Determination of Constrained Modulus of Granular Soil from In Situ Tests—Part 2 Application

: The paper demonstrates how the concepts presented in the companion paper: “Determina-tion of Constrained Modulus of Granular Soil from In Situ Tests—Part 1 Analyses” can be applied in practice. A settlement design based on the tangent modulus method is described. Extensive in situ tests were performed on a well-documented test site consisting of sand with silt and clay layers. The field tests comprised different types of penetration tests, such as the cone penetration test, the flat dilatometer, and the seismic down-hole test. The modulus number and the constrained tangent modulus were derived from the cone penetration test with pore water pressure measurement and the flat dilatometer test. In addition, the shear wave speed was determined from two seismic down-hole tests, from which the small-strain shear modulus could be evaluated. The constrained modulus obtained from the cone penetration test with pore water pressure measurement (CPTU) and the flat dilatometer (DMT) was compared with that from the seismic down-hole tests. The importance of the stress history on the constrained modulus was demonstrated. The range of modulus numbers, derived from different in situ tests, compares favorably with empirical values reported in the literature.


Introduction
For most structures founded on granular soils, total and differential settlements are the critical design parameters [1,2].In the past, elastic theory has been widely used to estimate the settlement of foundations [3,4].The most important parameters needed for settlement estimates are the compressibility of the soil and the stress history.In the case of fine-grained soils, undisturbed samples can be tested in the laboratory, from which the compression parameters can be derived.However, retrieving undisturbed soil samples that can be tested in the laboratory is generally difficult.Therefore, the compression parameters need to be estimated based on rules of thumb or from in situ tests, as discussed in [5][6][7].Empirical correlations have been proposed between Young's modulus, E, and the results of different penetration tests.These, however, must be seen as crude estimates [8,9].To obtain more reliable correlations between the cone penetration test, CPT, and the geotechnical properties of granular soils, extensive pressure chamber tests have been carried out [8][9][10].Correlations between different types of in situ tests and the deformation properties of sands have been reported in [11,12].
The tangent modulus method, described in [13] and updated in [14], offers a simple yet powerful concept for settlement analyses applicable to all soil types.A study [15] reports the results of comprehensive laboratory tests that estimated the deformation properties of granular soils (sand and gravel).
Recently, Ref. [16] introduced an approach for utilizing the small strain shear modulus, G 0 , to derive deformation parameters for foundation settlement prediction.This concept is also based on the tangent modulus method and is an extension of the research described in [17].
The companion paper, "Determination of Constrained Modulus of Granular Soil from In Situ Tests-Part 1 Analyses" [18], also applies the tangent modulus method.For its practical application, two key parameters must be selected: the modulus number, m, and the stress exponent, j.These were derived from three different in situ tests: the cone penetration test (CPTU), the flat dilatometer (DMT), and the seismic down-hole test (SCPT).The modulus number, m, can be estimated from CPT according to a method proposed in [19].An important step in this concept is the adjustment of the measured cone resistance, q c , with respect to the mean effective stress, taking into account the soil type.From the stress-adjusted cone resistance, q CM , the modulus number, m, can be determined.
The geotechnical literature describes different empirical methods for estimating the constrained modulus from DMT [20,21].These references suggest that the constrained modulus, determined from DMT (MDMT), is equivalent to the vertically drained confined (one-dimensional) tangent modulus as obtained by an oedometer.
Seismic field tests are increasingly used in geotechnical engineering for the solution of geotechnical problems [16,22,23] and earthquake problems (liquefaction) [24][25][26].The shear wave speed, C S , can be measured with high accuracy, from which the small-strain shear modulus, G 0 , can be derived [17].Seismic laboratory tests have demonstrated that the soil stiffness is affected by shear strain.Different concepts have been suggested to take into account the strain-softening behavior [27][28][29].
For the seismic down-hole test, the companion paper [18] presented a novel concept to correlate the shear wave speed, C S (and thus the small-strain shear modulus, G 0 ), to the tangent constrained modulus, M t .A review of published data from seismic laboratory tests has shown that void ratio, e, shear strain, γ, effective confining stress, σ ′ and stress history are the most important parameters affecting settlement behavior.G 0 reflects the stiffness properties of soils at a small strain.It can be used to determine the constrained modulus at a small strain, M t .An empirical relationship developed in [27] was used to describe the degradation of the secant shear modulus, G s , over a wide strain range (10 −4 to 10 −1 %).The tangent shear modulus, G t , was derived by integrating the secant shear modulus, G s , as a function of shear strain, γ.Assuming a strain-dependent Poisson's ratio, ν, the corresponding tangent constrained modulus, M t , could subsequently be derived.A relationship was obtained between the small-strain secant shear modulus, G 0 , and the tangent constrained modulus, M t , at large strain, which can be used to estimate the modulus number, m, from the small-strain shear modulus, G 0 .For details, reference is made to the companion paper.
An important but often neglected observation proposed in [20,28] is that G 0 is not sensitive to stress history (OCR) if PI is <10%.OCR denotes the overconsolidation ratio, and PI the plasticity index.Consequently, seismic tests do not reflect the preloading effect (stress history), which, therefore, needs to be considered separately in a settlement analysis.
This paper demonstrates how the constrained modulus and modulus number can be determined from different in situ tests performed at a well-documented test site consisting of a silty sand deposit.

