# Estimating Deformation Modulus and Bearing Capacity of Deep Soils from Dynamic Penetration Test

Authors: Shihan Shan; Xiangjun Pei; Weiwei Zhan
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

The dynamic penetration test (DPT) and the Menard pressuremeter test (PMT) have been widely used in geotechnical survey of deep soils for megadam foundations in western China. The DPT measures are not well utilized due to the lack of correction factors and of empirical relationships for deep soils. This study investigates the relationships between the corrected DPT blow counts (N120′), pressuremeter modulus (EPMT), limit pressure (pL), deformation modulus (E0), and bearing capacity (fak) derived from the PMT results. Meanwhile, a nonlinear regression model is developed to predict the DPT correction factor (a) based on the raw DPT blow counts (N120) and the rod length (L) by integrating the available correction factors for shallow gravelly soils suggested by the code provisions and the deep soil data in this work. It is concluded that the proposed DPT correction factors match well with the code suggestions and the new compiled dataset, and the corrected DPT blow counts can be used to reasonably predict the engineering properties of deep sand and clay soils. Although the proposed correlations need to be tested among different soil types and regions, the results shed the light on in situ geotechnical tests and data utilization for deep and thick overburden.


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## Body

## 1. Introduction

Many megadams have been constructed on the valleys in western China to utilize the hydropower resources. The dam foundations are usually placed on the deep and thick overburden soils, which demand engineering properties of deep soils that are deeper than 20 meters. It is expensive to obtain undisturbed soil samples from the deep subsurface for laboratory tests. In situ tests have been widely used to estimate the engineering properties of these deep soils. The challenges in the interpretation of in situ soil tests mainly come from two aspects: (1) the complex soil behavior is influenced by intrinsic soil properties and many environmental factors such as temperature, pressure, and water availability [1]; (2) the lack of control and choice of the boundary conditions in field tests [2]. With increasing numbers of construction projects involving deep soils, it is desirable to explore the applications of in situ tests for these deep soils.The dynamic cone penetration test (DPT) is widely used in the geotechnical survey in river valleys consisting of deep and thick overburden soils because of its characteristics of easy operation, wide applicability to different soil types, and relative low cost. The test consists of repeatedly dropping a hammer weighing 1177 N (120 kg) from a height of 100 cm onto an anvil that is connected by 60 mm diameter drill rods to a solid cone tip with a diameter of 74 mm and a cone angle of 60° [3]. Each hammer drop has potential energy that is theoretically equivalent to 1177 J. The number of blows by the hammer needed for the cone to penetrate the 10 cm strata is the counted N-value (N120). The DPT has been widely applied in Chinese geotechnical practices for foundation design since 1970s [3]. Recently, the DPT has been successfully applied to assess liquefaction of gravelly soils [3, 4]. However, the empirical correlation between DPT measures and soil properties such as deformation modulus and bearing capacity is limited to shallow gravelly soils with depth less than 20 m especially from the Chengdu Plain [5] (see Appendix A).There are many factors that could influence the energy transmitted from the impact of the hammer on the anvil to the rod string and cone and thus affect the value of the blow count of hammer-impact penetration tests [6]. Calibration chamber tests [7, 8] and in situ measurements [6] are usually conducted to evaluate the influential factors on penetration tests and standardization procedure. There are few studies about the influential factors on DPT blow count and its correction. The energy transfer ratio (ETR), defined as the ratio of the energy that passes through the rods to the theoretical potential energy, is the most direct measure of the energy loss within the penetration test system. Cao et al. [3] reported that the Chinese DPT has an average ETR of 89% according to 1,200 hammer energy measurements within the shallow gravelly soils for liquefaction assessment. Zuo and Zhao [9] conducted a series of physical model tests that penetrate the soils within a model box with incremental rod lengths (up to 83 m) and compute the correction factors as the blow count of any rod length to the blow count of 2 m long rod under the same soil condition. Their results suggest that the correction factors of DPT gradually decrease with the increase of rod length (correction factor is around 0.5 when rod length is 83 m), which is independent of soil type and overburden pressure. Li et al. [10] measured the stress distribution at several rod depths using a series of in situ DPT tests. Their results suggest that the maximum peak stress drops nonlinearly along the rod length (from the top and bottom) and the maximum peak stress drop ratio increases with the rod length. Based on numerical simulation results, they proposed empirical correlations to estimate the rod-length-dependent correction factors for DPT blow counts. Based on many engineering practices, the Chinese Code for Investigation of Geotechnical Engineering [11], hereinafter called Chinese Code, suggests that the correction factors for DPT blow counts are simultaneously affected by the raw DPT blow counts and the rod length. However, the DPT correction factors suggested by the Chinese Code are limited to rod length below 19 m and raw DPT blow count less than 40 (see Appendix B).This study attempts to expand the DPT correction factors for deep soils and to use the corrected DPT blow counts to predict deformation modulus and bearing capacity of deep soils. For these purposes, a database consisting of 74 pairs of DPT and pressuremeter test (PMT) results is compiled from a geotechnical survey project for a dam designed on a deep overburden site in southwestern China. The geology and geotechnical conditions of the study site are described in Section2, and the in situ tests and data processing are detailed in Section 3. The empirical relationships for estimating DPT correction factors and engineering properties of soil using DPT test results are shown in Section 4, and the last section draws the conclusions.


