Introduction Interface shear strength parameters are required for use in design calculations to assess the stability of a wide range of geotechnical structures incorporating geosynthetics.These include the design of landfill barriers and reinforced earth structures.
Limit equilibrium calculations can be carried out using a global safety factor (traditional approach) and using partial factors on both resisting and disturbing forces (limit state approach defined in Eurocode 7, 1994).
In the global safety factor approach it is necessary to obtain conservatively chosen mean values of shear strength.The Eurocode 7 approach is to obtain characteristic values of shear strength. In both cases a limited number of site-specific laboratory tests is usually supplemented by subjective experience. For practical purposes it can be assumed that characteristic value (EC7) and the conservatively chosen mean value (traditional) are equivalent (Schneider, 1997), and therefore the recommendations in this paper can be applied to both design approaches.
This paper provides guidance on obtaining characteristic values of the interface shear strength parameters (apparent adhesion, a kand friction angle, d k) for use in design calculations.A companion paper (Stoewahse et al 2002 - Ground Engineering February) discussed factors influencing the measurement of interface shear strength behaviour.
Characteristic values Selection of characteristic values of soil and geosynthetic properties must take account of:
l Inherent variability of soil l Inherent variability of manufactured geosynthetic materials l Measurement errors l Extent of zone governing behaviour of limit state being considered.
Measurement errors are a significant factor and are caused by equipment, procedural, operator and random test effects.These are discussed in the companion paper and typical variability of measured strengths is considered below.
In Eurocode 7 (1994), the characteristic value of a soil property is defined as: 'A cautious estimate of the value affecting the occurrence of the limit state'The characteristic value should be a cautious estimate of the mean value over the governing zone of soil (Orr and Farrell,1999).
Assessment of an interface between a geosynthetic and soil requires characteristic values of the shear strength parameters that produce a cautious calculated mean shear strength over the entire area of the interface involved in the potential failure.
Eurocode 7 advises: 'If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of a limiting state is not greater than 5%' Schneider (1997) proposed a statistical approach for determining the characteristic value (X k) using the mean value of the test results (X m) and the standard deviation of the test results (s m):
Xk= X m- 0.5s m(1) The approach aims to ensure in the order of 95% confidence that the real statistical mean of the interface strength is superior to the selected X k.This equation has been used in Switzerland for several years and has been proven to produce values that are in close agreement with values estimated by experienced geotechnical engineers (Schneider, 1997).
The process of obtaining design parameters is typically:
Selection of representative samples º Measured values (eg results of laboratory direct shear tests - peak and residual shear strengths at specific normal stress levels) º Calculated derived values based on theory, empirical relationship or correlations (eg obtaining a mand d mvalues that describe the best fit straight line through the measured strengths) º Calculated characteristic values a kand d k(a cautious estimate of a mand d mas discussed above) º Calculated design values a dand d dobtained by applying partial factors to a kand d k.Variability of measured interface shear strengths Expected variability of measured strengths Factors influencing measured values of interface shear strength can be categorised as either due to inherent material variability or measurement error.It is seldom possible to separate the relative contribution of the two factors.
However, Phoon and Kulhawy (1999) report comparative studies of errors in laboratory strength tests on soil. Statistical analysis of results from a number of test programmes indicates that measurement errors for most laboratory strength tests, expressed in terms of coefficient of variation, which is defined as standard deviation/mean, are in the range of 5% to 15%.
Inherent material variability results in coefficients of variation also of between 5% and 15%, and the combined influence of measurement error and inherent variability is expressed by coefficient of variation of measured strengths between 7% and 21%.
Stoewahse et al (2002) show a similar variation of measured strengths for geosynthetic interface shear tests obtained from repeatability and inter-laboratory comparison test programmes carried out at Loughborough University and Hanover University.This data adds to the existing information from the 1997 European (Gourc and Lalarokotoson, 1997) and 1995/1996 German (Blümel and Stoewahse, 1998) intercomparison test programmes.
Derived interface shear strength parameters Interface shear strength parameters are obtained by plotting peak and residual shear strengths measured in direct shear apparatus on a shear stress v normal stress graph.Coulomb failure criteria are defined by best-fit lines through sets of peak (p) and residual (r) data measured at normal stresses relevant to the design problem.Shear strength parameters are used to describe these lines (intercepts a pm and a rm , and slope angles d pm and d rm ).From the authors'experience it is rare for duplicate tests to be carried out at each normal stress, and hence failure envelopes are typically taken as the best-fit straight line through one point at each of three or four normal stresses.