Field Investigations
Extensive geotechnical investigations were conducted at the ISSMGE TC 212 (Deep foundations) reference test site in Santa Cruz, Bolivia.As part of a comprehensive testing program, different types of in situ tests were used to establish the strength and deformation properties of the silty sand deposit.The field investigations included cone penetration tests with pore water pressure measurements (CPTU), standard penetration tests (SPTs), and flat dilatometer tests (DMTs).The interpretation of the geotechnical investigations and the determination of the compressibility properties were reported in [29,30].In addition, seismic field investigations, comprising seismic down-hole tests combined with CPT (SCPT), seismic dilatometer tests (SDMT), and surface wave measurements (MASW), were performed.Experts of the participating testing companies interpreted the results, and the evaluations represent state-of-practice.The seismic tests have been reported previously in [29].This paper presents the constrained modulus derived from static in situ tests and those obtained from the seismic tests.The results of the field investigations were interpreted in [30].

Geotechnical Conditions
The geotechnical setting of the test site has been described in detail in [31].A geotechnical profile at a representative test location (A3) is shown in Figure 1.The soil deposit (about 20 m deep) consists of fine to medium sands with intermittent layers of silt or clay.The stress history of the soil deposit is complex, as it has been affected by a sedimentationerosion-sedimentation process from a nearby river.Below a 2 m thick surface crust, the following 4 m are composed of loose to medium dense silt, clayey sand, and sand, overlying a 6 m thick sand layer.Below about 12 m depth, layers of compact to dense silty sand and loose sand occur.The groundwater table varied seasonally and was located between 0.5 and 2 m below the ground surface.
Geotechnics 2024, 4, FOR PEER REVIEW 3 combined with CPT (SCPT), seismic dilatometer tests (SDMT), and surface wave measurements (MASW), were performed.Experts of the participating testing companies interpreted the results, and the evaluations represent state-of-practice.The seismic tests have been reported previously in [29].This paper presents the constrained modulus derived from static in situ tests and those obtained from the seismic tests.The results of the field investigations were interpreted in [30].

Geotechnical Conditions
The geotechnical setting of the test site has been described in detail in [31].A geotechnical profile at a representative test location (A3) is shown in Figure 1.The soil deposit (about 20 m deep) consists of fine to medium sands with intermittent layers of silt or clay.The stress history of the soil deposit is complex, as it has been affected by a sedimentation-erosion-sedimentation process from a nearby river.Below a 2 m thick surface crust, the following 4 m are composed of loose to medium dense silt, clayey sand, and sand, overlying a 6 m thick sand layer.Below about 12 m depth, layers of compact to dense silty sand and loose sand occur.The groundwater table varied seasonally and was located between 0.5 and 2 m below the ground surface.

Cone Penetration Test
The CPTU results were performed according to the guidelines in [5,32].Regarding the interpretation of the tests, reference is made to [33][34][35].The test results are shown in Figure 2. The CPTU gives more detailed information about the soil layer composition and strength properties than the SPT, cf. Figure 1.The pore water pressure adjusted cone resistance, qt, is presented in Figure 2a and shows a surface layer down to 2 m, consisting of dense sand (qt ~ 4 MPa), below which the soil becomes looser.Between 2 and 6 m, qt is <2.5 MPa, except for a denser layer between 4.5 and 6 m.From 6.5 m to about 12 m, qt varies generally between 8 and 12 MPa, except for three softer layers, which can be identified at 6, 7, and 10.5 m, respectively.