## 2. Geological and Geotechnical Conditions

The study area is a dam construction site located in southwestern China. A high-rise dam will be placed on the river valley that consisted of very deep and thick overburden. Many types of geological and geotechnical surveys (see Figure1) have been conducted at the project site to investigate the structure and properties of the underlying soils. According to borehole data, the maximum thickness of overburden sediments reaches 567 m at the middle point of the river valley (ZKm304 in Figures 1 and 2). The overburden thickness decreases from the middle to the two sides, which is consistent with the old U-shape valley topography. The bedrock in the study area mainly consists of Precambrian gray gneiss (Pt2-3Nqa) and is exposed on the valley slopes. The deep overburden can be divided to four major layers from the bottom to the top (i.e., from oldest to newest in geological age):Figure 1
Site map showing locations of geotechnical investigations.Figure 2
Soil profile map along the line A3-A3′ in Figure1.Layer I (Pleistocene gravelly soil, see Figure3(f)): it is located at the bottom of the old riverbed. Its burial depth ranges from 350 to 460 m according to borehole investigations at different site locations. The geological origin of this layer is glacial outwash deposits (Q3fgl+gl).Figure 3
Typical soil samples of different soil layers and depth (from ZKm304). (a) Layer IV. (b) Layer III-3. (c) Layer III-2. (d) Layer III-1. (e) Layer II. (f) Layer I.
(a)(b)(c)(d)(e)(f)Layer II (Pleistocene cobbly soil, see Figure3(e)): its burial depth ranges from 200 to 250 m. Its geological origin is alluvial and pluvial deposits (Q3al+pl).Layer III (Pleistocene sand and clay soil): its burial depth ranges from 6 to 12 m and thickness ranges from 200 to 250 m. It majorly consists of sand, sandy silt, and silty clay. The geological origin of Layer III is alluvial and lacustrine deposits (Q3al+l).Layer IV (Holocene gravelly soil, see Figure3(a)): this layer is the modern alluvial deposit (Q4al).The engineering properties of Layer III will be the focus of this work as this soil layer will be used as the foundation soil to support a high-rise dam. The Layer III is made up of the Pleistocene alluvium and lacustrine sediments. According to the soil characteristics explored by the boreholes, this layer is further divided into three sublayers, and the major soils within each sublayer are described as following (from the bottom to the top):Sublayer III-1: it is located at the bottom of Layer III. This sublayer majorly consists of dark gray to brownish-yellow sand (see Figure3(d)). The particle size distribution is shown in Figure 4. Its average density is 1.78 g/cm3 and average moisture content is about 4.8%. The void ratio is 0.515 and the specific gravity is 2.69. The liquid limit (LL) and plasticity index (PI) are 20.4 and 8.9, respectively. The soil gradation measures, uniformity coefficient (Cu), and coefficient of gradation (Cc) are 7.6 and 1.0, respectively. According to the Unified Soil Classification System (USCS) [12], the soil is classified as well-graded sand with clay, with the group symbol as SW-SC (see Table 1). The burial depth of this sublayer ranges from 70 to 95 m. The layer thickness has large variation along the transverse (cross river) direction, with thickness of 20 to 40 m at two sides and 150 to 170 m at the middle.Figure 4
Averaged grain size distribution curves of soil samples from soil Layer III.Table 1
Averaged soil parameters for soils within each sublayer of Layer III.
Sublayer IDUSCSGroup nameDensity (g/cm3)Moisture content (%)LLPICuCcIII-3SW-SCWell-graded sand with clay1.715.719.38.56.71.1III-2CLLean clay1.5616.337.316.6100.64III-1SW-SCWell-graded sand with clay1.784.820.48.97.61.0Sublayer III-2: it is located at the middle of Layer III. It majorly consists of dark-gray clay and silt (see Figure3(c)). The burial depth of this sublayer ranges from 50 to 80 m. The thickness ranges from 5.2 to 24.2 m, with an average value of 16 m. The major soil type of this sublayer is clay, with average density of 1.56 g/cm3 and moisture content of 16.3%. The void ratio is 0.746, and the specific gravity is 2.72. The liquid limit and plasticity index are 37.3 and 16.6, respectively. According to USCS, this soil is classified as lean clay with the group symbol of CL (see Table 1).Sublayer III-3: it is located at the top of Layer III. It is made up of dark gray to brown sand (see Figure3(b)). The burial depth ranges from 6 to 40 m. The thickness ranges from 36.85 to 53.8 m, with an average value of 46 m. The average density is 1.71 g/cm3, and the moisture content is 5.7%. The void ratio is 0.573, and the specific gravity is 2.68. The liquid limit and plasticity index are 19.3 and 8.5, respectively. The uniformity coefficient (Cu) and coefficient of gradation (Cc) are 6.6 and 1.1, respectively. According to USCS, the soil is classified as well-graded sand with clay, with the group symbol as SW-SC (see Table 1).