Given the inevitable scatter of measured interface strengths (Stoewahse et al, 2002), this approach provides insufficient information to enable characteristic strength parameters to be selected. If only one or two tests are conducted at each normal stress, it is not known whether the measured shear strengths are high, low or in between values and the potential scatter of measured strengths is also unknown.
Depending upon the position of the measured strengths within the possible range at each normal stress, the best-fit line can have a variety of positions, and hence a wide range of shear strength parameters could be obtained.
Figure 1 demonstrates possible strength envelopes that can be obtained if a limited number of tests are conducted.
The results are from a series of drained repeatability tests conducted on a smooth geomembrane vs nonwoven needle punched geotextile at low normal stresses.The scatter of measured peak shear strengths at a given normal stress is typical of the results obtained in other repeatability test programmes (eg textured geomembrane v geotextiles).
Shear strength envelopes are defined by pairs of apparent adhesion (a) and slope angle (d) parameters.
While it is common practice in soil mechanics to ignore apparent adhesion values in design, this approach is not recommended for geosynthetic interfaces.
Apparent adhesion values can be taken into consideration in design of structures incorporating interfaces when they are:
la measure of true strength at zero normal stress (e. g. the Velcro affect between non-woven needle punched geotextile and textured geomembranes and internal strength of a laminated geocomposite);
l used to define a failure envelope over a range of normal stresses (i. e. assuming a linear failure envelope) when the full envelope curves towards the origin at lower normal stresses; and l used to define a best-fit straight line through limited variable test data (Figure 1).
In these cases it would be over conservative to assume a = 0, especially for design cases with low normal stresses (eg design of cover systems).Therefore, as the quantification of interface shear strength requires two parameters (a and d) it is not appropriate to obtain characteristic values for the shear strength parameters derived directly from the best-fit straight line through the measured values. A methodology is proposed whereby characteristic shear strengths are calculated for each normal stress and then these 'corrected' strengths are used to derive characteristic shear strength parameters a kand d k.Example of interface test data variability An assessment has been made of the variation in peak strength parameters that can be obtained based on the repeatability data shown in Figure 1.
A Monte Carlo simulation has been carried out to obtain the distributions of peak strength parameters (a p, dp) that are calculated when sets of three strengths are selected randomly (ie one from each normal stress) and a best-fit straight line calculated.
The measured distributions of shear strength for each normal stress form the input data for the simulation.
These can typically be represented by a normal distribution.A total of 1,000 trials were conducted.An example of results from the Monte Carlo simulation for the smooth geomembrane/geotextile test data are shown in Figure 2 for the intercept (a p) and slope (d p) values.
Table 1 contains a summary of the results from simulations in terms of mean and standard deviation of the calculated parameters. In addition, the pairs of shear strength parameters that define each best-fit line have been used to calculate the shear strength for a normal stress of 20kPa (ie typical for a cover system). A summary is given in Table 1, also in terms of mean and standard deviation.
The magnitude of variation in measured shear strengths (Figure 1) leads to a wide range of possible failure envelopes and hence the calculated values of shear strength using these failure envelopes (Table 1) also have a significant range.
This is demonstrated further by Figures 3(a) and (b) showing the results of Monte Carlo simulations carried out on the results from each of five extensive repeatability/inter-laboratory test programmes. The coefficient of variation of calculated shear stresses (ie using generated shear strength parameters defining best-fit straight lines through sets of randomly selected data points) are plotted against the normal stress used in their calculation. Figure 3(a) shows the results from tests on geomembrane vs geotextile interfaces, and Figure 3(b) the results from sand vs geotextile interfaces.
It can be seen that significant variation of calculated shear strength occurs.Of note is that a larger variation is shown for the sand v geotextile tests.This is due to there being additional variation in the test materials, such as resulting from the compaction process used to form the sand test specimens and the wide range of different geotextiles used in the test programmes (eg non-woven needle punched and heat bonded).
The above analyses show that unconservative high shear strengths can be obtained from limited test data.
This has important implications for selection of characteristic values (a k, d k), as these must provide a cautious estimate of interface shear strength. It is clear that the present common practice of requesting one test at each normal stress is insufficient to calculate a mean value or to assess the variability of measured shear strengths.Hence current practice is inadequate to obtain characteristic interface shear strength parameters.
Guidance on selection of characteristic values is provided below.
Guidance on selection of characteristic values Three approaches for obtaining characteristic shear strength parameters from laboratory test data are summarised below.They are listed in order of preference.
Generation of site-specific statistical data Selection of characteristic values using a site-specific statistical analysis of test data is the most rigorous approach. It requires multiple performance tests to be conducted at each normal stress to enable the mean (X m) and standard deviation (s m) of measured strengths to be calculated for each stress level. The characteristic shear strengths (X k) can then be calculated from equation (1).The process is demonstrated in Figure 4.