Cone Penetration Test
The CPTU results were performed according to the guidelines in [5,32].Regarding the interpretation of the tests, reference is made to [33][34][35].The test results are shown in Figure 2. The CPTU gives more detailed information about the soil layer composition and strength properties than the SPT, cf. Figure 1.The pore water pressure adjusted cone resistance, q t , is presented in Figure 2a and shows a surface layer down to 2 m, consisting of dense sand (q t ~4 MPa), below which the soil becomes looser.Between 2 and 6 m, q t is <2.5 MPa, except for a denser layer between 4.5 and 6 m.From 6.5 m to about 12 m, q t varies generally between 8 and 12 MPa, except for three softer layers, which can be identified at 6, 7, and 10.5 m, respectively.eotechnics 2024, 4, FOR PEER REVIEW  The variation in the sleeve resistance, f s , with depth is shown in Figure 2b.In the top sand layer, the sleeve resistance is low.Between 1.5 and 2.5 m, f s increases sharply.From about 2.5 m to 6 m, f s is less variable, at about 40 kPa.From 6 m, the sleeve resistance increases to about 60 kPa except for looser (7 m) and denser (10.5-11 m) layers.
The excess pore water pressure, u (Figure 2c), indicates that at the time of testing, the groundwater table was located approximately 0.5 m below the ground surface.The excess pore water pressure increases in the more fine-grained layers with increasing depth.However, in the occasional, denser sand layers, the soil shows dilatant behavior with pore water pressures well below the hydrostatic pressure (6.3, 7.1, and 11 m).
The soil type can be assessed using the Soil Behavior Type (SBT) index, I c , which represents zones in the non-normalized SBT chart [36], as shown in Table 1.Ref. [37] proposed a method for estimating the modulus number, m.The modulus number can be derived from a stress-adjusted cone resistance, q CM : where a = empirical modulus factor and σ r = reference stress (100 kPa).q CM can be determined from the following relationship: where q c = cone resistance and σ ′ 0 = mean effective stress.The modulus factor, a, which reflects soil type, is shown in Table 1.The empirical modulus factor, a, has been related to the SBT index, I c , simplifying the application of Equation (2).
The soil classification according to Table 1 is shown in Figure 2d.Four major soil layers can be identified: top sand layer (0-1.5 m); clay with silt layers (1.5-4.5 m); sandy silt and clayey silt with sand layer (4.5-6 m); and sand (6-12 m) with layers of silt at 6.0, 7.0, and 10.5 m.The soil layer description agrees with the pore water pressure observations as shown in Figure 2c.
The stress history of the soil deposit affects settlements.Therefore, it is important to estimate the preloading stress, σ ' p , either based on geological information or by empirical methods.As it is difficult to obtain undisturbed soil samples, empirical correlations between in situ tests and preloading stress should be used.Ref. [37] proposed, for natural soils, including sands, silts, clays, and mixed soil types, the following relationship to estimate the preloading stress, σ ′ p : where (stresses in kPa) q t = stress-corrected cone resistance, σ v = vertical total stress, and m ′ = grain size parameter (not to be confused with the modulus number).The grain size parameter, m ′ , increases with fines content and decreases with mean grain size (clean quartz sands: m ′ ≈ 0.72, silty sands: m ′ ≈ 0.8, clays: m ′ ≈ 1.0).Although Equation (3) gives only an approximate estimate of the preloading stress, it is recommended to use the approximate value rather than completely neglecting the preloading effect.The overconsolidation ratio, OCR, can now be calculated from the pre-consolidation stress, σ ' p , and the vertical effective stress, σ ′ v : Based on the information derived from the CPTU, the OCR was calculated using Equations ( 3) and ( 4).The following values of the grain size parameter were assumed: sand m ′ = 0.72; silt m ′ = 0.8.The estimated OCR as a function of depth is shown in Figure 3. Due to its definition, OCR can be very sensitive (too high) at shallow depths due to the low vertical effective stress.The soil layer down to about 1.5 m is heavily preloaded with OCR ranging from 8 to 15. Below that depth, OCR varies typically between 1 and 5, with an average value of 2.5.For practical purposes, the sand deposit below 2 m depth can be classified as slightly overconsolidated, except for two layers between 3 and 4.5, 5.5 and 6.5, and 7.5 and 8 m.
Geotechnics 2024, 4, FOR PEER REVIEW 6 approximate value rather than completely neglecting the preloading effect.The overconsolidation ratio, OCR, can now be calculated from the pre-consolidation stress,  , and the vertical effective stress, σ′v: Based on the information derived from the CPTU, the OCR was calculated using Equations ( 3) and ( 4).The following values of the grain size parameter were assumed: sand m′ = 0.72; silt m′ = 0.8.The estimated OCR as a function of depth is shown in Figure 3. Due to its definition, OCR can be very sensitive (too high) at shallow depths due to the low vertical effective stress.The soil layer down to about 1.5 m is heavily preloaded with OCR ranging from 8 to 15. Below that depth, OCR varies typically between 1 and 5, with an average value of 2.5.For practical purposes, the sand deposit below 2 m depth can be classified as slightly overconsolidated, except for two layers between 3 and 4.5, 5.5 and 6.5, and 7.5 and 8 m.The modulus number, m, for normally consolidated conditions, can now be calculated based on Equation (1).The modulus modifier, a, was chosen according to Table 1.The effect of preloading on the modulus number was taken into account by applying the following relationship, proposed in [19]: where mu = modulus number determined from the unloading test.Equation ( 5) was applied to soil layers with OCR > 3, cf. Figure 3.The modulus number, m, for normally consolidated conditions, can now be calculated based on Equation (1).The modulus modifier, a, was chosen according to Table 1.The effect of preloading on the modulus number was taken into account by applying the following relationship, proposed in [19]: where m u = modulus number determined from the unloading test.Equation ( 5) was applied to soil layers with OCR > 3, cf. Figure 3.
Figure 4 shows the difference between m for normally consolidated (NC) and preloaded (OC) conditions.The stress history influences the modulus number, and this effect should be taken into account.
Geotechnics 2024, 4, FOR PEER REVIEW 7 Figure 4 shows the difference between m for normally consolidated (NC) and preloaded (OC) conditions.The stress history influences the modulus number, and this effect should be taken into account.The tangent constrained modulus, Mt, can be calculated according to [14]: where m = modulus number (dimensionless), σr = reference stress (equal to 100 kPa), σ′v = vertical effective stress, and j = stress exponent.The variation in the constrained modulus with depth for normally consolidated (NC) and overconsolidated (OC) conditions is shown in Figure 5.When calculating Mt, the stress exponent for normally consolidated sand, j = 0.5, and for preloaded (elastic) sand, j = 1, was used.The tangent constrained modulus, M t , can be calculated according to [14]: where m = modulus number (dimensionless), σ r = reference stress (equal to 100 kPa), σ ′ v = vertical effective stress, and j = stress exponent.The variation in the constrained modulus with depth for normally consolidated (NC) and overconsolidated (OC) conditions is shown in Figure 5.When calculating M t , the stress exponent for normally consolidated sand, j = 0.5, and for preloaded (elastic) sand, j = 1, was used.