## 3. In Situ Tests and Data Processing

This study uses the dynamic cone penetration test (DPT) and pressuremeter test (PMT) results to develop regression models for estimating DPT correction factors and engineering properties of soils (pressuremeter modulus, limit pressure, deformation modulus, and bearing capacity) within Layer III (burial depth ranges from 6 to 40 m). In total, 74 sets of data are collected from the nine boreholes shown in Table2. According to Table 2, there are 10, 15, and 49 pairs of data for soils within sublayers III-1, III-2, and III-3, respectively. The 11 pairs of data among the 49 ones within the III-3 layer have rod length less than 19 m where the correction factors in the Chinese Code (see Appendix B) can be applied. The remaining 63 DPT measures will require new correction factors that are not available in the Chinese Code. The testing procedure and data processing methods for the DPT and PMT are briefly described in the following sections.Table 2
The database consisting of DPT, PMT measures, and engineering parameters.
BoreholeIDSoil layerL (m)N120EPMT (MPa)p0 (kPa)pf (kPa)pL (kPa)E0 (MPa)fak (kPa)ZKm1021III-335.2167.73230740124030.98510ZKm1022III-348.8368.95270900175046.47630ZKm1023III-350.1156.18270740116027.57470ZKm1024III-358.22716.473601000148037.27640ZKm1025III-268.2114.2121055092022.21340ZKm1026III-277.583.0420050080019.46300ZKm1027III-182.5439.753001070182047.75770ZKm1028III-184.15214.934501100208054.13650ZKm1029III-193.54711.032401000184049.39760ZKm10210III-195.23213.2260860148037.92600ZKm10611III-348.2356.77180720160046.31540ZKm10612III-350.1165.93220700114028.34480ZKm10613III-352.53311.77240920172043.91680ZKm10614III-280.5163.98190600100026.18410ZKm10615III-282.4244.45180640118033.1460ZKm20416III-322.4105.346551094026.87445ZKm20417III-326.72713.8120800160044.03680ZKm20418III-338.5389.1140990172050.68850ZKm20419III-345.23610.86150790170047.58640ZKm20420III-275.5145.056544085024.36375ZKm20421III-278.2155.246049088025.33430ZKm40122III-330.12711.51140940156042.76800ZKm40123III-348.8359.24200850167046.19650ZKm40124III-350.1146.04270740114026.9470ZKm40325III-321.8158.47240800133032.51560ZKm40326III-323.21811.53250900138035.34650ZKm40327III-332.22510.21200920155040.27720ZKm40328III-3342210.67210900142037.03690ZKm40329III-345.53311.2280870174044.98590ZKm40330III-3472210.23380980156035.06600ZKm40331III-360.22615.63320880142036.32560ZKm40332III-271.2116.3120060093022.54400ZKm40333III-274.564.6420554576017.64340ZKm40334III-182.84513.073101070188048.66760ZKm40335III-184.2669.172701010220064.31740ZKm40436III-333.8107.18052090024.44440ZKm40437III-3361610110670109030.54560ZKm40438III-348.8239.63230810144035.9580ZKm40439III-3521912.22180640114031.55460ZKm40440III-264.544.6511042060015.43310ZKm40441III-267.273.9413041073018.88280ZKm50442III-340.63366.343201050174048.42730ZKm50443III-342.1428.083201040195053.64720ZKm50544III-325.5116.88110520100026.75410ZKm50545III-339.1165.34100560102029.61460ZKm50546III-340.832610.31250940160039.83690ZKm50547III-355.43414.04150850162043.84700ZKm50548III-263.8103.7926065096022.05390ZKm50549III-265.293.7610044076020.82340ZKm50550III-270.1174.75110520100028.14410ZKm50551III-186.1297.41160660132036.64500ZKm50552III-189.75113.231801190190052.881010ZKm50653III-321.598.638050089024.84420ZKm50654III-330.7104.638030083024.61220ZKm50655III-332.1117.56053092025.34470ZKm50656III-339.83014.87150820157043.77670ZKm50657III-355.8184.397048099029.98410ZKm50658III-268.2146.956043092025.64370ZKm50659III-270.1104.666038072020.9320ZKm50660III-179.85110.91140920189054.39780ZKm50661III-182.54614.18220920182049.89700ZKm10262III-3122017.423001180148039.98420ZKm10263III-315108.51200630105025.63430ZKm20464III-314.577.637545080021.45375ZKm20465III-316.297.178048091024.39400ZKm20466III-319.5229.63200800150040.39600ZKm40167III-315.8118.66165600105027435ZKm40168III-317.5149.33290850133031.68560ZKm40469III-313.998.0710062095025.6520ZKm40470III-316.186.4713053090023.98400ZKm50471III-310.562.5512048075021.58360ZKm50472III-31253.5216047079019.56310ZKm50473III-315.15124.49160720106029.9560ZKm50674III-319.8125.14047095028.62430Note. Columns 4∼5 were obtained from the dynamic penetration test (DPT), columns 6∼9 were obtained from the pressuremeter test (PMT), and columns 10∼11 were engineering parameters derived using equations (3) and (4).