Characteristic shear strength parameters (a kand d k) are obtained from the best-fit straight line through the characteristic shear strengths. As outlined above, this approach is based on assessing the variability of measured shear strengths and not the derived shear strength parameters.
A sufficient number of tests should be carried out to allow a valid statistical analysis. It is proposed that a minimum of four tests should be conducted at each of three normal stresses (ie a minimum of 12 tests in total).
However, the number of tests required is also dependent upon the level of existing information relating to the shear strength of the interface being tested.Although it should be noted that variability of geosynthetics and soils could result in significant differences in shear strength for what appear to be similar interfaces.
The level of experience of the engineer interpreting the test results should also be taken into consideration. This approach may appear an expensive option due to the large number of tests required, however the experience of the authors indicates that significant errors can result from carrying out an inadequate number of tests.
Lower bound of limited repeatability test data Present recommendations provided by the Germany Geotechnical Society related to the design of waterfront structures involving soils is for three tests to be conducted at each of three normal stresses (EAU 1990).
The failure line defining the characteristic shear strength parameters is taken as the best fit straight line through the lowest measured strength at each normal stress (ie a lower bound to the test data).
The selection of three tests is consistent with the guidance in Eurocode 7 (1997) Part 2, Table A.9.2, which suggests carrying out three tests in cases where the results exhibit significant scatter and there exists a medium level of comparable experience.While a smaller number of tests can be carried out than in the preferred method given above, it can lead to over conservative (ie low) strength parameters being calculated.
Method based on statistical data from inter-comparison tests A method of obtaining cautious characteristic values using a limited number of site-specific tests is proposed.
The approach is based on an analysis of the variability of measured interface shear strengths from the extensive repeatability and inter-comparison test programmes in which the authors participated.
These studies have been analysed to provide statistical information on the magnitude of scatter of measured shear strengths.Two commonly used interfaces are considered:
a) non-woven needle punched geotextile vs geomembrane b) non-woven needle punched geotextile vs sand.
The first includes results from tests using textured (both co-extruded and blown film types) and smooth high-density polyethylene and low-density polyethylene geomembranes.Results from tests on textured and smooth geomembranes were combined as the coefficients of variation were in the same range.The studies conducted by the authors take into consideration the affects of both measurement errors (ie equipment, procedural, operator and random test affects) and inherent material variability.
For each of the series of repeatability tests the standard deviation of the measured peak shear strengths has been calculated for each normal stress. The results from these individual tests series have then been combined to calculate a weighted average standard deviation for a range of normal stress levels (ie weighted in proportion to the number of tests conducted in each series).
The weighted standard deviation data is presented in Table 2 for the two interfaces.
The data is plotted in Figure 5 as weighted standard deviation vs normal stress. It shows clear linear relationships of increasing variability of measured strengths (indicated by increasing standard deviation) with increasing normal stress.This is demonstrated by the results of tests on both interface types.Significantly less scatter is exhibited by the geomembrane vs geotextile interface. As discussed above, this is because the interface does not incorporate soil with its inherent variability.
It is proposed that where there is insufficient test data for the shear strength of an interface to undertake statistical analysis of its variability, the characteristic values of shear strength for each normal stress should be calculated using the mean measured value of strength (X (s m) obtained from the relationships shown in Figure 5.The normal stress dependent standard deviation of test data (s m) can be used to calculate characteristic values from site-specific testing programmes using equation (1).
For the geomembrane vs geotextile type interfaces s m(kPa) is given by the relationship:
sm= 0.054. s n+ 1.9 (2) and for the geotextile vs sand interface:
sm= 0.106. s n+ 5.8 (3) Where: s nis the normal stress in kPa.
A limitation of this approach is that there is an inherent assumption that the measured strengths at each normal stress are approximately representing mean values.
As shown in Figure 1, this may not be the case and they could be significantly higher or lower than the mean.
Therefore, the engineer must decide whether the measured strengths approximate to mean values.Schneider (1997) proposed a possible approach for estimating the mean values by using the relationship:
X m' (a + 4. b + c) / 6 (4) Where:
a = estimated minimum value b = most likely value c = estimated maximum value For this application the estimated values will be shear strengths at a particular normal stress. The estimation of the values a, b and c can be based on the engineer's experience and personal judgement, backed by published data (eg Jones and Dixon,1998).
If measured strengths are considered to be high compared to estimated mean values, or there is limited experience of testing the interface, and hence difficulty defining minimum, maximum and most likely values, then further tests should be conducted and the characteristic values obtained using either of the first or second approaches described above.