Dilatometer Test
The DMT was performed at a lateral distance of 1.1 m from the CPTU.However, the DMT tests were carried out approximately one month later.For details regarding the evaluation and interpretation of the DMT, reference is made to [21].The results of the DMT measurements are shown in Figure 6.

Dilatometer Test
The DMT was performed at a lateral distance of 1.1 m from the CPTU.However, the DMT tests were carried out approximately one month later.For details regarding the evaluation and interpretation of the DMT, reference is made to [21].The results of the DMT measurements are shown in Figure 6.
Figure 6a shows the pressure readings, p 0 and p 1 , which vary significantly with depth.The pressure readings are typical for sandy soil in the surface sand layer down to 2 m.However, between 2 and 4.5 m, the pressure readings (p 0 and p 1 ) in the soft, fine-grained soil layer are very low and almost overlapping.Below 4.5, the p 1 -values increase gradually.From 7 to 12 m, the p 1 -readings rise sharply to unusually high values exceeding 1.500 kPa.
The material index, I D , can be derived from the pressure readings, which is an indicator of soil type, cf. Figure 6b.Below dense sand down to 2.5 m depth, the soil comprises fine-grained layers (silt and clay).From 5 to 12 m depth, the soil layer can be characterized as sand (I D > 2), except for occasional, more fine-grained layers (silt and clay).The I D values confirm the soil type classification based on the I c -values from the CPTU shown in Figure 2d.
The variation in the horizontal stress index, K D , is shown in Figure 6c.Below the sand layer down to 2 m (K D > 15), K D is relatively constant (2-4) down to about 7 m depth.In the sand layer between 7 and 9 m, K D increases significantly (8)(9)(10)(11)(12)(13) but returns in the underlying layers again to lower values (2.5-5).According to [20], the dilatometer modulus, E D , can be estimated from the following empirical relationship: where p 0 = dilatometer pressure reading at the start of the expansion, and p 1 = dilatometer pressure reading at the end of the expansion.The variation in E D with depth is shown in Figure 6c.From E D , the constrained modulus, M DMT , can be calculated based on the parameter R M, which has been defined in [38]: where R M = the empirical parameter that is dependent on I D and K D .The variation in M DMT with depth is shown in Figure 7. Ref. [20] suggested that the constrained modulus estimated from DMT corresponds to a range of vertical strains ε v ≈ 0.1 to 0.5%.However, it is not stated whether the empirical relationship given by Equation ( 8) reflects the pre-loading effect or applies only to normally consolidated soils.
clay).The ID values confirm the soil type classification based on the Ic-values from the CPTU shown in Figure 2d.The variation in the horizontal stress index, KD, is shown in Figure 6c.Below the sand layer down to 2 m (KD > 15), KD is relatively constant (2)(3)(4) down to about 7 m depth.In the sand layer between 7 and 9 m, KD increases significantly (8)(9)(10)(11)(12)(13) but returns in the underlying layers again to lower values (2.5-5).
According to [20], the dilatometer modulus, ED, can be estimated from the following empirical relationship: where p0 = dilatometer pressure reading at the start of the expansion, and p1 = dilatometer pressure reading at the end of the expansion.The variation in ED with depth is shown in Figure 6c.From ED, the constrained modulus, MDMT, can be calculated based on the parameter RM, which has been defined in [38]: where RM = the empirical parameter that is dependent on ID and KD.The variation in MDMT with depth is shown in Figure 7. Ref. [20] suggested that the constrained modulus estimated from DMT corresponds to a range of vertical strains εv ≈ 0.1 to 0.5%.However, it is not stated whether the empirical relationship given by Equation ( 8) reflects the preloading effect or applies only to normally consolidated soils.Assuming that M t is approximately equal to M DMT , the modulus number, m, can be derived according to [13]: which correlates the tangent modulus, M t , and the modulus number, m.To account for variations in the soil conditions, different values of the stress exponent, j, were chosen for different soil layers (silt: 0.25; sand: 0.5; preloaded soil: 1.0).The variation in the modulus number with depth derived from DMT is shown in Figure 8.The modulus number, m, obtained from DMT (Figure 8) reasonably agrees with the modulus number derived from the CPT (Figure 4) when the pre-consolidation stress is considered.
which correlates the tangent modulus, Mt, and the modulus number, m.To account for variations in the soil conditions, different values of the stress exponent, j, were chosen for different soil layers (silt: 0.25; sand: 0.5; preloaded soil: 1.0).The variation in the modulus number with depth derived from DMT is shown in Figure 8.The modulus number, m, obtained from DMT (Figure 8) reasonably agrees with the modulus number derived from the CPT (Figure 4) when the pre-consolidation stress is considered.

Seismic Tests
Seismic tests have the advantage that these can be performed with minimal soil disturbance.Two types of seismic down-hole tests (SCPT and SDMT) were performed according to ISSMGE guidelines [38].As can be observed from the static in situ tests, the site conditions are variable.The sand deposit includes layers of silt and clay.The SCPT down-hole test was carried out with one seismic sensor, while the SDMT used two seismic sensors located 0.5 m apart.The lateral distance at the ground surface between the two tests was 1.3 m.The first measurements started at 1.0 m (SDMT) and 1.5 m depth (SCPT), respectively.For details regarding the performance and interpretation of the seismic measurements, reference is made to [9].It should be mentioned that refraction and surface wave measurements (SASW) were also performed.However, both methods gave inconsistent results and were not included in this analysis.The results of the shear wave speed measurements by SCPT and SDMT are shown in Figure 9a.