### 3.1. Dynamic Penetration Test

The dynamic penetration test (DPT) was developed in China during the early 1950s to measure the penetration resistance of gravelly soils. DPT could provide an important new procedure for characterization of gravels and fill a gap in present geotechnical practice between CPT/SPT and BPT testing [4]. The DPT has been widely applied in Chinese geotechnical practices since the code provisions providing guidance for the foundation design using DPT were published in the 1970s [3]. The DPT apparatus consists of a 120 kg hammer with a free-fall height of 100 cm dropped onto an anvil attached to 60 mm diameter drill rods, which in turn are attached to a solid cone tip with a diameter of 74 mm and a cone angle of 60° (Figure 5) [11]. The blow counts for penetrating every 10 cm of soils are recorded and termed as N120. The DPT is applicable to gravelly soils and weathered extreme-soft and soft rocks [5]. The DPT is widely used in the geotechnical survey in valleys consisting of deep overburden in southwestern China because of its characteristics of easy operation, wide applicability to different types of soils, and cheap cost.Figure 5
(a) Photo of the in situ dynamic penetration test (DPT). (b) Sketch of the DPT apparatus [3].
(a)(b)It is controversial about whether or not to correct the DPT blow count and how to correct it [5]. Currently, the Chinese Code suggests multiplying a correction factor (α) to the raw DPT blow counts following equation (1) to get the corrected DPT blow count (N120′). Since DPT was widely used to support the foundation design on gravelly soils located in Chengdu Plain, the Design Code for Building Foundation of Chengdu Region [13], hereinafter called Chengdu Code, recommends empirical relationships to estimate the soil deformation modulus, compression modulus, and ultimate capacity of gravelly soils using N120′ based on large amount of engineering practices (see Appendix A):(1)N120′=αN120,where N120′ is the corrected DPT blow count, N120 is the raw DPT blow count, and α is the correction factor that is available for rod length (L) less than 19 m and N120 below 40 (see Appendix B).


### 3.2. Pressuremeter Test

The pressuremeter test (PMT) is an in situ test developed by Menard [14] to measure the deformation properties of soil and weak rock. The PMT consists of placing an inflatable cylindrical probe in a predrilled borehole and expanding this probe, while measuring the changes in volume and pressure in the probe [15]. The measured volume change of the probe is plotted against the applied pressure (see Figure 6). The pressuremeter modulus is determined as follows [15]:(2)EPMT=2·1+μ·Vo+Vm·ΔPΔV,where EPMT is the pressuremeter modulus (MPa), p0, pf, and pL are initial, yield, and limit pressure, respectively, V0 is initial volume of the probe (cm3), Vm is the corrected volume reading in the center portion of ΔV (volume increase), ΔP is corrected pressure increase in the center part of the straight line portion of the pressure-volume curve, and μ is Poisson’s ratio.Figure 6
Typical graphical form of pressure (p) versus total cavity volume change (V) from a PMT test.It is noted that the PMT measures are associated with the horizontal stresses compared with the vertical resistance measured by the penetration tests (e.g., SPT, CPT, and DPT). Many empirical correlations have been proposed to convert PMT measures to various soil parameters [5, 14] and other penetration test measures [16–23]. The PMT measures are commonly used [5] to calculate the bearing capacity and deformation modulus of foundation soils following equations (3) and (4). The bearing capacity and deformation modulus of soil samples in the compiled dataset are calculated and shown in Table 2:(3)fak=pf−p0,(4)E0=K·EPMT,where fak is bearing capacity (MPa), E0 is the deformation modulus (MPa), and K is the ratio between the deformation modulus and pressuremeter modulus and is dependent on the soil type. The empirical model for cohesive soils (clay, silt, and sand) is used here: K=1+61.1m−1.5+0.0065V0−167.6, where m is the ratio between the pressuremeter modulus and the difference of limited pressure and initial pressure, i.e., m=EPMT/pL−p0 [5].


