%)

Pile head displacement (mm)







Max shear force (kN)







Max. Bending Moment (kNm)







Table 4 Summary of pile analyses

7.0 Conclusions

TSP’s use of CSW ground stiffness profiling permitted the rapid measurement of soil stiffness at a number of sites along a length of busy London railway corridor under primarily daytime non-possession working. Despite the constraints associated with railway working an average of four CSW profiles per shift were obtained providing stiffness profiles down to depths of 5 to 10m.

The CSW ground stiffness profiles obtained were compared against borehole data at two study sites where there was found to be a good correlation between ground stiffness profile layers and geological strata. Review across all study sites has further demonstrated the reliability of the CSW testing in providing good correlations to the proven stratigraphy. This provided confidence the CSW tests were providing reliable data in terms of anticipated changes in stiffness at known levels of strata change.

The CSW stiffness values, softened to a conservative operational strain level of 0.1%, were significantly higher than the equivalent empirically derived values for shallow depths (2-3m). At greater depths there was a closer agreement between values. However, it is noted that there is significant subjectivity involved in the selection of the correct empirical relationship for determining stiffness values from SPT and undrained strength data which can lead to large differences in derived parameters and greater conservatism in design.

Simple comparative analysis of a shallow spread foundation at each study site found that calculated foundation settlements were approximately 35% greater using empirically derived values over CSW values. Similar comparative analysis for a piled foundation found pile head lateral displacements determined using empirically derived values to be approximately two and a half times those calculated using CSW values. These differences translate into opportunities to significantly reduce foundation sizes and pile lengths and section size. The benefits of this are not only to reduce material costs but also to improve the speed of construction, a factor which can be critical when undertaking work on busy railway sites.


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Burland, J B and Burbidge, M C (1985). Settlement of Foundations on Sand and Gravel, Proceedings of the Institute of Civil Engineers, Part 1, Vol 78, pp. 1325-1381.

Ciria Report No 143 (1995), Standard Penetration Test, Methods and Use

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