Seismic Tests
Seismic tests have the advantage that these can be performed with minimal soil disturbance.types of seismic down-hole tests (SCPT and SDMT) were performed according to ISSMGE guidelines [38].As can be observed from the static in situ tests, the site conditions are variable.The sand deposit includes layers of silt and clay.The SCPT down-hole test was carried out with one seismic sensor, while the SDMT used two seismic sensors located 0.5 m apart.The lateral distance at the ground surface between the two tests was 1.3 m.The first measurements started at 1.0 m (SDMT) and 1.5 m depth (SCPT), respectively.For details regarding the performance and interpretation of the seismic measurements, reference is made to [9].It should be mentioned that refraction and surface wave measurements (SASW) were also performed.However, both methods gave inconsistent results and were not included in this analysis.The results of the shear wave speed measurements by SCPT and SDMT are shown in Figure 9a.
Measurements were unreliable down to about 1.5 m as the seismic source was located too close (approximately 0.5 m) from the test point.From 2 to 5 m, in the silty clay and clayey silt with layers of silty sand, the shear wave speed, C S , varies between 100 and 200 m/s, except for the silty sand layer between 2 and 3 m.Between 5 and 7.5 m, the shear wave speed increases gradually to 275 m/s.Below that depth, the shear wave speed varies within more narrow boundaries from 200 to 250 m/s.Reasonable agreement exists between the two test types; however, the SCPT shows a slightly higher variability of shear wave speed measurements.This may be because only one seismic sensor was used by the SCPT, which could have caused some uncertainty regarding the identification of first arrival times.
A comparison between the results from the CPTU (Figure 2) and the DMT (Figure 6) with the shear wave speed measurements (Figure 9a) suggests that seismic measurements are less sensitive to soil layer variations than the CPTU and the DMT.Measurements were unreliable down to about 1.5 m as the seismic source was located too close (approximately 0.5 m) from the test point.From 2 to 5 m, in the silty clay and clayey silt with layers of silty sand, the shear wave speed, CS, varies between 100 and 200 m/s, except for the silty sand layer between 2 and 3 m.Between 5 and 7.5 m, the shear wave speed increases gradually to 275 m/s.Below that depth, the shear wave speed varies within more narrow boundaries from 200 to 250 m/s.Reasonable agreement exists between the two test types; however, the SCPT shows a slightly higher variability of shear wave speed measurements.This may be because only one seismic sensor was used by the SCPT, which could have caused some uncertainty regarding the identification of first arrival times.
A comparison between the results from the CPTU (Figure 2) and the DMT (Figure 6) with the shear wave speed measurements (Figure 9a) suggests that seismic measurements are less sensitive to soil layer variations than the CPTU and the DMT.
The shear modulus at a small strain, G0, can be calculated from the shear wave speed and the bulk density.The variation in G0 with depth for both seismic tests is shown in Figure 9b.There is generally good agreement between the SCPTU and the SDMT results.
In the companion paper [18], a relationship for normally consolidated sandy soils between the modulus number, m, and the small-strain shear modulus, G0, has been developed: where ν = Poisson's ratio, γ = shear strain, σr = reference stress (100 kPa), and σ′v = vertical effective stress.A shear strain level (γ) of 0.25% was used, which can be considered to The shear modulus at a small strain, G 0 , can be calculated from the shear wave speed and the bulk density.The variation in G 0 with depth for both seismic tests is shown in Figure 9b.There is generally good agreement between the SCPTU and the SDMT results.
In the companion paper [18], a relationship for normally consolidated sandy soils between the modulus number, m, and the small-strain shear modulus, G 0 , has been developed: where ν = Poisson's ratio, γ = shear strain, σ r = reference stress (100 kPa), and σ ′ v = vertical effective stress.A shear strain level (γ) of 0.25% was used, which can be considered to represent static loading conditions.The interpretation of Equation ( 10) is shown in a diagram presented in Figure 10.The diagram shows a relationship between the small-strain shear modulus and the modulus number for two levels of vertical effective stress level.Three different types of sandy soil (low, medium, and high) are identified.