## 3.1. Dynamic Penetration Test

The dynamic penetration test (DPT) was developed in China during the early 1950s to measure the penetration resistance of gravelly soils. DPT could provide an important new procedure for characterization of gravels and fill a gap in present geotechnical practice between CPT/SPT and BPT testing [4]. The DPT has been widely applied in Chinese geotechnical practices since the code provisions providing guidance for the foundation design using DPT were published in the 1970s [3]. The DPT apparatus consists of a 120 kg hammer with a free-fall height of 100 cm dropped onto an anvil attached to 60 mm diameter drill rods, which in turn are attached to a solid cone tip with a diameter of 74 mm and a cone angle of 60° (Figure 5) [11]. The blow counts for penetrating every 10 cm of soils are recorded and termed as N120. The DPT is applicable to gravelly soils and weathered extreme-soft and soft rocks [5]. The DPT is widely used in the geotechnical survey in valleys consisting of deep overburden in southwestern China because of its characteristics of easy operation, wide applicability to different types of soils, and cheap cost.Figure 5
(a) Photo of the in situ dynamic penetration test (DPT). (b) Sketch of the DPT apparatus [3].
(a)(b)It is controversial about whether or not to correct the DPT blow count and how to correct it [5]. Currently, the Chinese Code suggests multiplying a correction factor (α) to the raw DPT blow counts following equation (1) to get the corrected DPT blow count (N120′). Since DPT was widely used to support the foundation design on gravelly soils located in Chengdu Plain, the Design Code for Building Foundation of Chengdu Region [13], hereinafter called Chengdu Code, recommends empirical relationships to estimate the soil deformation modulus, compression modulus, and ultimate capacity of gravelly soils using N120′ based on large amount of engineering practices (see Appendix A):(1)N120′=αN120,where N120′ is the corrected DPT blow count, N120 is the raw DPT blow count, and α is the correction factor that is available for rod length (L) less than 19 m and N120 below 40 (see Appendix B).


## 3.2. Pressuremeter Test

The pressuremeter test (PMT) is an in situ test developed by Menard [14] to measure the deformation properties of soil and weak rock. The PMT consists of placing an inflatable cylindrical probe in a predrilled borehole and expanding this probe, while measuring the changes in volume and pressure in the probe [15]. The measured volume change of the probe is plotted against the applied pressure (see Figure 6). The pressuremeter modulus is determined as follows [15]:(2)EPMT=2·1+μ·Vo+Vm·ΔPΔV,where EPMT is the pressuremeter modulus (MPa), p0, pf, and pL are initial, yield, and limit pressure, respectively, V0 is initial volume of the probe (cm3), Vm is the corrected volume reading in the center portion of ΔV (volume increase), ΔP is corrected pressure increase in the center part of the straight line portion of the pressure-volume curve, and μ is Poisson’s ratio.Figure 6
Typical graphical form of pressure (p) versus total cavity volume change (V) from a PMT test.It is noted that the PMT measures are associated with the horizontal stresses compared with the vertical resistance measured by the penetration tests (e.g., SPT, CPT, and DPT). Many empirical correlations have been proposed to convert PMT measures to various soil parameters [5, 14] and other penetration test measures [16–23]. The PMT measures are commonly used [5] to calculate the bearing capacity and deformation modulus of foundation soils following equations (3) and (4). The bearing capacity and deformation modulus of soil samples in the compiled dataset are calculated and shown in Table 2:(3)fak=pf−p0,(4)E0=K·EPMT,where fak is bearing capacity (MPa), E0 is the deformation modulus (MPa), and K is the ratio between the deformation modulus and pressuremeter modulus and is dependent on the soil type. The empirical model for cohesive soils (clay, silt, and sand) is used here: K=1+61.1m−1.5+0.0065V0−167.6, where m is the ratio between the pressuremeter modulus and the difference of limited pressure and initial pressure, i.e., m=EPMT/pL−p0 [5].


## 4. Results

With the DPT and PMT dataset compiled inSection 3, this section develops the empirical relationships for estimating correction factors (Section 4.1) and soil parameters (Section 4.2) from DPT test results using the regression analysis.


### 4.1. Empirical Relationship for DPT Correction Factor

As mentioned inSection 3, the correction factors of N120 in the Chinese Code are only available for rod length less than 19 m and raw DPT blow counts less than 40. This section aims to extend the correction factors for longer rod lengths (i.e., deeper soils). To achieve this purpose, 11 pairs of data with correction factors suggested by the Chinese Code (see Appendix B) are firstly filtered out to build a regression model between the deformation modulus E0 and N120′. These data are from the sublayer III-3, with rod length ranging from 10.5 to 17.5 m. The regression results are shown in equation (5) and Figure 7. The adjusted R2 of this regression is 0.986, and the p value of the F-test and t-test is 0.000 (less than 0.05), indicating that the regression model is significant and reliable:(5)E0=11.7585+2.3674×N120′,AdjustedR2=0.986,where E0 is the deformation modulus (MPa) and N120′ is the corrected DPT blow count.Figure 7
Correlation between the deformation modulus and corrected DPT blow counts for shallow soils within sublayer III-3.Using the reverse form of (5), N120′ for the other 38 data from sublayer III-3 but with rod length exceeding 19 m is calculated in Table 2. Then, its correction factors are calculated as the ratio of N120′ over N120. Combining the inverted correction factors according to sublayer III-3 soil data and (5), with the correction factors suggested by Chinese Code (See Appendix B), nonlinear regression is undertaken using the Curve Fitting Toolbox of Matlab [24]. The empirical equation for predicting the DPT correction factor using raw DPT blow count and rod length is shown in the following equation:(6)α=1.021L−0.1033N120−0.0356LnL,AdjustedR2=0.991,where α is the DPT correction factor, L is the rod length (m), and N120 is the raw DPT blow counts.The 3D visualization of the regression model and the utilized dataset is shown in Figure8. The relationship between correction factors and rod length for selected N120 values (i.e., 10 to 50 with step of 10) is shown in Figure 9. According to Figure 9, we can see the correction factors decrease with rod length with gradually reducing change rates. The correction factors for higher N120 values decrease faster than the ones for lower N120 values. The DPT correction factors calculated using equation (6) are compared with ones suggested by Chinese Code (Figure 10). The results of the proposed model generally match well with the ones in code, except for very low and high N120 values. The model underestimates the correction factors for N120 of 1, while slightly overestimates the correction factors for N120 of 40 for rod length exceeding 16 m.Figure 8
3D visualization of the nonlinear regression model for DPT correction factors.Figure 9
DPT correction factors for the selectedN120 values.Figure 10
Evaluation of DPT correction factors for shallow soils. The scatters are correction factors suggested by the Chinese Code for differentN120 values, and the lines are corresponding predicted correction factors estimated using equation (6).