Blindly using a best-fit line through only three tests to define mean shear strengths could result in significant over-estimation of the characteristic values and hence to an unsafe design.
Example Figure 6 shows the results of three direct shear tests (each at a different normal stress) conducted to obtain peak shear strength parameters of the interface between a textured high-density polyethylene geomembrane and a polypropylene non-woven needle punched geotextile.
The best-fit straight line through the three measured shear strengths is defined by the parameters a m=6.9kPa, d m= 25.8infinity. The authors have significant experience in testing similar interfaces and consider the measured strengths to be typical for the type of interface tested.
Hence in this instance a decision has been made that the measured strengths can be taken as mean values.
As only one test has been conducted at each normal stress, it is not possible to assess the variability of the data and hence characteristic shear strength parameters cannot be calculated directly. Characteristic values can only be obtained by either:
a) carrying out more tests and undertaking a statistical analysis/using a lower bound, or b) using the approach based on typical variability of test data from this type of interface.
If the latter approach is taken, the measured shear strength at each normal stress (X m) is corrected (ie reduced) to a characteristic value by the amount of 0.5s m, where s mis obtained from equation (2).
Figure 6 shows the best-fit straight line through the characteristic shear strength values. It is defined by the characteristic shear strength parameters a k= 6.0kPa, d ak= a m/ 1.15 and tan d k= tan d m/1.07 These are considered to be reasonable and consistent with partial factors typically used by engineers based on experience to define characteristic values.
Summary An extensive programme of repeatability and inter-laboratory comparison testing has provided evidence of large variability in measured geosynthetic interface shear strengths.
Design approaches using both global safety factors and partial factors require the calculation of characteristic shear strength parameters from laboratory test results.These must provide a cautious estimate of interface shear strength affecting the occurrence of the limit state.
Present practice is to carry out one, and at best two, site-specific tests at each normal stress. This is inadequate to allow a statistical analysis of the results and hence to enable characteristic strength parameters to be obtained.The paper provides guidance on obtaining cautious characteristic values.Three approaches are discussed.In order of preference they are:
a)Carry out enough site-specific tests to enable a statistical analysis of the characteristic shear strength parameters b) Carry out three tests at each normal stress and obtain the characteristic shear strength parameters from the lower bound to the test results c) Correct limited strength test data using a proposed relationship between normal stress and standard deviation of results. This quantifies the variability of typical test data using the results from an extensive repeatability test programme. Use of the measured strengths as mean values is dependent upon an assessment by an experienced engineer. If there is limited prior information on an interface, this approach should not be used.
These are the parameters that are used in design, either with partial factors applied or a global safety factor calculated.The correction proposed is equivalent to applying the following partial factors to the measured shear strength parameters:
The guidance is based on an assessment of two typically used interfaces: non-woven geotextile vs geomembrane and geotextile vs sand.Extrapolation of the guidance to other types of geosynthetic interfaces should be carried out with caution.
While some will exhibit similar magnitudes of variability in strength tests due to common measurement errors, there are a number that will have specific modes of behaviour and hence factors affecting variability of test results. Further work is required to explain and quantify the variability in measured shear strength of the full range of geosynthetic interfaces.
Inherent variability of fill soils and manufactured geosynthetic materials dictates that compliance testing of interface shear strength should be carried out as a routine part of quality assurance procedures.
Construction processes influence the properties of compacted soils significantly. An increase in the moisture content of a cohesive soil local to a geosynthetic can result in large reductions in interface shear strength.Therefore, a frequency of compliance testing should be selected to demonstrate that the constructed interface has a strength consistent with that used in the design calculations. Frequency of testing must take into consideration the area of interface constructed, the number and complexity of factors influencing interface shear strength and the implications of failure.
The aim of the compliance testing is to validate the assumed values of shear strength used in design and hence to ensure the stability and integrity of the geosynthetic/soil system.
Acknowledgements The research described in this paper was part funded by The British Council and the German Academic Exchange Service as part of the British German Academic Research Collaboration Programme. Patience Kamugisha is funded by Golder Associates and Loughborough University and the work of Carl Stoewahse was conducted at Hannover University funded by a number of German civil engineering companies.
lGeosynthetic interface shear behaviour: Part 1, Test methods, appeared in last month's issue of Ground Engineering.
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*N Dixon and P Kamugisha, Department of Civil and Building Engineering, Loughborough University W Blümel, Institut für Grundbau, Bodenmechanik und Energiewasserbau, University of Hannover C Stoewahse, Gesellschaft für Grundbau und Umwelttechnik, Braunschweig DRV Jones, Golder Associates (UK), Nottingham