According to Equation (10), it is now possible to estimate the modulus number, m, for normally consolidated conditions from the small-strain shear modulus, G 0 .For soil layers with OCR > 3, the preloading effect can be accounted for according to Equation (5), from which the preloading constrained modulus (m OC ) was derived for both tests.The variation in the modulus number for normally and overconsolidated conditions is shown in Figure 11 for both seismic tests.
represent static loading conditions.The interpretation of Equation ( 10) is shown in a diagram presented in Figure 10.The diagram shows a relationship between the smallstrain shear modulus and the modulus number for two levels of vertical effective stress level.Three different types of sandy soil (low, medium, and high) are identified.According to Equation (10), it is now possible to estimate the modulus number, m, for normally consolidated conditions from the small-strain shear modulus, G0.For soil layers with OCR > 3, the preloading effect can be accounted for according to Equation ( 5), from which the preloading constrained modulus (mOC) was derived for both tests.The variation in the modulus number for normally and overconsolidated conditions is shown in Figure 11 for both seismic tests.
As outlined in the above-described concept, the small-strain shear modulus, G0, can be calculated from the tangent constrained modulus (Mt,NC) for normally consolidated conditions.
For soil layers with OCR > 3, the preloading effect was accounted for according to Equation (3), from which the preloading constrained modulus (Mt,OC) was derived for both tests.
The variation in the tangent constrained modulus from seismic tests (SCPTU and SDMT) for normally consolidated (NC) and overconsolidated (OC) conditions is shown in Figure 12.
As is indicated by the stress exponent, n, in Equation ( 4), in granular soils, the smallstrain shear modulus, G0, is not sensitive to preloading (OCR).This is illustrated by the following example.Assuming OCR = 5 in sand (PI = 0), according to Equation (4), n = 0.045 (Equation ( 4)), G0 will increase by less than 6%.It can be concluded that, in sand, the preloading effect on G0 is negligible for practical purposes.Even in the case of more finegrained granular soils (PI = 10) and OCR = 5, G0 will increase only slightly due to preloading (by less than 16%).As outlined in the above-described concept, the small-strain shear modulus, G 0 , can be calculated from the tangent constrained modulus (M t,NC ) for normally consolidated conditions.
For soil layers with OCR > 3, the preloading effect was accounted for according to Equation (3), from which the preloading constrained modulus (M t , OC ) was derived for both tests.
The variation in the tangent constrained modulus from seismic tests (SCPTU and SDMT) for normally consolidated (NC) and overconsolidated (OC) conditions is shown in Figure 12.As is indicated by the stress exponent, n, in Equation ( 4), in granular soils, the smallstrain shear modulus, G 0 , is not sensitive to preloading (OCR).This is illustrated by the following example.Assuming OCR = 5 in sand (PI = 0), according to Equation (4), n = 0.045 (Equation ( 4)), G 0 will increase by less than 6%.It can be concluded that, in sand, the preloading effect on G 0 is negligible for practical purposes.Even in the case of more fine-grained granular soils (PI = 10) and OCR = 5, G 0 will increase only slightly due to preloading (by less than 16%).
As pointed out in the companion paper, in granular soils, the small-strain shear modulus, G 0 , is less sensitive to preloading (OCR).Thus, it can be concluded that G 0, determined by seismic measurements, does not reflect stress history (overconsolidation).Therefore, the preloading effects should be incorporated by considering OCR values that can be estimated from the in situ tests.The preloading effect can then be accounted for in a separate step, e.g., Equation (4).