### 4.2. Empirical Relationships Using Corrected DPT Blow Count

Empirical relationships are widely used to predict unknown engineering properties of soils [25–27]. In this section, the relationships between the corrected DPT blow counts (N120′) and soil parameters derived from pressuremeter measures (i.e., pressuremeter modulus and limit pressure) and engineering parameters used in the foundation design (i.e., soil deformation modulus and bearing capacity) were developed separately. The empirical relationships for engineering parameters are expected to be useful for geotechnical practices in China since soil deformation modulus and bearing capacity parameters are calibrated following the Chinese Codes (see equations (3) and (4)). Linear regression analyses are undertaken using all 74 data pairs belonging to soil Layer III and the reduced number of data pairs belonging to different sublayers of soil Layer III. The best-fit regression equations for soil Layer III (including both sand and clay soils) are shown in equations (7)–(10). The regression coefficients (intercept and slope values for linear regression) and corresponding statistical test results using data from each sublayer and all data from Layer III are summarized in Tables 3–6 and visualized in Figures 11 and 12. The coefficient of determination (adjusted R2 value) is used to evaluate the goodness of fit of the regression model. The F-test and t-test are used to assess the statistical significance of the regression models and the estimated regression coefficients, respectively. Models with larger F-statistic, t-statistic, and adjusted R2 value are better:(7)EPMT=3.4437+0.5194N120′,adjustedR2=0.439,(8)pL=0.4655+0.0845N120′,adjustedR2=0.957,(9)E0=11.07+2.40N120′,adjustedR2=0.996,(10)fak=0.2399+0.0305N120′,adjustedR2=0.775,where EPMT is the pressuremeter modulus (MPa) derived using equation (2), pL is limit pressure (MPa) measured in the pressuremeter test, E0 is the deformation modulus (MPa) derived using equation (4), fak is bearing capacity (MPa) derived using equation (3), and N120′ is the DPT blow counts corrected using equations (1) and (6).Table 3
Results of regression models correlating corrected DPT blow countsN120′ with pressuremeter modulus EPMT.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp value∗III743.4437 (0.7223)0.5194 (0.0681)0.43958.27.62820.000III-11010.094 (4.4029)0.0985 (0.2675)−0.1060.1360.36820.722III-2153.9537 (0.7947)0.1292 (0.1439)−0.0140.8050.89740.386III-3494.3713 (1.1086)0.4747 (0.1080)0.27619.34.39370.000p∗ value in italic font indicates that the corresponding regression model is not statistically significant for a p value of 0.1 (i.e., a 90% confidence level).Table 4
Results of regression models correlating corrected DPT blow countsN120′ with limit pressure pL.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp valueIII740.4655 (0.0222)0.0845 (0.0021)0.957163040.3920.000III-1100.5619 (0.1263)0.0779 (0.0077)0.91910310.160.000III-2150.5059 (0.0532)0.0692 (0.0096)0.78351.67.180.000III-3490.4869 (0.0330)0.0838 (0.0032)0.93467826.0340.000Table 5
Results of regression models correlating corrected DPT blow countsN120′ with soil deformation modulus E0.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp valueIII7411.07 (0.1913)2.4015 (0.0180)0.99617700133.190.000III-1108.6856 (0.4229)2.5279 (0.0257)0.999968098.3950.000III-21510.361 (0.2748)2.3912 (0.0498)0.994231048.0460.000III-34911.891 (0.2306)2.3472 (0.0225)0.9961090104.470.000Table 6
Results of regression models correlating corrected DPT blow countsN120′ with soil bearing capacity fak.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp valueIII740.2399 (0.0204)0.0305 (0.0019)0.77525215.8830.000III-1100.3511 (0.2051)0.0232 (0.0125)0.2163.471.8640.099III-2150.2408 (0.0222)0.0238 (0.0040)0.70834.95.9110.000III-3490.2626 (0.0288)0.0294 (0.0028)0.69310910.4610.000Figure 11
Correlations between corrected DPT blow countsN120′, pressuremeter modulus EPMT, and limit pressure pL for different soil sublayers.
(a)(b)Figure 12
Correlations between corrected DPT blow countsN120′, soil deformation modulus E0, and bearing capacity fak for different soil sublayers.
(a)(b)Overall, the regression models using all data (equations (8)–(10)) have adjusted the R2 value higher than 0.75 except for the regression model for estimating pressuremeter modulus (7). The regression models using all data generally have higher adjusted R2 than the models using a subset data for different sublayers (see Tables 3–6). In total, 14 of the 16 regression models shown in Tables 3–6 have the p value for the F-test and t-test associated with the slope coefficient less than 0.1, which indicates that the linear regression models and regression coefficients are statistically significant for a 90% confidence level. The other two regression models (models for III-1 and III-2 data in Table 3) have not passed the F-test and t-test possibly due to the limited number of data used in the regression analyses. Nevertheless, these regression results show that the dynamic penetration tests can be used to provide a preliminary estimation of soil parameters calibrated by more expensive pressuremeter tests. Towards improving the predictive ability and reliability of these empirical relationships, future works can collect more explanatory variables and case data, integrate theoretical/numerical analyses [28, 29], and use more advanced regression algorithms [30, 31].


## 4.1. Empirical Relationship for DPT Correction Factor

As mentioned inSection 3, the correction factors of N120 in the Chinese Code are only available for rod length less than 19 m and raw DPT blow counts less than 40. This section aims to extend the correction factors for longer rod lengths (i.e., deeper soils). To achieve this purpose, 11 pairs of data with correction factors suggested by the Chinese Code (see Appendix B) are firstly filtered out to build a regression model between the deformation modulus E0 and N120′. These data are from the sublayer III-3, with rod length ranging from 10.5 to 17.5 m. The regression results are shown in equation (5) and Figure 7. The adjusted R2 of this regression is 0.986, and the p value of the F-test and t-test is 0.000 (less than 0.05), indicating that the regression model is significant and reliable:(5)E0=11.7585+2.3674×N120′,AdjustedR2=0.986,where E0 is the deformation modulus (MPa) and N120′ is the corrected DPT blow count.Figure 7
Correlation between the deformation modulus and corrected DPT blow counts for shallow soils within sublayer III-3.Using the reverse form of (5), N120′ for the other 38 data from sublayer III-3 but with rod length exceeding 19 m is calculated in Table 2. Then, its correction factors are calculated as the ratio of N120′ over N120. Combining the inverted correction factors according to sublayer III-3 soil data and (5), with the correction factors suggested by Chinese Code (See Appendix B), nonlinear regression is undertaken using the Curve Fitting Toolbox of Matlab [24]. The empirical equation for predicting the DPT correction factor using raw DPT blow count and rod length is shown in the following equation:(6)α=1.021L−0.1033N120−0.0356LnL,AdjustedR2=0.991,where α is the DPT correction factor, L is the rod length (m), and N120 is the raw DPT blow counts.The 3D visualization of the regression model and the utilized dataset is shown in Figure8. The relationship between correction factors and rod length for selected N120 values (i.e., 10 to 50 with step of 10) is shown in Figure 9. According to Figure 9, we can see the correction factors decrease with rod length with gradually reducing change rates. The correction factors for higher N120 values decrease faster than the ones for lower N120 values. The DPT correction factors calculated using equation (6) are compared with ones suggested by Chinese Code (Figure 10). The results of the proposed model generally match well with the ones in code, except for very low and high N120 values. The model underestimates the correction factors for N120 of 1, while slightly overestimates the correction factors for N120 of 40 for rod length exceeding 16 m.Figure 8
3D visualization of the nonlinear regression model for DPT correction factors.Figure 9
DPT correction factors for the selectedN120 values.Figure 10
Evaluation of DPT correction factors for shallow soils. The scatters are correction factors suggested by the Chinese Code for differentN120 values, and the lines are corresponding predicted correction factors estimated using equation (6).