Discussion
Settlement requirements generally govern the design of foundations on granular soil deposits.However, little guidance can be found in the geotechnical literature regarding the determination of soil stiffness (constrained modulus).The tangent modulus method, which applies to all soil types, was introduced in [14] and is a useful concept for settlement analyses.A critical step in any settlement analysis is the estimation of the compression properties of the soil.However, undisturbed soil samples are difficult or impossible to obtain from granular soil deposits.Therefore, soil stiffness properties must be based on situ tests.In the past, general rules of thumb or simplified empirical relationships have been used for design purposes, even in the case of complex projects.
The companion paper [18] presents novel concepts for determining the constrained soil modulus from different in situ tests.This paper describes the results of in situ tests performed in a silty sand deposit, the data interpretation for calculating the constrained modulus, and a comparison of obtained values.
Tests were carried out at a well-documented test site, consisting of a sandy soil deposit with layers of silt and clay.The had experienced a complex stress history.Initially, the site conditions were established based on conventional tests such as the SPT and analyses of disturbed soil samples.Subsequently, more advanced in situ tests (CPTU, DMT, and SCPT/SDMT) were performed.The geotechnical conditions of the soil deposit were complex (sand with layers of silt and clay).
A comparison of results from different in situ tests shows that the SPT does not reflect the complexity of soil stratification.The CPTU and the DMT results are in good agreement and provide a more detailed description of the soil layers and their geotechnical properties.
The CPTU is a widely used test for settlement design from which the constrained modulus, M t , can be derived, cf.Equation (1).As a first step, the modulus number, m, is calculated using the stress-adjusted cone resistance, q CM, and a modulus factor, a, to be selected for different soil types, as suggested in Table 1.The obtained values of the modulus number, m, agree with the data published in the literature [14,19,30].The tangent constrained modulus, M t , can then be calculated according to Equation (6).
Stress history is an important factor affecting settlement analyses.Laboratory compression tests are difficult to perform on granular soils.The empirical relationship from CPT investigations, proposed in [37], appears to give reasonable results for granular soils.The effect of preloading on the modulus number can be taken into account by applying Equation ( 5), which suggests that the modulus number at unloading/reloading, m u , is significantly higher than in the case of normally consolidated soil, m.
DMT investigations were also performed at a close distance from the CPTU.The pressure readings (p 0 and p 1 ) from the DMT, and consequently the dilatometer modulus, E D , showed a wider range of values than expected.Ref. [20] proposed a method for estimating the constrained modulus, M t , based on E D values.In the present investigation, the constrained modulus values were variable: very low in the fine-grained soils but unexpectedly high in the denser layers.Many of the derived values of the modulus number, m, fell outside their typical range [13].
Two types of seismic downhole tests (SCPT and SDMT) were performed.The results of the two tests are in good agreement.However, the derived shear wave speed appears to be less sensitive to soil layer variations than the CPTU and the DMT.The shear wave speed determined by the SDMT (two seismic sensors 0.5 m apart) gave a higher resolution than that of the SCPT, which employed only one sensor.
It is important to recognize that in granular soils (PI < 10%), the shear wave speed is less sensitive to OCR [28].Therefore, the constrained tangent modulus, M t , derived from the small strain shear modulus, G 0 , does not reflect stress history.Thus, the modulus number based on seismic tests must be adjusted in preloaded soils.