## 4.2. Empirical Relationships Using Corrected DPT Blow Count

Empirical relationships are widely used to predict unknown engineering properties of soils [25–27]. In this section, the relationships between the corrected DPT blow counts (N120′) and soil parameters derived from pressuremeter measures (i.e., pressuremeter modulus and limit pressure) and engineering parameters used in the foundation design (i.e., soil deformation modulus and bearing capacity) were developed separately. The empirical relationships for engineering parameters are expected to be useful for geotechnical practices in China since soil deformation modulus and bearing capacity parameters are calibrated following the Chinese Codes (see equations (3) and (4)). Linear regression analyses are undertaken using all 74 data pairs belonging to soil Layer III and the reduced number of data pairs belonging to different sublayers of soil Layer III. The best-fit regression equations for soil Layer III (including both sand and clay soils) are shown in equations (7)–(10). The regression coefficients (intercept and slope values for linear regression) and corresponding statistical test results using data from each sublayer and all data from Layer III are summarized in Tables 3–6 and visualized in Figures 11 and 12. The coefficient of determination (adjusted R2 value) is used to evaluate the goodness of fit of the regression model. The F-test and t-test are used to assess the statistical significance of the regression models and the estimated regression coefficients, respectively. Models with larger F-statistic, t-statistic, and adjusted R2 value are better:(7)EPMT=3.4437+0.5194N120′,adjustedR2=0.439,(8)pL=0.4655+0.0845N120′,adjustedR2=0.957,(9)E0=11.07+2.40N120′,adjustedR2=0.996,(10)fak=0.2399+0.0305N120′,adjustedR2=0.775,where EPMT is the pressuremeter modulus (MPa) derived using equation (2), pL is limit pressure (MPa) measured in the pressuremeter test, E0 is the deformation modulus (MPa) derived using equation (4), fak is bearing capacity (MPa) derived using equation (3), and N120′ is the DPT blow counts corrected using equations (1) and (6).Table 3
Results of regression models correlating corrected DPT blow countsN120′ with pressuremeter modulus EPMT.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp value∗III743.4437 (0.7223)0.5194 (0.0681)0.43958.27.62820.000III-11010.094 (4.4029)0.0985 (0.2675)−0.1060.1360.36820.722III-2153.9537 (0.7947)0.1292 (0.1439)−0.0140.8050.89740.386III-3494.3713 (1.1086)0.4747 (0.1080)0.27619.34.39370.000p∗ value in italic font indicates that the corresponding regression model is not statistically significant for a p value of 0.1 (i.e., a 90% confidence level).Table 4
Results of regression models correlating corrected DPT blow countsN120′ with limit pressure pL.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp valueIII740.4655 (0.0222)0.0845 (0.0021)0.957163040.3920.000III-1100.5619 (0.1263)0.0779 (0.0077)0.91910310.160.000III-2150.5059 (0.0532)0.0692 (0.0096)0.78351.67.180.000III-3490.4869 (0.0330)0.0838 (0.0032)0.93467826.0340.000Table 5
Results of regression models correlating corrected DPT blow countsN120′ with soil deformation modulus E0.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp valueIII7411.07 (0.1913)2.4015 (0.0180)0.99617700133.190.000III-1108.6856 (0.4229)2.5279 (0.0257)0.999968098.3950.000III-21510.361 (0.2748)2.3912 (0.0498)0.994231048.0460.000III-34911.891 (0.2306)2.3472 (0.0225)0.9961090104.470.000Table 6
Results of regression models correlating corrected DPT blow countsN120′ with soil bearing capacity fak.
Soil layerSample sizeIntercept (std)Slope (std)AdjustedR2F-statt-statp valueIII740.2399 (0.0204)0.0305 (0.0019)0.77525215.8830.000III-1100.3511 (0.2051)0.0232 (0.0125)0.2163.471.8640.099III-2150.2408 (0.0222)0.0238 (0.0040)0.70834.95.9110.000III-3490.2626 (0.0288)0.0294 (0.0028)0.69310910.4610.000Figure 11
Correlations between corrected DPT blow countsN120′, pressuremeter modulus EPMT, and limit pressure pL for different soil sublayers.
(a)(b)Figure 12
Correlations between corrected DPT blow countsN120′, soil deformation modulus E0, and bearing capacity fak for different soil sublayers.
(a)(b)Overall, the regression models using all data (equations (8)–(10)) have adjusted the R2 value higher than 0.75 except for the regression model for estimating pressuremeter modulus (7). The regression models using all data generally have higher adjusted R2 than the models using a subset data for different sublayers (see Tables 3–6). In total, 14 of the 16 regression models shown in Tables 3–6 have the p value for the F-test and t-test associated with the slope coefficient less than 0.1, which indicates that the linear regression models and regression coefficients are statistically significant for a 90% confidence level. The other two regression models (models for III-1 and III-2 data in Table 3) have not passed the F-test and t-test possibly due to the limited number of data used in the regression analyses. Nevertheless, these regression results show that the dynamic penetration tests can be used to provide a preliminary estimation of soil parameters calibrated by more expensive pressuremeter tests. Towards improving the predictive ability and reliability of these empirical relationships, future works can collect more explanatory variables and case data, integrate theoretical/numerical analyses [28, 29], and use more advanced regression algorithms [30, 31].


## 5. Conclusions

The dynamic penetration test (DPT) has been increasingly used in the geotechnical survey of deep soils in western China. However, the correction factors and empirical relationships for estimating engineering parameters using dynamic penetration test blow counts are still limited to gravelly soils with depth less than 20 m. This work collects 74 DPT measures at a valley site in southwestern China that consists of more than 500-meter-thick overburden soils. A nonlinear empirical relationship dependent on the raw DPT blow counts and rod length is developed to predict the DPT correction factors for shallow and deep soils through analyzing the deep soil data collected in this work and the existing correction factors for the shallow soils suggested by Chinese Code. Then, the corrected DPT blow counts are used to predict pressuremeter modulus, limit pressure, soil deformation modulus, and bearing capacity derived from more expensive and accurate pressuremeter tests. The results suggest that the proposed empirical relationships are significant and reliable for the investigated deep clay and sand soils. Further studies will be needed to explore the applicability of the proposed relationships to other soil types and other regions.



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