Summary and Conclusions
This paper applies the concepts presented in the companion paper: "Determination of Constrained Modulus of Granular Soil from In Situ Tests-Part 1 Analyses" [18].Extensive field tests were performed at a well-documented test site consisting of sand with silt and clay layers.Different types of in situ tests were performed: penetration tests, flat dilatometer tests, and seismic down-hole tests.The constrained modulus and modulus number were derived from CPTU and DMT investigations, respectively.The shear wave speed was measured by two seismic down-hole tests (SCPT and SDMT), from which the small-strain shear modulus, G 0 , could be evaluated.The constrained tangent modulus was derived based on the concepts outlined in the companion paper, from which the range of modulus numbers for different soil layers could be determined.The results of seismic down-hole tests were compared with CPTU and DMT results and with empirical data from the literature.
Equation (10) gives a relationship between the maximum shear modulus, G 0 , from seismic tests and the modulus number, m, at 0.25% shear strain.From Figure 10, the modulus number, m, can be estimated from G 0 , for medium-dense, normally consolidated sand.
The examination of the results from the static (CPTU and DMT) and seismic (SCPTU and SDMT) tests leads to the following conclusions: • The CPTU and the DMT results are in good agreement and provide detailed informa- tion regarding soil type and layering.

•
In sandy soil, values of the modulus number, m, and the constrained modulus, M t , derived from CPTU were in good agreement with data published in the literature.However, in soft soils (silt and clay), the constrained modulus should be determined from laboratory compression tests instead.

•
DMT pressure measurements (p 0 and p 1 ) varied widely and sometimes gave unreasonable values.In some cases, E D values were very low in fine-grained soils and very high in denser, granular layers.• The derived modulus numbers, m, and constrained modulus, M t , were in some cases in poor agreement with published data.The high stiffness values could possibly be attributed to a pre-loading effect.• The SCPT and SDMT measurements are in good agreement.However, neither of the two seismic methods could detect softer layers embedded in the dense sand.Thus, seismic tests should be combined with other in situ tests to detect soft layers.
The field investigations reported in this paper show that in situ tests can be useful for estimating the deformation properties of granular soils.The outlined methods for calculating the constrained modulus are based on transparent concepts, which, however, need to be verified and improved in the future, preferably by field observations.The concepts outlined in the companion paper are of practical significance for geotechnical design.However, it is necessary to interpret the derived data (modulus values) diligently and apply the results to major projects with judgment.
Funding: The author declares that no funding has been received.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.The data are not publicly available due to ethical.

Conflicts of Interest:
The author declares that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figure 1 .
Figure 1.Soil sample from borehole A3 and SPT N-values and cone resistance, q c , adapted from [31].

Figure 4 .
Figure 4. Modulus number derived from CPTU for assuming normally consolidated (NC).The effect of preloading (OC) was considered according to Equation (5).

Figure 4 .
Figure 4. Modulus number derived from CPTU for assuming normally consolidated (NC).The effect of preloading (OC) was considered according to Equation (5).

Figure 5 .
Figure 5. Tangent constrained modulus as a function of depth, determined from modulus number, m, according to Equation (9) given in the companion paper.

Figure 5 .
Figure 5. Tangent constrained modulus as a function of depth, determined from modulus number, m, according to Equation (9) given in the companion paper.

Figure 8 .
Figure 8.The variation in modulus number with depth from DMT derived from the tangent modulus according to Equation (9).

Figure 8 .
Figure 8.The variation in modulus number with depth from DMT derived from the tangent modulus according to Equation (9).

:
This paper is dedicated to the late Bengt B. Broms, my academic advisor and personal friend over many years.The comprehensive field investigations at the ISSMGE Test site in Bolivia were only possible with the technical and financial support of the company Incotec S.A.The enthusiasm of its managing director, H. M. Terceros, and his competent staff during the planning and implementation of the investigation is gratefully acknowledged.The support from ISSMGE TC 212 (Deep Foundations) and its chairman, A. Mandolini, provided the framework for the present and future investigations.Studio Prof. Marchetti s.r.l.conducted the dilatometer measurements.The support by D. Marchetti was most beneficial during the in situ test.The fruitful discussions with C. Wersäll, B. H. Fellenius, and P. Mayne are acknowledged.

Table 1 .
[36] classification according to the SBT chart[36]and comparison with empirical modulus factor, a.